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page This intentionally left blank P1: JZP 0521818648agg.xml CB902/Hirshleifer 0 521 81864 8 June 30, 2005 10:49 PRICE THEORY AND APPLICATIONS SEVENTH EDITION This new seventh edition of Price Theory and Applications adds extensive discussion of information, uncertainty, and game theory. It contains more than 100 real-world examples illustrating the applicability of economic analysis not only to mainline economic topics but also to issues in politics, history, biology, the family, and many other areas. These discussions generally describe recent research published in scholarly books and articles, giving students a good idea of the scientic work done by professional economists. In addition, at appropriate places the text provides Applications representing more extended discussions of selected topics including rationing in wartime (Chapter 5), import quotas (Chapter 7), alleged monopolistic suppression of inventions (Chapter 9), minimum wage laws (Chapter 12), the effects of Social Security on saving (Chapter 15), fair division of disputed property (Chapter 16), and whether one should pay ransom to a kidnapper (Chapter 17). Jack Hirshleifer is Distinguished Professor of Economics, Emeritus, at the University of California, Los Angeles (UCLA). He is the author or coauthor of the six previous editions of Price Theory and Applications and the author or coauthor of six other books, including The Analytics of Uncertainty and Information (1992, with John G. Riley) and The Dark Side of the Force (2001), both published by Cambridge University Press. Professor Hirshleifer is a Fellow of the American Academy of Arts and Sciences and the Econometric Society, a former president of the Western Economic Association, and a former vice president of the American Economic Association, which named him a Distinguished Fellow in 2000. He has served on the editorial boards of the American Economic Review, the Journal of Economic Behavior and Organization, and the Journal of Bioeconomics. Amihai Glazer is Professor of Economics at the University of California, Irvine. He has taught at the Hebrew University, Carnegie Mellon University, and the University of Tampere, Finland. The author of more than 80 articles in professional journals, Professor Glazer is coauthor with Jack Hirshleifer of the fth edition of Price Theory and Applications, coauthor with Laurence Rothenberg of Why Government Succeeds and Why It Fails (2001), and coeditor with Kai Konrad of Conict and Governance (2003). He is a coeditor of the journal Economics of Governance. David Hirshleifer is the Ralph M. Kurtz Professor of Finance at the Ohio State University. He previously taught at the Anderson School of UCLA and the University of Michigan Business School. The coauthor with Jack Hirshleifer of the sixth edition of Price Theory and Applications, David Hirshleifer has served as a director of the American Finance Association, as editor of the Review of Financial Studies, and as associate editor or coeditor of several other journals in nance, economics, and corporate strategy. His papers have received a number of research awards, including the 1999 SmithBreeden Award for the outstanding paper in the Journal of Finance. i P1: JZP 0521818648agg.xml CB902/Hirshleifer 0 521 81864 8 June 30, 2005 10:49 ii P1: JZP 0521818648agg.xml CB902/Hirshleifer 0 521 81864 8 June 30, 2005 10:49 PRICE THEORY AND APPLICATIONS Decisions, Markets, and Information SEVENTH EDITION JACK HIRSHLEIFER University of California, Los Angeles AMIHAI GLAZER University of California, Irvine DAVID HIRSHLEIFER Ohio State University iii CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, So Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521818643 Jack Hirshleifer, Amihai Glazer, and David Hirshleifer 2005 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2005 eBook (EBL) ISBN-13 978-0-511-34451-0 ISBN-10 0-511-34451-1 eBook (EBL) ISBN-13 ISBN-10 ISBN-13 ISBN-10 hardback 978-0-521-81864-3 hardback 0-521-81864-8 paperback 978-0-521-52342-4 paperback 0-521-52342-7 Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. P1: JZP 0521818648agg.xml CB902/Hirshleifer 0 521 81864 8 June 30, 2005 10:49 Contents Preface page xiii part one. introduction 1 The Nature and Scope of Economics 1.1 Economics as a Social Science 1.2 Economic Man Rationality Human Goals The Self-Interest Assumption Ignorance and Uncertainty 1.3 Market and Nonmarket Interactions 1.4 Allocation by Prices The Market System 1.5 Behavior within Organizations 1.6 Positive and Normative Analysis: Is versus Ought 1.7 Elements of the Economic System Decision-Making Agents in the Economy Scarcity, Objects of Choice, and Economic Activities 1.8 Microeconomics and Macroeconomics summary questions 2 Working Tools 2.1 Equilibrium: Supply-Demand Analysis Balancing Supply and Demand How Changes in Supply and Demand Affect Equilibrium Algebra of Supply-Demand Analysis An Application: Introducing a New Supply Source Taxes on Transactions An Application: Interdicting Supply Price Ceilings and Price Floors 2.2 Finding an Optimum The Logic of Total, Average, and Marginal Concepts How Total, Average, and Marginal Magnitudes Are Related An Application: Foraging When Is It Time to Pack Up and Leave? 3 4 9 9 12 16 16 18 20 20 21 21 22 23 23 24 27 28 28 30 36 38 39 43 46 49 50 54 59 v P1: JZP 0521818648agg.xml CB902/Hirshleifer 0 521 81864 8 June 30, 2005 10:49 vi CONTENTS summary questions part two. preference, consumption, and demand 3 Utility and Preference 3.1 The Laws of Preference 3.2 Utility and Preference Cardinal versus Ordinal Utility Utility of Commodity Baskets 3.3 Characteristics of Indifference Curves 3.4 More on Goods and Bads An Application: Charity 3.5 The Sources and Content of Preferences summary questions 4 Consumption and Demand 4.1 The Optimum of the Consumer The Geometry of Consumer Choice Optimum of the Consumer (Cardinal Utility) Optimum of the Consumer (Ordinal Utility) 4.2 Complements and Substitutes 4.3 The Consumers Response to Changing Opportunities The Income Expansion Path The Engel Curve Price Expansion Path and Demand Curve 4.4 Income and Substitution Effects of a Price Change An Application: How Can the Giffen Case Come About? How Likely Is It? 4.5 From Individual Demand to Market Demand 4.6 An Application: Subsidy versus Voucher summary questions 5 Applications and Extensions of Demand Theory 5.1 The Engel Curve and the Income Elasticity of Demand 5.2 The Demand Curve and the Price Elasticity of Demand 5.3 The Cross-Elasticity of Demand 5.4 Fitting a Demand Curve Constant Slope versus Constant Elasticity General Demand Functions 5.5 Determinants of Responsiveness of Demand to Price 5.6 Multiple Constraints Rationing Coupon Rationing Point Rationing summary questions 61 62 69 70 72 73 77 79 83 85 86 90 90 93 94 94 97 100 104 107 107 110 112 115 117 118 120 122 124 127 128 132 136 137 138 139 142 144 144 146 151 152 P1: JZP 0521818648agg.xml CB902/Hirshleifer 0 521 81864 8 June 30, 2005 10:49 CONTENTS vii part three. the rm and the industry 6 The Business Firm 6.1 Why Firms? Entrepreneur, Owner, Manager Economic Prot versus Accounting Prot The Separation of Ownership and Control 6.2 The Optimum of the Firm in Pure Competition The Shutdown Decision An Application: Division of Output among Plants 6.3 Cost Functions Short Run versus Long Run Rising Costs and Diminishing Returns 6.4 An Application: Peak versus Off-Peak Operation summary questions 7 Equilibrium in the Product Market Competitive Industry 7.1 The Supply Function From Firm Supply to Market Supply: The Short Run Long-Run and Short-Run Supply External Economies and Diseconomies 7.2 Firm Survival and the Zero-Prot Theorem 7.3 The Benets of Exchange: Consumer Surplus and Producer Surplus An Application: The Water-Diamond Paradox An Application: Benets of an Innovation 7.4 Transaction Taxes and Other Hindrances to Trade Transaction Taxes Supply Quotas An Application: Import Quotas Price Ceilings and Shortages summary questions 8 Monopolies, Cartels, and Networks 8.1 The Monopolists Prot-Maximizing Optimum Price-Quantity Solution Monopoly versus Competitive Solutions An Application: Author versus Publisher An Application: Monopolist with Competitive Fringe 8.2 Monopoly and Economic Efciency 8.3 Regulation of Monopoly 8.4 Monopolistic Price Discrimination Market Segmentation Block Pricing Perfect Discrimination 8.5 Cartels 157 158 160 160 165 172 174 176 176 180 182 186 187 191 192 192 195 199 201 203 205 206 207 208 209 210 213 217 218 221 222 222 226 228 231 231 234 238 238 241 243 244 P1: JZP 0521818648agg.xml CB902/Hirshleifer 0 521 81864 8 June 30, 2005 10:49 viii CONTENTS 8.6 Network Externalities Demand for a Network Good Monopoly or Competition? The Lock-in Issue summary questions 9 Product Quality and Product Variety 9.1 Quality Quality under Competition and Monopoly An Application: Suppression of Inventions Cartels and Quality 9.2 Variety Product Variety under Monopoly Blending Monopoly and Competition Monopolistic Competition summary questions 10 Competition Among the Few: Oligopoly and Strategic Behavior 10.1 Strategic Behavior: The Theory of Games Patterns of Payoffs An Application: Public Goods Two-Person versus Multiperson Prisoners Dilemma Pure Strategies Mixed Strategies 10.2 Duopoly Identical Products Quantity Competition Price Competition An Application: Most-Favored-Customer Clause 10.3 Duopoly Differentiated Products Quantity Competition Price Competition 10.4 Oligopoly, Collusion, and Numbers An Application: The Kinked Demand Curve Oligopoly and Numbers summary questions 11 Dealing with Uncertainty The Economics of Risk and Information 11.1 Decisions under Uncertainty Expected Gain versus Expected Utility Risk Aversion Risk-Bearing and Insurance 11.2 The Value of Information 11.3 Asymmetric Information Adverse Selection The Lemons Problem 248 248 250 250 253 254 257 258 259 263 265 266 268 270 275 276 279 280 280 282 283 286 288 289 293 295 297 297 298 300 300 302 304 304 307 308 308 309 312 316 317 317 P1: JZP 0521818648agg.xml CB902/Hirshleifer 0 521 81864 8 June 30, 2005 10:49 CONTENTS ix Conveying Quality through Reputation Do Prices Signal Quality? Information as a Public Good Conveying Information Advertising 11.4 Herd Behavior and Informational Cascades 11.5 Copyright, Patents, and Intellectual Property Rights summary questions 321 323 325 325 328 332 334 part four. factor markets and income distribution 12 The Demand for Factor Services 12.1 Production and Factor Employment with a Single Variable Input The Production Function Diminishing Returns From Production Function to Cost Function The Firms Demand for a Single Variable Input 12.2 Production and Factor Employment with Several Variable Inputs The Production Function Factor Balance and Factor Employment The Firms Demand for Inputs 12.3 The Industrys Demand for Inputs 12.4 Monopsony in the Factor Market 12.5 An Application: Minimum-Wage Laws summary questions 13 Resource Supply and Factor-Market Equilibrium 13.1 The Optimum of the Resource-Owner An Application: The Incentive Effects of Welfare and Social Security 13.2 Personnel Economics: Managerial Applications of Employment Theory The Principal-Agent Problem Paying by the Piece Signalling 13.3 Factor-Market Equilibrium From Individual Supply to Market Supply Demand and Supply Together An Application: Sources of Growing Wage Inequality 13.4 Monopolies and Cartels in Factor Supply 13.5 The Functional Distribution of Income The Traditional Classication: Land, Labor, and Capital Capital, Rate of Return, and Interest 13.6 Economic Rent summary questions 339 340 340 340 343 345 349 350 355 358 362 364 366 371 373 375 376 382 385 385 386 389 390 390 391 392 395 397 397 398 402 403 404 P1: JZP 0521818648agg.xml CB902/Hirshleifer 0 521 81864 8 June 30, 2005 10:49 x CONTENTS part ve. exchange 14 Exchange, Transaction Costs, and Money 14.1 Pure Exchange: The Edgeworth Box 14.2 Supply and Demand in Pure Exchange An Application: Market Experiments in Economics 14.3 Exchange and Production 14.4 Imperfect Markets: Costs of Exchange How Perfect Are Markets? Proportional Transaction Costs Lump-Sum Transaction Costs 14.5 The Role of Money Money as Medium of Exchange Money as Temporary Store of Value 14.6 An Application: Auctions The English Auction Sealed-Bid Second-Price Auction Sealed-Bid First-Price Auction The Dutch Auction summary questions 409 410 416 420 423 430 430 433 437 440 440 442 443 445 445 445 446 448 449 part six. economics and time 15 The Economics of Time 15.1 Present versus Future 15.2 Consumption Choices over Time: Pure Exchange Borrowing-Lending Equilibrium with Zero Net Investment An Application: Double Taxation of Saving? 15.3 Production and Consumption over Time: Saving and Investment 15.4 Investment Decisions and Project Analysis The Separation Theorem The Present-Value Rule The Rate of Return (ROR) Rule 15.5 Real Interest and Monetary Interest: Allowing for Ination 15.6 The Multiplicity of Interest Rates An Application: The Discount Rate for Project Analysis 15.7 The Fundamentals of Investment, Saving, and Interest summary questions 455 456 459 459 461 464 468 468 469 475 479 482 485 486 490 491 part seven. political economy 16 Welfare Economics: The Market and the State 16.1 Goals of Economic Policy Efciency versus Equity Utilitarianism 497 498 498 500 P1: JZP 0521818648agg.xml CB902/Hirshleifer 0 521 81864 8 June 30, 2005 10:49 CONTENTS xi Efciency as the Sum of Consumer Surplus and Producer Surplus Efcient Allocations in the Edgeworth Box Equity Reconsidered An Application: How to Divide a Cake 16.2 The Theorem of the Invisible Hand: The Role of Prices Efcient Consumption Efcient Production Efcient Balance between Production and Consumption 16.3 Market Failures Monopoly Externalities The Coase Theorem 16.4 The Commons: The Consequences of Unrestricted Access 16.5 Public Goods Efcient Production and Consumption of Public Goods Voluntary Provision of Nonexcludable Public Goods Free-Riding An Extension: Weakest-Link versus Best-Shot Models of Public Goods 16.6 Appropriative Activity and Rent-Seeking summary questions 17 Government, Politics, and Conict 17.1 The Other Side of the Coin: Government Failures Corruption as Government Failure Political Competition and Its Limits Politics and Special Interests 17.2 Voting as an Instrument of Control Majority and Minority Log-Rolling The Cycling Paradox The Median-Voter Theorem 17.3 Conict and Cooperation Sources of Cooperation and Conict Conict and Game Theory An Application: Should You Pay Ransom? summary questions Answers to Selected Questions Name Index Subject Index 500 501 502 504 506 506 506 507 508 508 508 513 515 518 518 521 525 529 533 534 537 538 538 539 541 543 544 545 546 550 550 557 561 563 564 567 597 601 P1: JZP 0521818648agg.xml CB902/Hirshleifer 0 521 81864 8 June 30, 2005 10:49 xii P1: JZP 0521818648agg.xml CB902/Hirshleifer 0 521 81864 8 June 30, 2005 10:49 Preface Theory is useless unless it leads to applications. But real-world problems remain a buzzing, blooming confusion absent a systematic theory to put them in intellectual order. Earlier editions of this book pioneered an approach, not totally new but given unusual emphasis by us, that weaves together economic theory and real-world applications. Most current intermediate microtheory texts have come to follow our lead and also now try to enrich the theoretical exposition with selected applications. Our enthusiasm for and experience in discovering, describing, and analyzing how microtheory works out in the real world nevertheless lend a special strength to Price Theory and Applications. To this end the many brief Examples that direct attention to specic applications remain, as in previous editions, a hallmark of Price Theory and Applications. This edition contains more than a hundred such examples. These discussions generally describe recent research published in scholarly books and articles and so also give students a better idea of the scientic work that professional economists actually do. (The media typically picture economists as a band of squabbling soothsayers some saying business will be good, others always predicting doom. Students may be surprised to nd that there are any scientically validated results in economics.) In addition, at appropriate places the text provides Applications representing a wide range of topics, among them rationing in wartime (Chapter 5), import quotas (Chapter 7), alleged monopolistic suppression of inventions (Chapter 9), minimum wage laws (Chapter 12), the effects of Social Security on saving (Chapter 15), fair division of disputed property (Chapter 16), and whether you should pay ransom to a kidnapper (Chapter 17). Two other key themes guide this text. First, that economics is not a body of facts or propositions to be memorized. It is instead a way of thinking about the world. There are diligent students who say, Prof, just tell me what pages you want me to learn and I guarantee Ill know every word. But memorization is not enough. Even the ability to derive and prove logical or mathematical propositions does not sufce. Insight and intuition must also be cultivated. Insight and intuition tell us what theories or propositions apply in any given context. Yet not everything can be left to inspiration. Insight and intuition have to be earned by hard intellectual labor. Second, traditional economic theory has been guilty of tunnel vision in focusing so strictly on rationalistic individual behavior and market interactions. Humans are not always entirely rational, and market interactions are only one of the many domains of social life. Economics as a universal science applies outside these boundaries, whenever humans (or even animals!) have to cope with resource scarcity. Market decisions are of xiii P1: JZP 0521818648agg.xml CB902/Hirshleifer 0 521 81864 8 June 30, 2005 10:49 xiv PREFACE course amenable to economic analysis. But so are personal choices (how many children to have, whether to live in the city or the suburbs, whom to seek as friends) and political ones (balancing between afuence and defense, between regulation of improper behavior and individual freedom, between relief for persons unable or unwilling to work versus providing incentives to those who are productive). Accordingly, the text employs a range of materials from scientic work in anthropology, psychology, political science, social biology, and other elds that all serve to illustrate economic principles. Critics of economics sometimes object that, under the pressures of everyday life, people have to make decisions without using esoteric economic concepts such as marginal analysis. But biologists have discovered that marginal analysis explains many aspects of the behavior of animals (see the Smart Ants! example in Chapter 4), and humans are surely cleverer than ants. Yet people, individually or collectively, do sometimes make irrational choices. During the high-tech stock market boom in the late 1990s, investors seem to have displayed irrational exuberance (see Example 1.5 in Chapter 1). Critics have also accused economics of being unscientic in failing to test theories by experiments. This is an uninformed criticism. Experiments are playing an increasingly important role in economic research. The examples in the text report on many experimental studies. Among them are ingenious methods devised to test whether economics students are more selsh than noneconomics students (Chapter 1), whether children make choices that are logically consistent with one another (Chapter 3), whether markets work well even when there are only a few traders on each side (Chapter 14), and whether residents of different countries vary in how much they are inclined to cooperate (Chapter 16). As to coverage and level of difculty, this is not a minimal thin gruel book. Apart from meeting immediate classroom needs, we aimed to achieve growth potential. The material is ample enough in scope and rich enough in content to serve as reference and guide for additional self-study or coursework beyond the intermediate level. But perhaps the main reason for the wide coverage is to illustrate the wealth of fascinating implications and applications of economic theory. In consequence, this text contains more than can usually be handled in a one-term microeconomics course. Instructors and students in more compact courses will nd that Chapters 1 through 8 can serve as core readings covering the essentials of individual optimization and supplydemand equilibrium in product markets. Some teachers, in accordance with student interests and time constraints, may want to add selections from the remaining chapters. A two-term undergraduate price theory course can cover the entire text. A number of expository aids are provided to facilitate readability and comprehension. First, detailed descriptive legends accompany the diagrams. The analytical high points of a chapter can often be efciently reviewed by studying the diagrams, with their legends, in sequence. Second, almost every chapter contains worked numerical exercises. Third, each chapter ends with a summary and two groups of questions one group to test recollection and recall, the other to provide challenges for further thought and discussion. (Answers to about half of the questions, those marked by a dagger, appear at the back of the book.) This seventh edition of Price Theory and Applications bears the subtitle Decisions, Markets, and Information. Reecting recent exciting advances in economic analysis, the subtitle highlights the increased emphasis in this edition on the economics of information. Especially but not exclusively in Chapter 11, there is new coverage of risk P1: JZP 0521818648agg.xml CB902/Hirshleifer 0 521 81864 8 June 30, 2005 10:49 PREFACE xv and its distribution in the economy, of information acquisition as a way of overcoming risk, and of rights in intellectual property especially patents and copyright. Specic new topics include option value, the problem of lemons, herd behavior, and the informative content of advertising. The text employs game theory from time to time, with emphasis on practical relevance rather than on abstract theorems. Game theory is notably helpful in addressing topics such as oligopoly (Chapter 10), public goods (Chapter 16), and cooperation versus conict (Chapter 17). Several additional features of this book improve on conventional textbook coverage: r r r r r Traditional intermediate texts slight the topic of transaction costs. In Part Five the analysis of exchange subject to transaction costs shows, among other things, why and how a monetary commodity comes into being. Even earlier, Part Three indicates that the costliness of exchange explains why business rms exist. And Part Seven emphasizes how transaction costs affect the real-world relevance of the Coase theorem. Textbooks rarely discuss product quality and product variety. Chapter 9 examines how markets, under both competitive and monopolistic conditions, determine the quality levels and the product assortments that suppliers offer to consumers. Saving and investment, often treated as topics entirely separate from mainline microeconomics, are explained in Chapter 15 in terms of the economic theory of choice and equilibrium over time. The analysis here provides a bridge to macroeconomics and to the business nance literature. In addition to the traditional normative issues of welfare economics, Chapter 16 provides a unied treatment of public goods. The nal Chapter 17 presents a positive analysis of government. The same chapter puts forward a unique game-theoretic approach to the broad social problem of conict versus cooperation. As in previous editions, calculus is used only in marked mathematical footnotes. However, students who know calculus can interpret the delta ( ) notation used for marginal concepts as signifying a derivative or differential. Whether we have struck a proper balance between coverage and simplicity, between theory and application, between technical accuracy and intuitive suggestion, only the reader can judge. We will be grateful for guidance on this point from instructors and students, and also for specic corrections where errors appear. Over the years the authors have been dismayed to observe so many intermediate texts putting out repeated editions, in machine-gun style, every 4 or even every 3 years! That might possibly be smart business practice, creating forced obsolescence in order to discourage students from buying used copies of the current edition. But it is not warranted on educational or intellectual grounds. The subject simply does not change that fast. Nor can authors on a 3-year cycle devote enough time to really think through needed improvements in style and content. The 6 years since the previous (sixth) edition of this textbook have given us the chance to add many new examples, applications, and questions and to include new topics such as the economics of information and networks. Finally, we have been delighted to work with Cambridge University Press as publisher of this seventh edition. P1: JZP 0521818648agg.xml CB902/Hirshleifer 0 521 81864 8 June 30, 2005 10:49 xvi PREFACE As in past editions, the Instructors Manual for Price Theory and Applications, Seventh Edition, contains teaching tips and expanded answers to a number of questions in the textbook, plus an assortment of additional numerical, essay, and multiple choice questions for each chapter. It was prepared by Ray Bromley, building on work done for earlier editions by Michael Sproul. Resources for instructors and students using Price Theory and Applications are available online at http://www.pricetheoryapplications.com. These include additional applications and examples, studying tips, text corrections, and downloadable teaching aids. Previous editions of this text have beneted from helpful reviews by many colleagues, too numerous to be individually named here. For this seventh edition we are particularly grateful for a detailed and insightful analysis and commentary by Eric Rasmusen. We also thank the teachers, students, and other readers who have independently taken the trouble to send valuable corrections and comments. For the current edition we have beneted especially from input by Robert Murphy of Hillsdale College. Over the years a number of research assistants have worked mainly on the examples and on the questions and answers for the various chapters. Once again the number has grown too large for a complete listing, but we would especially like to name Charles Knoeber for his outstanding assistance on the initial edition of the book and KyooIl Kim for his help on this edition. Thanks are due to Enpei Lan, who prepared the indexes. We also thank Scott Parris of Cambridge University Press for shepherding this new edition through the publication process. Finally, the senior author is happy to report that his coauthors on several earlier editions, Amihai Glazer and David A. Hirshleifer, both participated as coauthors for this edition. P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 I INTRODUCTION 1 P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 2 P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 1 1.1 1.2 The Nature and Scope of Economics Economics as a Social Science 4 Economic Man 9 Rationality 9 Human Goals The Self-Interest Assumption 12 Ignorance and Uncertainty 16 1.3 1.4 1.5 1.6 1.7 Market and Nonmarket Interactions 16 Allocation by Prices The Market System 18 Behavior within Organizations 20 Positive and Normative Analysis: Is versus Ought 20 Elements of the Economic System 21 Decision-Making Agents in the Economy 21 Scarcity, Objects of Choice, and Economic Activities 22 1.8 Microeconomics and Macroeconomics 23 SUMMARY 23 QUESTIONS 24 EXAMPLES 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 The Ecologist, the Economist, and the Statistician 6 Earnings of Male College Graduates, by Field 8 Rational Drivers? 10 Rational Malingering? 11 Irrational Exuberance 11 Selsh Economics Students? 14 Selsh Economics Profs? 15 Crime as an Economic Choice Three Strikes 16 Bidding for Faculty Ofces 18 When Do Economists Disagree? 21 3 P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 4 1. THE NATURE AND SCOPE OF ECONOMICS Economics concerns decisions choices among actions. Every action has its pros and cons, pluses and minuses, benets and costs. Are you thinking about taking up tennis? The game may trim your gure and improve your disposition, but will take time from your studies and could damage your joints. How about dropping out of college to take a job? You would likely earn more money now, but earn less later in life. Similarly in business and government. Whether its a small action, as when your neighborhood market sets its price for potatoes, or a big one, as when Congress decides on declaring war, almost always there are valid arguments for and against. Faced with such opposed considerations, how should individuals, rms, or governments make decisions? Economics shows how to determine the best action, through a systematic assessment of the costs and benets. Few decisions are made in a vacuum. Other people are likely to react. Thinking like an economist means taking these reactions into account. A law rm that raises its billing rates may nd customers switching to another provider of legal services so the higher price might not increase prot after all. Or imagine that Congress, aiming to widen use of the Internet, were to require Internet service providers (ISPs) to charge very low prices. Before concluding that this is a good idea we would need to know how the ISPs would react. They might provide access at those low prices. Or they might reduce the quality of service, so that consumers nd busy signals when trying to connect. (Although this might seem a rather wild example, something similar occurs when rent-control legislation freezes apartment rents during a period of general price ination. Such a price freeze makes landlords less willing to supply and to maintain rental housing.) Economics has been called the dismal science.1 Thats probably because economists are often messengers bringing bad news; for example, that a supercially appealing project or scheme may not be such a great idea once all the consequences are taken into account. Table 1.1 lists a number of individual and social problems, together with some purported solutions. Also shown are possible bad consequences that an economist might point out. Can you add other possible objections? And on the other side, can you think of counterarguments that might rebut these objections? Proponents of plans and projects tend to overlook possible aws, while opponents tend to ignore the evidence in favor. Because people committed to one side of a question generally do not want to listen to contrary arguments, thinking like an economist trying to impartially weigh the pros and cons may not make you popular. But it is likely to improve your private decisions, enhance your prospects of business success, and make your views on social issues more balanced. 1.1 ECONOMICS AS A SOCIAL SCIENCE Economics is a science. Like other sciences it consists of explanations (theories) that help us understand and make valid predictions about the real world, together with the empirical evidence for and against them. More specically, economics is a social science. Its subject matter is the interplay of choices made by living beings. Economics addresses 1 Not a gay science . . . no, a dreary, desolate, and indeed quite abject and distressing one: what we might call, by way of eminence, the dismal science. Thomas Carlyle (17951881) P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 1.1 ECONOMICS AS A SOCIAL SCIENCE 5 Table 1.1 Finding solutions to social problems Possible adverse consequences a. The price of steel will rise, so steel-using industries will have higher costs and will have to raise prices to consumers. b. Foreigners, because they will be selling less steel to us, will buy fewer of our countrys exports. a. Landlords will skimp on upkeep and repair of apartments. b. In the longer run, fewer rental units will be constructed. a. Employers will become less willing to hire women. b. Costly bureaucratic and judicial proceedings will be involved in setting wages. a. Consumers will have to pay more for tuna. b. Foreign sheries, not subject to our laws, will take over more of the tuna trade. a. Doctors bills and hospital charges will rise even more than they have previously. b. Taxes will have to go up. a. Street prices of narcotics will rise, forcing addicts to steal to feed the habit. b. Huge nancial stakes in the narcotics trade will lead to more corruption of the police and judiciary. Increased availability and lower prices of narcotics will increase usage and addiction. Problem 1. Our countrys steel producers are threatened by competition from imports. Solution Impose a tariff on imported steel. 2. Apartment rents are rising, putting decent housing out of reach for the poor. Freeze apartment rents. 3. Womens wages are lower than mens. Adopt comparable worth laws requiring equal pay for men and women doing comparable jobs. Require domestic sheries to use special nets that let dolphins escape. 4. Commercial shing for tuna kills large numbers of dolphins. 5. Medical costs are very high. Require government to pay a share of medical bills, especially for the poor. Toughen enforcement of narcotics laws. 6. Many people are addicted to drugs. 7. Many people are addicted to drugs. Abandon enforcement of narcotics laws. questions such as: Will a reduction in the capital gains tax make the stock market rise? Will higher tariffs make consumers better off? Will increased prison terms reduce crime? Will easier divorce improve the status of women? Will a high-price (meaning low volume of sales) strategy lead to more prot for a rm than a low-price strategy? A cynic might deny that economics is a science. Here is a possible complaint: Economists always disagree with one another. That doesnt give me much condence that economics has arrived at scientic truth. Furthermore, if economists can scientifically predict nancial and commercial events, why arent they all rich? P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 6 1. THE NATURE AND SCOPE OF ECONOMICS Its easy to exaggerate the disagreement among economists. Controversy makes news; consensus rarely does. The great majority of economists agree that price controls lead to shortages, that free trade improves the international division of labor, and that uncontrolled printing of money will bring about ination.2 What is more important, disagreement is essential if a science is to advance. In astronomy the heliocentric hypothesis of Copernicus challenged Ptolemys 1,000-year-old geocentric model. In chemistry the phlogiston theory of combustion was superseded by Lavoisiers oxidation theory. And in biology creationism was countered by Darwins theory of evolution. It is not universal agreement that characterizes science, but rather willingness to examine the evidence. All important issues of economics for example, how taxes affect incentives to work, whether trade unions raise workers wages, whether stronger copyright laws promote creativity are under continuous re-evaluation in the light of the evidence. Economists may continue to disagree, perhaps because the problems are complex or the investigators insufciently skilled, but unresolved issues persist in any living science. Engineers, despite having well-validated theories and a vast amount of evidence as to strength of materials, commonly add a huge safety factor (50 or even 100%) before building a bridge or a dam. And even so, bridges still collapse and dams wash away. In Los Angeles during the 1994 earthquake, reinforced freeways designed to withstand an even more severe jolt than actually occurred nevertheless collapsed. As another example, meteorology is certainly a natural science, yet meteorologists hardly even claim to predict the weather for more than a week or so ahead. If economists predicting the extent of unemployment or forecasting the rate of ination were permitted as wide a safety factor as engineers or meteorologists, they would rarely be seen as going very far astray. EXAMPLE 1.1 THE ECOLOGIST, THE ECONOMIST, AND THE STATISTICIAN In 1990 the ecologist and popular author Paul Ehrlich sent a check for $576.07 to the economist Julian L. Simon. It was a payoff on a bet made 10 years previously. Ehrlich, though not an economist, had made startling economic predictions in his 1968 bestseller The Population Bomb. Take, for example, his opening sentences: The battle to feed all of humanity is over. In the 1970s hundreds of millions of people are going to starve to death. Ehrlichs predictions utterly failed. Despite an oil crisis in mid-decade and again toward the end, overall the 1970s were a decade of remarkable economic growth. Yet the author continued to be highly acclaimed. In books, speeches, and articles that received worldwide attention he prophesied that accessible supplies of many key minerals would be nearly depleted by 1985. Meanwhile the economist Julian L. Simon had been predicting just the reverse for the 1970s and 1980s: continuing improvements in human well-being, and lower prices for raw materials. Simon challenged Ehrlich to back his contrary forecast with hard cash, and Ehrlich accepted the challenge. The result was a 1980 bet about whether the prices of ve important metals chrome, copper, nickel, tin, and tungsten would, after allowing for ination, rise or fall by 1990. The economist let the ecologist choose the specic commodities. Once again, the economist Simon was proved right and 2 Scientic consensus need not imply general agreement about policy, however. See the section on Positive versus Normative Analysis below. P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 1.1 ECONOMICS AS A SOCIAL SCIENCE 7 Ehrlich wrong. The 1980s were also a decade of prosperity, and raw materials prices generally fell. The ecologist had to pay off on the bet. Ehrlichs analytic error was to look only at the demand side, and specically at growing world population (more mouths to feed). Julian Simon, with his better economic understanding, also considered the supply side. More people mean more mouths, but also more hands and brains. Simon also took account of other favorable economic trends such as greater liberalization of national economies and increased international trade. So the predictions of economic analysis were vindicated. Nevertheless, Paul Ehrlich continued to publish highly popular books forecasting, as mistakenly as before, environmental doom in the near future. Just as regularly, up to his death in 1998 Julian Simon was providing sound analysis and well-validated economic forecasts, culminating in his volume The Ultimate Resource (2nd ed., Princeton University Press, 1998). But none of his books were best-sellers. What was going on here? An economic interpretation might be that these two authors were supplying different commodities. Julian Simon was supplying correct economic analysis. Paul Ehrlich was and is in a different business, rather comparable to horror-story writers such as Stephen King. Evidently, at least when it comes to selling books, the demand for horror stories far exceeds the demand for sound economic analysis.a A later exhaustive and careful study by the Danish statistician Bjorn Lomborg (The Skeptical Environmentalist, Cambridge University Press, 2001) has updated Simons results. Initially intending to refute Simons analysis, Lomborg found his research instead conrming it. Despite rising world population, per capita incomes have maintained their upward trend and real prices of important resources have continued to fall. As a rather strange sidelight, upon publishing these results Lomborg became the target of personal attacks that reached an extraordinary level of intensity. At one of his public presentations a cream pie was dumped on his face and clothing. He was even accused of intellectual dishonesty by a scientic body with ofcial standing in Denmark. Ultimately, all the charges were conclusively refuted, and the improperly motivated proceeding against Lomborg was dismissed. (Which does not necessarily mean, of course, that all of Lomborgs estimates and forecasts will ultimately prove to be correct.) One possible lesson: sound economic analysis can sometimes be riskier than you might think!b a For a detailed history of the Ehrlich-Simon wager see John Tierney, Betting the Planet, New York Times Magazine, December 2, 1990. b A summary of the Lomborg controversy is provided in Jim Giles, The Man They Love to Hate, Nature, v. 423, May 15, 2003. The cynics second challenge to economists Why arent you all rich? sounds crass. But economists, of all people, cannot dismiss it. First of all, as the preceding Example showed, correct economic analysis need not have greater market appeal than incorrect but psychologically appealing assertions. More generally, scientic knowledge in any eld does not guarantee riches. If Michael Jordan had studied the aerodynamic equations governing the motion of spheroidal missiles, would that have improved his basketball point scores? This argument shouldnt be pressed too far, though. After all, P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 8 1. THE NATURE AND SCOPE OF ECONOMICS whats the use of economics (or of aerodynamics, for that matter) if not the practical results obtained? So its reasonable to expect that better understanding of economics and markets would lead to more wealth. Although most people can hardly match the life achievements of geniuses like Tiger Woods in sports or Bill Gates in business, training in economics ought to increase income. And, as the next Example shows, apparently to some extent it does. EXAMPLE 1.2 EARNINGS OF MALE COLLEGE GRADUATES, BY FIELD The table shows median annual earnings for men with bachelors degrees, by selected elds, for the year 1993 the latest year for which such data have been published. Only selected elds are shown here, and the ranking is among those selected elds. (The source also tabulates earnings for women graduates, but the female tabulation unfortunately omits economics.) Median annual earnings for men, by selected elds, 1993 Field Engineering Mathematics Pharmacy Physics Economics Accounting Nursing Business, other Political science and government Psychology Biological/life sciences Sociology History English language and literature Education Visual and performing arts Social work Philosophy, religion, and theology 1993 earnings $51,600 50,500 50,500 50,400 48,100 47,800 43,500 43,000 41,600 40,700 39,600 38,800 38,300 37,600 34,500 32,100 30,600 29,700 Rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Source: Table 5 in Daniel E. Hecker, Earnings of College Graduates, 1993, Monthly Labor Review, December 1995. In this tabulation, economics is the best-paying social science degree, ranking just below a high-earnings group that includes engineering, physics, mathematics, and (surprisingly perhaps) pharmacy. (Though not shown in this tabulation, pharmacy is actually the top-ranking eld for women.) One cannot be sure that these high incomes are due specically to educational preparation. To earn a degree in engineering, math/stat, or physics you have to be pretty smart to begin with, and perhaps that applies also to economics. Also, the life styles associated with different occupations may be attractive or repellent. Higher pay may be needed to induce people to become bill collectors or hangmen, and conceivably economics suffers from a mild version of such distaste. Perhaps the category of philosophy, religion, and P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 1.2 ECONOMIC MAN 9 theology ranks at the very bottom of the tabulated wage distribution because many people nd such employment to be a noble activity, a higher calling. (How such nonpecuniary considerations inuence occupational wage patterns will be studied in Chapter 12.) Overall, it seems reasonable to conclude that studying economics does pay off, to some extent, in terms of higher income. What about the other social sciences? Sociology, anthropology, political science, social psychology, and sociobiology also attempt to explain behavior. The boundaries between economics and these other sciences are indistinct, in part because economic reasoning has shown itself to be of value in those elds as well. Anthropologists use economic techniques to analyze the foraging choices and birth-spacing decisions of primitive peoples. Political scientists use cost-benet analysis to predict how many citizens will cast ballots and which way they will vote. And sociobiologists, on the hypothesis that economically sound strategies are more likely to survive the test of evolutionary selection, employ economic analysis to explain, for example, why some animals choose to defend territories while others do not. (This book will be illustrating economic principles with instances drawn from these and other related social sciences.) Although the boundaries may be indistinct, economics has a central core. First, on the individual level of choice economists generally postulate economic man,3 a hypothetical being whose decisions are based upon the rational pursuit of self-interest. Second, economics concentrates upon one type of human interaction: market exchange. In this book we necessarily emphasize the narrow economics associated with these core ideas. But there is a broad economics that goes beyond them. Economists can and do attempt to take account of irrational and nonselsh behavior. And economists certainly devote effort to studying nonmarket interactions, ranging from family relations to violent conict. However, rst steps rst. We must begin with the central core of economic reasoning. 1.2 ECONOMIC MAN The term economic man is frequently used in a derogatory sense, as an implicit criticism of economic reasoning. Since people are not always rational and not always self-interested, economics is, critics allege, built on bad foundations. But the economist does not contend that rational and self-interested behavior are universal and absolute facts. Rather, they constitute a working hypothesis, whose validity in any context can only be assessed only by its usefulness. Does that assumption help us understand what actually happens in markets and elsewhere? Rationality Rational behavior has at least two meanings in common use. The rst meaning refers to method, the second to result. When speaking of method, rational behavior is action selected on the basis of reasoned thought rather than habit, prejudice, or emotion. When speaking of result, rational behavior is action that is effective in achieving desired goals. The two meanings differ. Good methods can sometimes lead to bad results. (The best 3 Note: economic man includes economic woman! P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 10 1. THE NATURE AND SCOPE OF ECONOMICS laid schemes o mice and men/Gang aft a-gley Robert Burns.) And the seemingly inferior methods available to animals, even some with tiny brains, often work very well. A human being chasing a y with a swatter often loses the contest. But in general, we expect that considered thought leads to better action. Everyone behaves irrationally to some extent out of passion, thoughtlessness, mental defect, or just plain perverseness. So how can rationality be assumed in economics? Assuming rationality is justied only if doing so helps predict how people will behave. Economists nd that for the most part, though not literally always, the assumption of rationality does work. Operating a motor vehicle involves many decisions, among them how aggressively to drive. It might seem that driving aggressively is always irrational, but that depends upon ones ends. A rational person values safety, but also values other goals such as saving time and avoiding inconvenience. EXAMPLE 1.3 RATIONAL DRIVERS? Airbags reduce, on average, the severity of auto injuries and the risk of death from motor accidents. But given that additional safety margin, it might well be rational for motorists to drive more aggressively! Is such an adaptation observed? Steven Peterson, George Hoffer, and Edward Millner examined statistics collected by the state of Virginia about fatal two-car accidents in 1993.a In 30 such accidents, one car was equipped with an air bag and the other was not. The accident reports identied in each case the supposed initiator, the party driving more aggressively. The table indicates that in 22 of the 30 accidents (73%) the initiators drove cars with airbags, although only 50% of the cars involved in accidents were equipped with airbags. So, the indications are, having an airbag increased the likelihood of a driver initiating an accident. Two-car accidents with/without airbags (Virginia, 1993) With airbags Number of cars Number of initiators 30 (50%) 22 (73%) Without airbags 30 (50%) 8 (27%) Source: Adapted from Peterson et al., p. 262. Any single bit of evidence such as this can only be indicative, not conclusive. And even if entirely valid, these results do not necessarily imply that regulations requiring airbags are inadvisable. Although drivers of airbag-equipped vehicles may indeed be more inclined to take risks, the increased aggressiveness may not entirely cancel out the overall benecial safety effect of airbags. a Steven Peterson, George Hoffer, and Edward Millner, Are Drivers of Air-Bag-Equipped Cars More Aggressive? A Test of the Offsetting Behavior Hypothesis, Journal of Law and Economics, v. 38 (October 1995). For a person receiving disability pay, the rational choice of when to return to work depends upon the costs and the benets. What would you expect to happen if disability benets were increased? P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 1.2 ECONOMIC MAN 11 EXAMPLE 1.4 RATIONAL MALINGERING? Under U.S. federal regulations, each states workmens compensation program reimburses injured workers at a certain replacement ratio (usually around 2/3 of pre-injury wages) up to a specied maximum. For a rational decision-maker, the higher the compensation for remaining on disability status, the less the incentive to return to work. Bruce D. Meyer, W. Kip Viscusi, and David L. Durbin examined a natural experiment testing whether changes in incentives had any visible effect upon the return-to-work decision.a In 1980 the state of Kentucky raised its maximum weekly benet from $131 to $217 by about 66%. In 1982 the state of Michigan raised its maximum from $181 to $307 by about 70%. (Other provisions of the states compensation arrangements were largely unchanged.) Crucially, these adjustments impacted only upon relatively high-wage workers, those with incomes big enough to benet from the higher compensation caps. If remaining on disability status were purely a medical matter, higher payoffs would not have affected returning to work. But taking monetary incentives into account, a rationally calculating high-wage worker would be more likely than before to remain on disability status. In contrast, low-wage workers, unaffected by the higher cap on disability payments, had no nancial incentive to defer returning to work. After the change in regulations in Kentucky, the median duration of temporary total disabilities for high-wage workers rose from 4 to 5 weeks, while remaining at 3 weeks for low-wage workers. Similarly in Michigan, the median duration for highwage workers rose from 5 to 7 weeks, while the low-wage median remained constant at 4 weeks. So both high-wage and low-wage workers responded in ways consistent with the rationality assumption. COMMENT We ought not jump to the conclusion that workers who chose to remain longer on disability status were malingering. It may well be that family responsibilities and other nancial needs had previously induced some workers to return to work too early, before their injuries were fully healed. a Bruce D. Meyer, W. Kip Viscusi, and David L. Durbin, Workers Compensation and Injury Duration: Evidence from a Natural Experiment, American Economic Review, v. 85 (June 1995). Despite these and many other examples of rational choices being made even in somewhat unexpected contexts such as automobile driving, one often hears about irrational behavior even from so eminent an economist as the Chairman of the Federal Reserve Board. EXAMPLE 1.5 IRRATIONAL EXUBERANCE On December 5, 1996 Alan Greenspan, the chairman of the Federal Reserve Board, expressed concern that the high level of stock prices represented irrational exuberance. And indeed, by historical standards, the stockmarket was extraordinarily high. At the beginning of 1980 the Dow Jones Industrial Index had stood at about 800. A decade later it had risen to about 1,800 and by December 1996 to around 6,900. Although the market dipped a bit after Greenspans remark, by the beginning of the year 2000 it reached almost 11,000. P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 12 1. THE NATURE AND SCOPE OF ECONOMICS Stock prices can be said to be too high or too low only in relation to actual and anticipated corporate earnings. In his book Irrational Exuberance (Princeton University Press, 2000), the economist Robert Shiller contended that not only were stock prices historically high, but the price-earnings ratio (P/E) also far exceeded all historical levels. According to his data, the ination-adjusted P/E, whose previous high had been around 32 (just before the 1930s Depression), had reached an unprecedented 44 in the year 2000 (as estimated visually from Figure 1.2 in the Shiller book). But other analysts maintained that the unusually high stock prices reected ongoing favorable economic developments such as the computer revolution, which promised continued gains in productivity. Also important, though less often mentioned, were the reduced risks of cataclysmic war after the collapse of the Soviet Union. Along with that, there was an improved climate of opinion for private business, owing to the declining appeal of communist and socialist ideologies. So at the time it was not so clear whether the stockmarket levels were irrational. The table here indicates that the Dow Jones Industrial Index did indeed move downward for some years after the publication of Shillers book in 2000, but it recovered almost all the lost ground by early 2004. Whether stockmarket levels of 8,000 or 10,000 or whatever are truly irrational is something all investors (including the authors of this book!) would really like to know. Date (January) 2000 2001 2002 2003 2004 Dow Jones industrial index 10,940 10,887 9,920 8,053 10,544 Human Goals The Self-Interest Assumption Economic man is supposed to be not just rational but also self-interested. Who can doubt that self-interest, though certainly not the only human goal, is an important aspect of what humans seek in life? Adam Smith said: It is not from the benevolence of the butcher, the brewer, or the baker, that we expect our dinner, but from their regard to their own interest.4 Traditional narrow economics does not inquire into the origins of our goals in life, our tastes or preferences. In one society individuals may protect children but eat cattle; another society may protect cattle but permit infanticide. Often, however, peoples goals and preferences do have analyzable sources. Psychologists explain them in terms of primitive instincts, as reinforced or suppressed by socialization. Anthropologists analyze how culture helps determine individual purposes; sociologists examine the role of class or of other group identications. Sociobiologists explain human tastes and preferences as the product of evolution through natural selection. Partly stimulated by this line 4 The Wealth of Nations (1776), Book I, Chapter 2. P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 1.2 ECONOMIC MAN 13 of scientic work, broad economics has begun to study the cultural and biological sources of preferences. As one example, teenage boys take more risks than do teenage girls, as evidenced by the higher auto accident rates (and correspondingly higher auto insurance premiums) for young males. Male risk-taking may make biological sense, since males must compete harder with one another to gain the attention of the opposite sex.5 (Biological and other possible sources of preferences will be discussed in more detail in Chapter 3.) Another question is whether tastes and preferences are stable. In analyzing taxes on alcohol, economists usually assume that the craving for alcohol, a taste, will be constant. If so, taxing alcohol makes drinking more costly but will not affect the underlying desire to drink. As a matter of historical fact, however, the taste for liquor has been known to change dramatically. Around 1850 the remarkable temperance campaign of Father Matthew in Ireland cut the consumption of spirits in that country from 12,000,000 to 5,000,000 gallons per annum. (But only temporarily!) And think of the fashion industries their very existence is based upon ever-changing tastes. What is far more important, many of the crucial social changes in human history have been due to shifts in peoples goals for living. Economic analysis may trivialize fundamental values and goals by suggesting that they are mere arbitrary tastes. From the prophets of ancient Israel to the ministries of Jesus and Mohammed to the recent decline in religious belief in the West, the changes in the kinds of rewards that people seek from life have enormously affected human societies. Economists have mostly not attempted to explain these important determinants of human behavior. Self-interest is the human goal attributed to economic man. But benevolence (wishing well to others) certainly exists,6 and malevolence (wishing ill) as well. For biologically evident reasons, people are mainly benevolent toward their own children, or at any rate to close kin. Yet people also extend very large sums, in the form of charity, to strangers. Economists for the most part do not attempt to explore the underlying sources of such behavior. Nevertheless, economists would assert that, if it were cheaper to be benevolent (for example, if tax deductions for charitable giving were to become more generous), more benevolence would be elicited. And even though there is a biological explanation of parental aid to children, economists would still predict that greater nancial inducements would induce even more assistance to ones offspring. It has been alleged that this emphasis upon self-interest makes economists more selsh than they would otherwise be. Perhaps economics students are being taught to be selsh!7 5 6 See Paul H. Rubin and Chris W. Paul II, An Evolutionary Model of the Taste for Risk, Economic Inquiry, v. 17 (October 1979). Indeed, Adam Smith also said: How selsh soever man may be supposed, there are evidently some principles in his nature, which interest him in the fortune of others, and render their happiness necessary to him, though he derives nothing from it, except the pleasure of seeing it. 7 This is the opening sentence of The Theory of Moral Sentiments (1759). This allegation has been made even by economists: Robert H. Frank, Thomas Gilovich, and Dennis T. Regan, Does Studying Economics Inhibit Cooperation? Journal of Economic Perspectives, v. 7, 1993. P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 14 1. THE NATURE AND SCOPE OF ECONOMICS EXAMPLE 1.6 SELFISH ECONOMICS STUDENTS? In a study at George Washington University the economists Anthony M. Yezer, Robert S. Goldfarb, and Paul J. Poppena examined two questions: (1) When asked about hypothetical situations, do students in economics courses report they would be more selsh than before they took the course, as compared with students taking non-economics courses? (2) When the actual behavior of students is observed, are economics students in fact more selsh? Table A compares the self-reported unselshness of students in economics versus noneconomics classes. Each student was asked to state the percent chance that, after receiving a bill containing a substantial error in his/her favor, he/she would voluntarily ask to be charged the correct amount due. The same question was asked at the beginning of the course (Before) and at the end (After). Table A Results of survey question (self-reported hypothetical unselsh actions) Before Two economics classes Two noneconomics classes 53.4% 52.5% After 50.0% 53.8% Source: Calculated from Yezer, Goldfarb, and Poppen, Question 2, in Table 1, p. 181. Though the difference is small, these data do provide some slight support for the contention that economics instruction led to an increase in student selshness as self-estimated for such a hypothetical situation. The investigators then went on to conduct a much more signicant experiment, this time with real money. Envelopes containing $10 in cash were lost in economics and noneconomics classrooms. Each envelope was addressed and stamped, and also contained a message to the effect that the money was in repayment of a loan. Since the envelopes were already addressed and stamped, an unselsh person had only to seal the envelope and drop it in a mailbox. A selsh person could just keep the money. The investigators left 32 envelopes in economics classes and 32 in noneconomics classes. See Table B for the results. Table B Results of lost letter experiment Returned 32 letters in economics classes 32 letters in noneconomics classes 18 (56%) 10 (31%) Not returned 14 (44%) 22 (69%) Source: From description in Yezer, Goldfarb, and Poppen, p. 181. Table B shows that, when it came to real decisions with real nancial stakes involved, fewer economics students acted selshly. The self-estimated hypothetical survey reported in Table A, which appeared to indicate the contrary, may have shown P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 1.2 ECONOMIC MAN 15 only that economics students are more frank in admitting they might sometimes behave selshly. a Anthony M. Yezer, Robert S. Goldfarb, and Paul J. Poppen, Does Studying Economics Discour- age Cooperation: Watch What We Do, Not What We Say or How We Play, Journal of Economic Perspectives, v. 10 (Winter 1996). So, it appears, studying economics does not make a person more selsh. However, economics instruction may make the student more willing to admit that he or she will, in certain circumstances, act selshly. What about economics professors? EXAMPLE 1.7 SELFISH ECONOMICS PROFS? In a number of academic professional associations the dues schedules rise with income. But members are permitted to t themselves voluntarily into the appropriate income category (the honor system). David N. Laband and Richard O. Beil studied a number of professional associations using this procedure.a A member of the American Economic Association (AEA) in 1994 who placed himself or herself in the lowest dues category (declared income less than $37,000) would pay dues of $50, whereas self-placement in the highest category (declared income greater than $50,000) required dues of $70. For the American Sociological Association (ASA), the dues structure ran from $34 at the bottom end (for income less than $15,000) to $180 at the top (for income greater than $50,000). For the American Political Science Association (APSA) the comparable numbers were $65 (for income less than $30,000) and $125 (for income greater than $70,000). Were the self-placements into dues categories truthful? The authors tested this by sending a separate questionnaire asking members of each association about their incomes during the year. The questionnaires had no obvious connection with professional dues, but replicated the income categories in members annual billing statements. It was found, for example, that in responding to the questionnaire only 3% of American Economic Association members indicated that they fell into the lowest income category. But when it came to paying dues, 25% placed themselves in that category. So evidently, many members cheated. Somewhat similar results were found for the other associations. One way of comparing the different professional associations is to calculate what the true average dues payment would have been, if members of each association had placed themselves in the correct categories as indicated by the independent questionnaire. Some of the relevant averages are indicated in the table. Average dues liabilities and payments in 1994/95 True dues liability AEA ASA APSA $67.74 $147.60 $105.15 Actual dues payments $62.83 $112.52 $96.05 Actual/true 93% 78% 91% Source: Laband and Beil, pp. 9697. P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 16 1. THE NATURE AND SCOPE OF ECONOMICS Although in percentage terms the economists appear to be relatively truthful (and, to that extent, unselsh), the comparison in the table is perhaps biased. Since the AEA is considerably cheaper than the ASA and APSA, the temptation to cheat is less. Still, it is at least doubtful whether economists are any more selsh than other academics. a David N. Laband and Richard O. Beil, Are Economists More Selsh than Other Social Scientists? Public Choice, v. 100 (1999), pp. 85101. Ignorance and Uncertainty To say that people are rational is not to say that they are all-knowing. Almost all decisions are subject to uncertainty. A consumer may not be aware of the quality of the goods offered for sale, a job-seeker may not know which employer would be willing to pay the highest salary, a computer manufacturer may be unsure about what products its competitor may bring to market, a politician may be doubtful whether the public will approve of a proposed policy. Much of this book deals with decision-making under uncertainty. How much should one be willing to pay as an annual premium for re insurance? Should a person choose a safe but lower-paying job over a risky one offering higher rewards? Which stocks should an investor buy? As a subtler point, individual decision-makers should take into account the behavior of others. A person who thinks a stock is underpriced ought to ask why other investors let that stocks price get so low. Moreover, any one person should recognize that others may attempt to take advantage of his or her own ignorance. Later chapters will analyze how these considerations affect the terms of insurance contracts, the prices of assets, and the employment contracts that rms offer. 1.3 MARKET AND NONMARKET INTERACTIONS We all need food. But there are many ways to go about getting it. Someone who wants bread from the baker can work at a job and earn the price of a loaf. An alternative would be to steal the bread. As still another option, consumers might try to persuade bakers that it is their charitable duty to give away bread. Or consumers might organize a political movement aimed at forcing bakers to do so. Narrow economics concentrates upon the rst of these interactions, that is, upon voluntary exchange through the market. For the most part, crime has been left to sociology, the techniques of persuasion to psychology, and the uses of state power to political science, and. But broad economics goes beyond these boundaries. EXAMPLE 1.8 CRIME AS AN ECONOMIC CHOICE THREE STRIKES Crime sometimes does pay. It may be entirely rational, though certainly not ethical, for a criminal to steal rather than work if he feels the gains are worth the risks. Conventional criminology, a eld historically dominated by sociologists, has regarded criminals as deviant individuals who do not make rational choices. According to this traditional view, the solution to crime lies on the psychological level for example, improving the mental health of potential lawbreakers, or providing them with P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 1.3 MARKET AND NONMARKET INTERACTIONS 17 better role models. Economic analysis, without necessarily denying that criminals are psychologically deviant in some ways, suggests that even criminal activity will respond to incentives. Imprisonment can reduce the crime rate in two main ways: incapacitation or deterrence. Incapacitation does not involve rationality: a person in jail is simply not in a position to commit crimes against the public. Deterrence, in contrast, operates through the potential lawbreakers calculation of the costs versus the benets of criminal activity. So a deterrence policy implies at least some degree of rationality on the part of potential law-breakers. This distinction became crucial in the debate over three strikes laws proposals to sentence habitual criminals to life imprisonment. If incapacitation is the important consideration, three strikes laws are seriously awed. The propensity to commit crimes is known to decrease with age, so such laws would ll the prisons with relatively aged inmates who would not be committing offenses anyway. But if deterrence matters most, the threat of being put away for life might discourage even young criminals. A study by Steven Levitt attempted to separate the two effects.a Using data for the period 19701992, he examined how the number of crimes in one statistical category such as assault responded to arrest rates in another category such as burglary. Given that a large number of lawbreakers commit both types of crimes then, if incapacitation is the main force at work, a higher arrest rate for assault would reduce both assaults and burglaries. But if deterrence is the predominant inuence, a higher arrest rate for assault should lead criminals to commit fewer assaults but just as many (or maybe even more!) burglaries and other crimes. The evidence suggested that deterrence was more important than incapacitation in reducing the crime rate. In fact, deterrence alone explained about 75% of the overall impact of higher arrest rates on crime. The study therefore provides some support for three strikes laws, though of course the effect on crime rates is not the only consideration in evaluating such legislation. (Another element that needs to be weighed are the costs of building more prisons and dealing with a larger inmate population.) Recent evidence from the states of Washington and California tends to conrm that, in those states as well, the higher incarceration rates associated with three strikes have reduced the number of offenses. In another study, the same author asked why juvenile crime rates rose much more than nonjuvenile rates in the period 19781993.b (In that period the adult arrest rate for murder fell by 7%, but the juvenile arrest rate rose by an extraordinary 177%!) The main explanation, he concluded, was that in the period of study the average juvenile punishment rate per crime already lower than the adult rate fell by around 20%, whereas the adult punishment rate rose by about 60%. He also noted that the crime rate falls sharply in the year that an age cohort moves out of the (more lenient) juvenile justice system and into the (more severe) adult system. a Steven D. Levitt, Why Do Increased Arrest Rates Appear to Reduce Crime: Deterrence, Incapaci- tation, or Measurement Error? Economic Inquiry (July 1998). b Steven D. Levitt, Juvenile Crime and Punishment, Journal of Political Economy (December 1998). So it appears that economic analysis can be usefully applied to crime as one form of nonmarket behavior. Charity is another. A third form of nonmarket interaction, sometimes not too far removed from crime, is politics. The economic approach to politics will be covered in Part Seven of this book. P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 18 1. THE NATURE AND SCOPE OF ECONOMICS Market interactions have two crucial characteristics: they are mutual and they are voluntary. Among the possible nonmarket interactions, charitable giving is voluntary but is a unilateral rather than a mutual transaction. Theft, of course, is involuntary on the part of the victim. But is the market interaction really voluntary? Can a poor person refuse a job that pays low wages but will at least put food on the table? Isnt he just a wage slave? Or suppose a highwayman threatens his victim, Your money or your life! Isnt he offering a voluntary deal? Then how can criminal extortion be distinguished from market exchange? The explanation of these puzzles rests upon the concept of property. The highwayman is proposing a market deal: he will refrain from murder, in exchange for money. But under our legal system each person has property in his or her own life. The seemingly voluntary transaction proposed by the highwayman is based on his seizing power over something to which he has no legal title the victims life. As for the wage slave contention, it is true that a rich person can buy more of what he or she wants than can a poor person. This may or may not be inequitable, but poor people are not enslaved. Their working capacity is their own property, and they can bargain with alternative employers for the best available terms. Slaves cannot market or trade their labor, for it is not legally theirs to sell. 1.4 ALLOCATION BY PRICES THE MARKET SYSTEM Consider the allocation of seats in your economics classroom. Some seats are more desirable than others. One possible rule is rst come rst served. Or the professor could make the assignments on any basis he or she preferred. Or the students might elect a committee to work out the assignment. In less friendly situations such as rock concerts, good seating might depend on your ability to jostle and trample others. All of the above represent nonmarket ways of apportioning a scarce resource. On the other hand, rights to seats might be assigned by a market technique, for example, by an auction. EXAMPLE 1.9 BIDDING FOR FACULTY OFFICES William J. Boyes and Stephen K. Happel reported on how the College of Business at Arizona State University, upon moving to a new building, dealt with the problem of assigning faculty ofces.a The Management Department gave rst choice to the most senior professors. The Finance Department followed a rst come rst served rule: a sign-up sheet was posted outside the Chairmans ofce, and choices were awarded in order of signing up. The Statistics Department used a randomizing device rolling dice. The Economics Department chose to hold an auction. (The nancial proceeds, which turned out to be around $3,200, went to a fund supporting graduate student scholarships and dissertation research.) The single highest bidder paid $500 for the right to have the rst choice of ofces available. COMMENT The auction led to some adverse publicity. A number of citizens felt that the professors were auctioning off public property for their own benet. The complaint was unwarranted, since the ofces were not being sold to the detriment of the taxpayers. What was being sold was only the right to choose ahead of other professors. Also, P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 1.4 ALLOCATION BY PRICES THE MARKET SYSTEM 19 the proceeds were not used for the benet of the bidders but for the benet of graduate students. Once this was made clear, opposition dissipated. a William J. Boyes and Stephen K. Happel, Auctions as an Allocation Mechanism in Academia: The Case of Faculty Ofces, Journal of Economic Perspectives, v. 3 (Summer 1989). The key feature of markets is price the terms on which goods are exchanged. To acquire a commodity buyers must be willing to pay the market price, while successful sellers are the ones willing to give up control of the good in exchange for the same market price. Market prices ration goods and resources to consumers. As the preceding discussion has shown, there are other ways of rationing: rst come rst served, dictatorship, violence, lottery, and so on. But price has one feature these other methods lack: the commodities go to those individuals with the highest willingness to pay. Economists do not claim that this principle is necessarily ethically attractive. Among other things, wealthier people are able to pay more. So anyone who has acquired wealth, even unethically, has the power to buy lots of desired goods. On the other hand, all other conceivable methods for rationing goods and resources might also be subject to objection on ethical grounds, perhaps more so. Setting ethics aside, it is efcient (in a sense to be made more explicit in the chapters that follow) for goods and resources to end up in the hands of those most willing to pay. From the point of view of sellers or providers, prices guide production. Whenever the current market price of a commodity exceeds its cost of production, producing more of the good becomes protable. Not only are current producers likely to increase output, but new providers will have an incentive to enter the industry. In consequence, more goods will be provided precisely where consumers willingness to pay is highest. This is the principle that Adam Smith called the invisible hand.8 Even if a person seeks only private advantage, he or she is led to serve the public by producing those goods or services that others most desire. Perhaps this idea, that self-interested motivations can lead to actions that end up helping other people, seems obvious. Yet many people, in Adam Smiths day and in ours, believe that the only way to help others is by intentionally doing good. More sophisticated individuals appreciate, as did Adam Smith, that in helping others trade can be more effective than charitable aid. Still, it is not immediately evident just how self-interested behavior manages to avoid mutual harm or even total chaos. Los Angeles is fed by converging food shipments from all corners of the earth without any benevolent dictator to make sure that the Kansas farmer, the New England sherman, and the Florida orange grower deliver food to the city. Though no one is ordered to do so, and none of these suppliers need be motivated by any particular love and concern for Angelenos, the city is fed. Why? Because Kansas farmers simply nd it more protable to ship their wheat to Los Angeles than to eat their crops themselves, and similarly for all the others. Adam Smith put it this way: in civilized society [man] stands at all times in need of the cooperation and assistance of great multitudes, while his whole life is scarce sufcient to gain the friendship of a few persons.9 How can a person who has only a few friends 8 9 Adam Smith, The Wealth of Nations, Book IV, Chapter 2. Adam Smith, The Wealth of Nations, Book I, Chapter 2. P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 20 1. THE NATURE AND SCOPE OF ECONOMICS nevertheless get the assistance of multitudes? The answer lies with the invisible hand of self-interest, which leads an individual to work for the good of persons practically unknown to him. The market system leads us all to work for the good of one another. The result is an orderly economy that meets peoples needs and desires without anyone having planned for it to do so. (Ironically, it was the planned economies of Communist China and Soviet Russia that had difculty keeping the grocery shelves stocked.) 1.5 BEHAVIOR WITHIN ORGANIZATIONS Though traditional narrow economics has concentrated on the study of markets, one of the directions in which broad economics has moved has been to examine behavior within organizations. Within organizations, to some extent at least, resources are allocated not by exchange but by command. Government is the most prominent example. American congressmen enact legislation without buying one anothers votes. (But, as will be seen in Chapter 17, log-rolling represents a kind of exchange of votes among members of a legislature.) In the executive branch, the President is empowered by law to direct the activities of the subordinate ofcers of government. Similarly within business rms, managers exercise authority over the actions of subordinates. Yet economic man is also at work within organizations. In democratic political systems, voters are likely to support the candidate regarded as most likely to improve their well-being. Politicians are likely to adopt positions that maximize their career prospects. Within rms, managers are notoriously interested in their compensation packages. And when a Board of Directors res a CEO, the usual reason is inadequate performance in terms of maximizing shareholder income. 1.6 POSITIVE AND NORMATIVE ANALYSIS: IS VERSUS OUGHT In its scientic aspect economics is strictly positive. It answers questions such as Is this theory (explanation) really true of the actual world? But economics also has a normative aspect, dealing with questions such as Should this policy be adopted? Given an objective, economists can use their knowledge of what is true to analyze the problem and suggest ways of achieving what ought to be done. Adam Smith had in part a normative purpose in writing The Wealth of Nations. He opposed the then politically dominant mercantilists,10 favoring instead the policy he called natural liberty free trade among nations, and laissez faire within. This book is less concerned with normative issues (policy recommendations) than with positive matters (scientic understanding). Looking at the positive aspect, Adam Smiths even more fundamental thesis was that the economy follows objectively determinable laws. In early times, some people thought the planets were pushed in their courses by angels. Newton showed how the principle of gravity explains planetary motions. Similarly, to explain the universe of economic behavior, Smith put forward the idea of the market system as a mechanism, driven by the self-interest of participants, yet integrated so that each is led to serve the desires of others. The distinction between positive and normative analysis sheds new light upon the question raised earlier about disagreement among economists. Economists may disagree 10 The mercantilists believed that national well-being required the accumulation of gold and silver. To achieve this end, they recommended regulations to encourage exports and discourage imports. P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 1.7 ELEMENTS OF THE ECONOMIC SYSTEM 21 on policy issues because they seek different normative goals. One might be more concerned with social equality, another with individual freedom. Even complete scientic understanding will not resolve such philosophical conicts. But often disagreement among economists is over means rather than goals: not over what to do, but how to do it. Scientic progress in positive economics will, over time, tend to eliminate this source of disagreement. EXAMPLE 1.10 WHEN DO ECONOMISTS DISAGREE? In the early 1990s several surveys of economists collected opinions on a variety of important positive and normative issues. The table here summarizes results for six questions, which we have classied as either positive or normative. Agreement among economists Proposition Generally agree Agree with provisions Generally disagree 20.5% Index of consensus 36.0 POSITIVE ISSUES A minimum wage increases 56.5% 22.4% unemployment among young and unskilled workers. A ceiling on rents reduces the quantity 76.3% 16.6% and quality of housing available. The cause of the rise in gasoline prices 11.4% 20.3% that occurred in the wake of the Iraqi invasion of Kuwait is the monopoly power of the large oil companies. NORMATIVE ISSUES The distribution of income in the 48.5 24.4 United States should be more equal. Antitrust laws should be enforced 34.9 36.9 vigorously to reduce monopoly power from its current level. The level of government spending 35.6 19.03 relative to GNP should be reduced. 6.5% 67.5% 69.8 56.1 26.7 27.6 21.8 7.3 44.6 9.0 Note: The column labeled Index of consensus was constructed by comparing Generally agree with Generally disagree, subtracting the smaller of these from the larger. (Agree with provisions, the middle position, was omitted.) Source: Adapted from Richard M. Alston, J. R. Kearl, and Michael B. Vaughan, Is There a Consensus among Economists, American Economic Review, v. 82 (May 1992), pp. 2045. COMMENT Notice that the Index of Consensus among economists is quite high for the positive issues, but considerably less so when it comes to normative issues of public policy. 1.7 ELEMENTS OF THE ECONOMIC SYSTEM Decision-Making Agents in the Economy There are three main types of economic decision-makers: individuals, rms, and governments. P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 22 1. THE NATURE AND SCOPE OF ECONOMICS Individuals are the basic units of a society. The consumption decisions of individuals are discussed in Part Two of the text, and their resource-supply decisions in Part Four. Actually, recognizing the mutual support and cohesiveness of the family, economists sometimes consider the household to be the effective consumption unit. Except where otherwise specied, the individual here will be understood as making decisions for his or her family or household. Business rms are articial units. Every rm is ultimately owned by or operated for the benet of one or more individuals. Surprisingly, this fact is often overlooked. One hears it said, for example, that we should tax corporations, not the people. But taxes levied upon a corporation must ultimately come from the pockets of human beings. The companys owners will likely earn lower prots, its workers may have to forego wage increases, its customers may pay higher prices. At the same time, of course, the tax revenues might be used in ways that benet other people. (As usual, every choice of policy involves both costs and benets.) The rm is best regarded as an aggregation of individuals gathered together for the purpose of production, for converting resource inputs into desired outputs. The market supply decisions of rms will be discussed in Part Three, and their resource demand decisions in Part Four. Governments are also economic decision-makers. The most important activity of a government is to set the legal framework within which the entire economy works. Like rms, governments are articial groupings. Unlike rms and individuals, governments have the legal right to take property without consent (as by taxation). Furthermore, government decision-making is determined by political rather than market processes, a topic that will be examined in Part Seven. Modern economies have still other decision-making units. Trade unions and cartels are organizations of sellers in markets. And there are also voluntary associations such as clubs, foundations, and religious institutions, through which individuals combine for collective consumption choices. Scarcity, Objects of Choice, and Economic Activities The source of all economic problems is scarcity. Peoples desires can never all be satised. Even if all material commodities were present in unlimited quantities, we would have insufcient time to enjoy them all. And, in addition, we all desire intangibles such as power, love, and prestige. There can never be enough of these. Scarcity is what forces people to make economic decisions where to work, what to produce, how much to sell with a view to obtaining what we most desire. The objects of economic choice are called commodities or goods. These terms are usually understood to include not only merchandise but also services. Services represent a ow of benets over a period of time, which might be derived either from physical goods (e.g., the shelter provided by a house) or else from human activities (e.g., the entertainment provided by concert performers). Consumption is the ultimate economic activity, and in a sense the explanation for all the others. In their consumption decisions, individuals choose the goods they like best, given their incomes and the prices they face. Production by individuals and rms is a second economic activity. Production transforms resources into consumable goods. The process of production can modify physical form, as in the conversion of leather and human labor into shoes, but not necessarily so. Moving goods over space (shipment of oranges from Florida to Maine) and over time P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 SUMMARY 23 (storing potatoes after harvest to distribute consumption over the year) are also forms of production. Of course, to be economically rational, production should represent conversion from a less desired to a more desired conguration. Burning an antique Chippendale chair for heat is production, but would normally be ill-advised. (Yet a person in danger of freezing to death might nd the conversion from chair to warmth highly advantageous.) The third main economic activity is exchange (to be discussed in Part Five). For the individual, exchange, like production, is also a kind of conversion a sacrice of some objects for others. But from the social point of view, exchange is distinguished from production by the fact that the totals of commodities are unaffected. Trade neither creates nor destroys goods and services, but only reshufes them among the different decision-making agents in the economy. 1.8 MICROECONOMICS AND MACROECONOMICS A distinguished professor of logic, deploring the division of his subject between deductive reasoning and inductive reasoning, once declared: In our textbooks on deduction we explain all about logical fallacies; in our textbooks on induction, we then commit them. Economic theory has a similar split. In much of microeconomics we explain how and why the Invisible Hand operates so well, how and why self-interest leads people to serve one another in a spontaneous system of productive cooperation. But macroeconomics examines why the system of coordination of economic activity through markets may sometimes break down. Microeconomics concentrates on equilibrium in particular markets, presuming an equilibrium of the market system as a whole. But, it seems, the overall equilibrium of the market system is not always robust. Economic activity may become disrupted, with consequences such as ination or large-scale unemployment. Macroeconomics investigates how and why such disruptions occur. For some time starting with the Keynesian ideas of the 1930s, macroeconomists attempted to develop modes of reasoning largely independent of any microeconomic foundation. Some theorists even dismissed classical microeconomics as obsolete or irrelevant. It is now generally recognized that the study of microeconomics is necessary even for a proper understanding of macroeconomics. However, it may be that such an understanding will require employing broad economics, and in particular taking account of imperfect rationality. SUMMARY The core of economic analysis deals with the rational and self-interested behavior of individuals and rms, as they interact with one another through market exchange. Rational behavior is the appropriate choice of means for achieving given ends, which requires comparing the benets and costs (advantages and disadvantages) of all the available courses of action. Economists do not ordinarily ask why people are self-interested or why they have specic desires, but instead treat these as facts to be studied by the other social sciences. Individuals can try to satisfy their desires in a number of ways, for example by persuasion, by force, by theft, or by calling upon government assistance. But economics P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 24 1. THE NATURE AND SCOPE OF ECONOMICS mainly studies market relations, in which people seek to achieve their aims through voluntary exchange. Economic thinking has, however, moved outward from this central core. In an attempt to achieve more complete understanding of reality, broad economics applies economic methods of analysis to nonmarket interactions such as crime and politics. It also attempts to allow for non-self-interested actions (such as benevolence in the family) and for the fact that humans sometimes deal with one another in ways that seem irrational. Adam Smiths principle of the Invisible Hand shows how persons who are interested only in their own welfare are nevertheless led to cooperate with one another through market exchange. The market economy is an unplanned yet integrated arrangement, whose functioning follows scientically determinable laws. The main decision-making agents in the economic system are individuals (possibly acting on behalf of their families or households), rms, and governments. Individuals are the only agents who consume. Though individuals may also produce goods and services, in modern economies production mainly takes place through business rms articial agents created by individuals for that purpose. Production transforms the physical shape, location, or availability of commodities. Exchange reshufes the existing goods and services among the economic agents to better accord with individual desires. Economics has both a positive and a normative aspect. From the positive or scientic point of view, economics attempts to explain what the real world is like. In its normative aspect economics studies questions of policy, for example, how large a fraction of the tax burden should be borne by the rich. Although scientic progress in economics tends to eliminate disagreements among economists on positive matters, when it comes to normative issues unanimity can never be expected. The reason is that economists, like other citizens, diverge in the policy goals they seek to achieve. This book concentrates upon the positive aspect of economic analysis. QUESTIONS The answers to daggered questions appear at the end of the book. 1. a. b. c. In what respects can economics be considered a science? Give an example of a prediction that modern economic science can condently make. What predictions has economics not yet been able to make? What is rational behavior? Give examples of rational and irrational behavior. Can the economists postulate of rationality be useful even when irrational elements strongly inuence behavior? For Review 2. a. b. c. 3. Does the economist assume stable preferences? Give an example of a change in preferences that has had important economic effects. 4. Does the economist assume that everyone is selsh? Give an example of unselsh behavior that has important economic consequences. 5. Market transactions are said to be both mutual and voluntary. Give an example of a nonmarket interpersonal transaction that is not voluntary and an example of one that is voluntary but not mutual. P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 QUESTIONS 25 6. What are positive issues in economics? What are normative issues? Give an example of each. 7. a. b. c. d. How does the Invisible Hand lead self-interested individuals in a market economy to cooperate? Would self-interested behavior lead to voluntary cooperation in a monastic economy where all income was equally divided? In a dictatorship where the political authorities conscated the lions share? In an economy with no property, so that any person could try to seize whatever he or she needed from other people? 8. The principle of the Invisible Hand asserts that self-interested behavior on the part of resource-owners leads inevitably to chaos. True or false, and why? 9. What is the difference between production and exchange? For Further Thought and Discussion 1. Jack Vance, in his novel Wyst: Alastor 1617, described a planet whose economy was based upon egalism, a system in which all resources are shared and accumulation of private property is considered a crime. In this self-styled utopia, theft is considered a virtue, as it prevents anyone from accumulating private property. Would you like to live in such a society? What would be the advantages and disadvantages? 2. a. b. Other things being equal, would you expect the murder rate to be lower in jurisdictions applying capital punishment? If the income-tax exemption granted for each child were increased, would you expect the birth rate to rise? 3. The psychiatrist T. S. Szasz argues that mental illness is the result of rewarding people for disability. Not only is the patient motivated to become ill, but there is a nancial advantage to the healing professions in declaring personal problems to be illnesses. How could mental illness be made less rewarding? Would doing this reduce mental illness? 4. If government were to increase relief payments to the unemployed, would you expect unemployment to rise? 5. Explain why some individuals are wealthy (in a position to consume a great deal in the product market) and others are poor. 6. If the Invisible Hand leads individuals to serve their own interests by serving others, why are some people led to a life of crime? Why do some corrupt politicians nd it advantageous to serve themselves at the expense of their constituents? Why are dictators motivated to seize power? [Hint: Does the principle of the Invisible Hand apply to all kinds of social interactions, or does it hold only when individuals interact in a particular way?] 7. Would an effectively enforced law requiring drivers to wear seat belts tend to reduce driver deaths? Pedestrian deaths? 8. Dr. Samuel Johnson said, There are few ways in which a man can be more innocently employed than in getting money. But the French writer Charles Baudelaire declared Commerce is satanic, because it is the basest and vilest form of egoism. What do you think each had in mind? 9. Classify each of the following statements or propositions as either positive or normative. (Does the classication positive versus normative have any bearing upon truth or falsity?) a. Smoking in enclosed public spaces should be banned. b. Prohibiting smoking in public places would reduce the demand for cigarettes. P1: JZP 0521818648c01agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:19 26 1. THE NATURE AND SCOPE OF ECONOMICS c. d. e. Legislation to limit the places where smoking is permitted would be opposed by the tobacco industry. Nonsmokers rights to breathe clean air are more important than smokers rights to pollute the air. Antismoking laws will have no effect on sales of cigarettes because smokers will light up just as much as before but conne their pufng to legal areas. 10. It may become possible to predict the place and time of earthquakes, weeks or even months before their occurrence. Some inuential writers have argued that such predictions should be kept secret, or even that investigations leading to such predictions should be banned. Allegedly, the panic caused by predicting an earthquake would be more damaging than the earthquake itself. What does this view imply about individual rationality? Would you favor or oppose a ban on earthquake prediction? 11. According to traditional economic analysis in which all economic agents have perfect information about market opportunities, a worker who is unemployed can get a job promptly simply by agreeing to accept a lower wage. In a sense, any unemployment would be voluntary. a. Suppose that employers do not know whether a particular worker will be a good match for the rm without interviewing the worker. How do you think this would affect the unemployment rate? b. Suppose that some workers prefer to be temporarily unemployed rather than receive a pay cut. Consider a company that faces a drop in demand, and needs to pay its employees less. Do you think it matters whether price levels are stable, or whether the economy is in a period of rapidly rising prices (so that each dollar is worth less each year in terms of the real goods and services it can command)? P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2 2.1 Working Tools Equilibrium: Supply-Demand Analysis 28 Balancing Supply and Demand 28 How Changes in Supply and Demand Affect Equilibrium 30 Algebra of Supply-Demand Analysis 36 An Application: Introducing a New Supply Source 38 Taxes on Transactions 39 An Application: Interdicting Supply 43 Price Ceilings and Price Floors 46 2.2 Finding an Optimum 49 The Logic of Total, Average, and Marginal Concepts 50 How Total, Average, and Marginal Magnitudes Are Related 54 An Application: Foraging When Is It Time to Pack Up and Leave? 59 SUMMARY 61 QUESTIONS 62 EXAMPLES 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 Scarcity and Prices in Medieval Winchester 32 Potatoes/Dry Beans versus Strawberries 33 Baby Booms, Marriage Squeezes, and Women in the Labor Force 34 Dowries 35 Beer Taxes and Drinking by High School Students 41 Postwar Shortages and Trekking 47 Agricultural Price Supports 48 Professors and Publications 53 The Oil Entitlement Program 58 Taxes 58 Foraging Choices 60 27 P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 28 2. WORKING TOOLS Table 2.1 Optimization problems versus equilibrium problems Optimization problems 1. Should I buy a new car or keep my old one a while longer? 2. Will I be happier working, or should I drop out of the rat race and live on handouts? 3. Should I buy a condo or live in a rental apartment? 4. Should narcotics laws be made stricter or more lenient? 5. Should our union go on strike, or had we better accept managements offer? Equilibrium problems 1. Are new car prices likely to be lower next year? 2. Would generous welfare benets for the unemployed raise the unemployment rate? 3. What determines the ratio between the annual rental of an apartment and its purchase price as a condominium? 4. If use of narcotics were decriminalized, would drug usage increase? 5. Do strikes raise the wage of workers? Lets start with some good news. Remarkably, the microeconomics we study in this book deals with only two classes of problems: (1) nding an optimum and (2) nding an equilibrium. Facing any economic question, your rst step should be to ask: Is this an optimization problem, or is it an equilibrium problem? Look at Table 2.1. Notice that optimization problems always take the form: Would it be better for me (or possibly, depending upon the point of view, for my business or for my nation or even for humanity as a whole) to choose this action or that action? In short, whats the best thing to do? Equilibrium problems ask instead: How can we explain what we observe in the real world? For instance, why are diamonds so expensive when a more essential commodity, water, is cheap? The questions listed in Table 2.1 all concern market dealings. But as argued in Chapter 1, optimization problems and equilibrium problems arise not just in markets but in all areas of life. Some optimization examples: an airplane designer is considering titanium versus stainless steel for an aircraft wing; a physician is choosing whether to prescribe an antibiotic or a placebo; an army commander is deciding whether to attack or retreat; a manager is considering whether to buy or lease new ofce space. Some equilibrium examples: in biology, why is the male/female sex ratio at birth almost always close to 1:1; in anthropology, what makes some cultures egalitarian and others highly hierarchical; in international relations, why are some nations large and others small; in nance, what determines the prices of different shares traded on the New York Stock Exchange? In each group of questions, all but the last lie outside the range of narrow economics, yet the methods of economic reasoning remain entirely applicable. For each of the two classes of problems, economics uses a characteristic technique. (1) To deal with equilibrium problems economists look for a balance between supply and demand. (2) To solve optimization problems economists nd a minimum or maximum by comparing marginal magnitudes. This chapter reviews the two techniques. 2.1 EQUILIBRIUM: SUPPLY-DEMAND ANALYSIS Balancing Supply and Demand The supply-demand diagram of Figure 2.1 should be familiar from earlier courses, but lets review some of the details. The horizontal axis shows the quantity Q of some P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.1 EQUILIBRIUM: SUPPLY-DEMAND ANALYSIS 29 P D S Supplycur ve At the equilibrium point E, the quantity that consumers wish to purchase equals the quantity that sellers want to sell. The equilibrium price is P and the equilibrium quantity is Q . Price($ /Q ) Figure 2.1. Demand and Supply P P P E Equilibrium Demandcur ve S D 0 Qd Q s Q Qd Qs Q Quantity good, for example, memory chips.1 The vertical axis represents price P, in dollars per megabyte. [Note: Prices are usually quoted in money terms, but more fundamentally a price is the ratio of exchange between two goods. If a megabyte of memory costs $1.00 while an inkjet cartridge costs $15, then the price of memory, in terms of a cartridge, is 1/15.] The demand curve DD shows the quantity that consumers would want to buy at each price P. The negative slope of DD reects The Law of Demand: the fact that, as the price of memory chips or telephone calls or shoes decreases, buyers generally want to buy more. Though there are exceptions, surely the Law of Demand broadly describes behavior. Heres a bit of evidence: Stores often place ads claiming they offer low prices. Have you ever seen a retail store advertise that its prices are exceptionally high? Since that never or almost never occurs, retailers must generally believe that lower prices increase sales. (And if they are to remain in business, they had better be correct about such beliefs.) Similarly, the supply curve shows how much sellers would offer at each possible price. The positive slope of the supply curve indicates that the higher the price, the greater the quantity offered. In Figure 2.1 market equilibrium occurs at point E where the supply curve and demand curve intersect. The coordinates of E are the equilibrium quantity Q and equilibrium price P . To see why this is an equilibrium, consider a market price higher than P for example, P in the diagram. At price P suppliers want to sell the quantity Q s , while consumers want to buy only Q d . Since suppliers in aggregate are unable to sell all they want to at price P , at least some of them are likely to offer buyers better terms. So, as indicated by the downward-pointing arrow, at P there would be downward pressure on price. Consider next a market price initially lower than P , say P in Figure 2.1. At such a low price, the quantity Q d that consumers want to buy exceeds the quantity 1 Sometimes it is convenient to interpret quantity on the horizontal axis as a rate per unit time, for instance, thousands of chips per month or per week. P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 30 P 2. WORKING TOOLS D2 S Supplycur ve D1 P 2 Price($ /Q ) E2 Newdemand curve P 1 E1 Original demand curve S D1 0 Q 1 Q 2 Quantity Qd Q D2 Figure 2.2. Increase in Demand When consumers preferences change, so that they desire to purchase more at each price, the demand curve shifts to the right from D1 D1 to D2 D2 . Equilibrium price and equilibrium quantity both increase. Q s that suppliers want to sell. As indicated by the upward-pointing arrow at price P , there would be upward pressure on price. Whenever price differs from P , one or the other process will always be at work. Only at P , where the supply curve and demand curve intersect, does the quantity that consumers want to buy exactly match the amount suppliers are willing to sell. This equality denes the market equilibrium quantity Q . CONCLUSION The point where the demand curve intersects the supply curve determines the equilibrium price P and quantity Q . There is no implication that being in equilibrium is either good or bad. Recalling the distinction made in Chapter 1, that would be a normative question whereas here we are engaged in strictly positive analysis. There are an equilibrium price and quantity of good things like housing, but also an equilibrium price and quantity of bad things like heroin. How valid is this analysis? Economics, like all sciences, employs models that only imperfectly depict reality. A model of reality is like a map of a city. A good street map is a highly incomplete picture of the real city, but it tells you enough to get you where you want to go. So one ought to ask not that models be literally true, but rather that they be useful. Supply-demand analysis is useful in explaining why prices for disk drives or for potatoes or for politicians are sometimes high, sometimes low. How Changes in Supply and Demand Affect Equilibrium What happens if circumstances change, for example, if costs of production fall or if consumers incomes rise? Such changes affect the equilibrium pictured in Figure 2.1 by altering the supply curve, by altering the demand curve, or by altering both. Suppose that, perhaps as a result of increased income or changed preferences, people now want to buy more paper goods than before at each possible price P. This is called an increase in demand. As shown in Figure 2.2, the demand curve shifts to the right (from P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.1 EQUILIBRIUM: SUPPLY-DEMAND ANALYSIS 31 P D S1 Original S2 supply curve E2 Newsupply curve P 1 Price($ /Q ) P 2 E1 S1 S2 0 Q 1 Quantity Q 2 Demand curve D Q Figure 2.3. Increase in Supply When a change in conditions induces sellers to offer more at each price, the supply curve shifts to the right from S1 S1 to S2 S2 . Equilibrium quantity increases, but equilibrium price falls. D1 D1 to D2 D2 ). The old equilibrium price and quantity were P1 and Q , and the new 1 equilibrium price and quantity are P2 and Q . 2 How does the change come about? Suppose that after the demand curve shifted to D2 D2 the price had initially remained unchanged at P1 Then consumers would want to buy the amount Q d . But at price P1 suppliers still want to sell only the quantity Q . s Since the quantity demanded exceeds the quantity offered, price tends to rise until it reaches its new equilibrium level P2 . This description is oversimplied in several ways. In the model all transactions are assumed to take place at the equilibrium price. But in actual markets some sales may occur at wrong (nonequilibrium) prices. Furthermore, these wrong transactions may affect the terms at which later sales take place. An apple seller at a local farmers market might be lucky enough to dispose of half his barrels early in the day, at a high (disequilibrium) price. He might choose to go home and celebrate rather than bother selling his remaining stock. But once the remaining barrels are taken off the market, prices for the remainder of the day could be affected. Economists analyze such issues under the heading of economic dynamics, a topic that requires more advanced techniques than used in this text. Instead, we will use what is called the method of comparative statics. This means that, as shown in Figure 2.2, two supply-demand equilibria are compared, one under the initial conditions, the other under the changed conditions. So, in analyzing some change in economic circumstances, the basic technique is simply to ask: Does the change shift the supply curve, or does it shift the demand curve, or both? Consider next an increase in supply. This means that at each price sellers want to sell more than before, so the supply curve shifts to the right (from S1 S1 to S2 S2 ), as shown in Figure 2.3. Here the new equilibrium quantity Q is larger than the old 2 Q , but the new equilibrium price P2 is less than P1 . [Caution: Resist thinking of 1 an increase in supply or demand as an upward shift of the corresponding curve. That P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 32 2. WORKING TOOLS would be correct for shifts of the demand curve, but wrong for shifts of the supply curve. To avoid error, always interpret an increase in supply or in demand as a rightward shift, as a larger quantity offered or desired at each possible price.] Last, you can verify that a simultaneous increase in both supply and demand will make the new equilibrium quantity greater than before, but the equilibrium price might move either way. PROPOSITION: An increase in demand causes the equilibrium price P and quantity Q to both rise. An increase in supply causes equilibrium Q to rise but equilibrium P to fall. A simultaneous increase in both supply and demand makes the equilibrium quantity Q greater than before, but the new equilibrium price P could be higher, be lower, or remain unchanged. EXAMPLE 2.1 SCARCITY AND PRICES IN MEDIEVAL WINCHESTER That unusually scarce supply leads to high prices is sometimes denied. In 1973 and again in 1979, the Organization of Petroleum Exporting Countries (OPEC) sharply reduced their petroleum exports. Oil prices rose sharply. Nevertheless, some commentators attributed the price increases not to the reduced oil supply but instead to corporate greed or to consumer irrationality. Yet the connection between low supply and high prices has been observed since earliest times. The table here is derived from records of wheat production in the period 12111448 on estates owned by the Bishopric of Winchester, as reported in a study by H. Flohn.a As can be seen, in periods with low yield/seed ratios (bad weather), wheat prices were high. The top row, for example, indicates that when the yield/seed ratio was the least favorable (in the range 2.0 to 2.5), the wheat price was the highest (12.0 shillings per quarter of wheat). Wheat yields and prices, Winchester 12111448 Average yield/seed ratio 2.02.5 2.53.0 3.03.5 3.54.0 4.04.5 4.45.0 >5.0 Average price (shillings per quarter) 12.0 8.8 7.1 6.2 5.5 4.8 5.1 Source: Estimated visually from Figure 12.1 in Flohn. a H. Flohn, Short-Term Climatic Fluctuations and Their Economic Role, in T. M. L. Wrigley, M. J. Ingram, and G. Farmer, Climate and History (Cambridge University Press, 1981). What brings about shifts in demand curves or supply curves? It is sometimes useful to distinguish between changes that originate outside and inside the economic system. Possible outside sources of variation include: (1) changes in tastes (a news report about the dangers of cholesterol may make some people avoid butter) P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.1 EQUILIBRIUM: SUPPLY-DEMAND ANALYSIS 33 (2) changes in technology (the integrated circuit greatly increased the supply of electronic devices) (3) changes in resources (an important oil discovery would enlarge the worlds supply of petroleum) (4) changes in legal rules (decriminalizing marijuana would increase both its market supply and its market demand). Inside sources, inuences upon supply and demand for a particular good that originate elsewhere within the economy, might include: (1) changes in prices or quantities of other goods that are related in demand (a decrease in the price of printers increases the demand for paper) (2) changes in prices or quantities of other goods related in supply (increased beef production boosts the supply of hides) (3) changes in income (the higher incomes received by stock brokers in the 1990s increased their demand for luxury cars). EXAMPLE 2.2 POTATOES/DRY BEANS VERSUS STRAWBERRIES Vegetables and fruits are cheapest at harvest time. The reason is not hard to explain. The demand for food is fairly uniform over the year, but the supply can vary drastically over the seasons. The table here compares seasonal price variations for potatoes and dry beans versus strawberries. Potatoes, which dominate the potatoes/dry beans totals, are usually most expensive in July, just before the main potato harvest in August and September. As the new crop arrives, prices fall for several months before beginning to rise again in November. The strawberry price pattern is strikingly different. The price is usually much higher in the winter months (December and January) before strawberries begin to arrive in early spring. Although the potato harvest is highly concentrated in the fall, notice how small the price variation is over the year: the highest monthly price (July) exceeds the lowest monthly price (October) by less than 50%. The main reason is that potatoes are easily storable. Although few potatoes are produced in winter, prices remain low owing to carryover from the fall harvest. As the stored potatoes are gradually consumed, prices rise toward their peak in July. The main strawberry crop comes in earlier, and prices are lowest in late spring and early summer. Also, since strawberries are less storable, their price varies considerably more over the year. Indeed, strawberries are so perishable that it may seem surprising the seasonal price variation is not greater. The reason is that the strawberry harvest is more evenly distributed over the months of the year. Monthly prices (20002002) Potatoes/dry beans (19901992 = 100) Jan Feb Mar 99.3 105.0 110.3 Strawberries ($/CWT) 129.4 96.1 76.6 P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 34 2. WORKING TOOLS Apr May Jun Jul Aug Sep Oct Nov Dec 112.7 114.3 118.3 128.0 117.3 95.3 86.7 95.7 100.0 68.2 53.7 59.7 59.7 73.2 66.2 81.5 102.2 122.5 Source: U.S. Dept. of Agriculture, National Agricultural Statistics Service, Agricultural Prices (April 2003). The original source of agricultural supply variation over the year is the outside element of God-given seasonal climate. But, as the Example shows, human decisions in the form of storage activities modify the force of the external factors. Other inside responses improved transportation, changed agricultural practices, development of new seed varieties, and so on also tend to stabilize prices over the year. Examples 2.1 and 2.2 dealt with the supply and demand of ordinary commodities like wheat and strawberries. But supply and demand are also relevant in many other contexts, among them the marriage market. EXAMPLE 2.3 BABY BOOMS, MARRIAGE SQUEEZES, AND WOMEN IN THE LABOR FORCE Shoshana Grossbard-Shechtman and Clive W. J. Grangera studied how the relative numbers of marriageable men and women affect female labor force participation. An important feature of the marriage market is that women tend to marry men a few years older than themselves. Therefore, when women born in a baby-boom year mature, they nd suitable (slightly older) male partners relatively scarce. The marriage rate necessarily being lower, women are then more likely to enter the labor force. Baby booms and female labor force participation Increases in womens labor force participation (in comparison with preceding cohort) Sex ratio 0.96 0.94 0.92 1.0 At age 2024 3.6% 7.8 6.4 4.8 At age 2529 6.3% 12.1 9.4 4.7 At age 3034 7.2% 12.1 6.2 3.1 Dates (bb = baby boom) 1965 (pre-bb) 1970 (1st bb) 1975 (2nd bb) 1980 (3rd bb) Ratio of unmarried men 2029 to unmarried women 1829. Source: Adapted from Table 1 and Figure 2 in Grossbard-Shechtman and Granger. Moving downward in each of the last three columns, we see that all the entries are positive: every female age group had a higher percentage in the labor force than did the preceding cohort. That of course is mainly the consequence of the strong P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.1 EQUILIBRIUM: SUPPLY-DEMAND ANALYSIS 35 long-term trend toward increasing womens labor force participation. But notice that the percentage increases in the second row are all markedly greater than those in the row above. This reects the fact that women in 1970 found marriageable men relatively scarce compared to 1965, and hence were more likely to enter the labor force. The remaining rows show that the increases tapered off for the later (and smaller) baby booms. By 1980 the sex ratio had recovered to the 1.0 level (relatively favorable to women). And so the increases in female labor force participation were lowest in this time period. a Shoshana Grossbard-Shechtman and Clive W. J. Granger, Womens Jobs and Marriage, Baby-Boom versus Baby-Bust, Population, v. 53 (September 1998). [In French.] Supply and demand affect not only the frequency of marriage but the terms on which brides and grooms get together. EXAMPLE 2.4 DOWRIES In some societies the family of the bride pays a dowry to the groom (or to his family). Actually, the reverse pattern brideprice, a payment from the groom or his family to purchase a wife has been far more common over the range of human societies. Most societies have permitted polygyny (when a man can have several wives). In communities where powerful or wealthy men can bid for multiple wives, it is not surprising that marriageable women become relatively scarce and command a high brideprice. Building upon these supply-demand considerations, Steven J. C. Gaulin and James S. Bostera hypothesized that dowry rather than brideprice would be observed mainly in nonpolygynous societies, where a man is limited to one wife. Such societies are either monogamous or, rarely, polyandrous (when a woman can have multiple husbands). And since dowries are payments to obtain a more highly desired husband, they argued, dowries should also be more common in highly stratied societies where power and wealth disparities among potential grooms are large. The table here compares the prevalence of dowries among societies classied as (1) polygynous versus nonpolygynous and (2) stratied versus nonstratied. Each cell indicates the number of societies in each category, as described in the Ethnographic Atlas, and the number of societies where dowry payments were observed. The table shows that dowries are indeed paid almost exclusively in societies that are both nonpolygynous (usually monogamous) and stratied. Prevalence of dowries as determined by polygyny and stratication Polygynous societies Stratied Nonstratied Number of societies 5 of 268 1 of 625 893 Nonpolygynous societies 27 of 72 2 of 101 173 Source: Adapted from Gaulin and Boster, Table 1. a Steven J. C. Gaulin and James S. Boster, Dowry as Female Competition, American Anthropologist, v. 92 (December 1990). P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 36 2. WORKING TOOLS P P 10 Price($ /Q ) Price($ /Q ) Demandcur ve A Demandcur ve 4 1/2 1 1 6 Quantity Panel(a) 1 Supplycur ve P D C 1 E Supplycur ve B 1 1 10 Q Q Quantity Panel(b) Q Figure 2.4. Linear Supply and Demand Curves Panel (a) pictures the specic linear demand curve P = 10 Q and linear supply curve P = 1 + Q /2. The equilibrium is the point of intersection where Q = 6 and P = 4. Panel (b) pictures the more general straight-line demand equation P = A B Q d and supply equation P = C + D Q s . At the equilibrium point E, the quantities demanded and supplied are equal. Algebra of Supply-Demand Analysis The preceding analysis showed how equilibrium price and quantity are determined diagrammatically, by the intersection of the supply curve with the demand curve. To nd the equilibrium algebraically, supply can be expressed as an equation relating price to the quantities offered. And demand can be expressed as an equation relating price to the quantities that buyers are willing to buy. The solution to these simultaneous equations determines the two unknowns: price P and quantity Q. The algebra is especially easy when the demand and supply curves are straight lines, as pictured in Figure 2.4. Panel (a) shows a hypothetical demand curve with the equation P = 10 Q . The supply curve corresponds to the equation P = 1 + Q /2. To nd the equilibrium, either the prices or the quantities in the two equations can be set equal to one another. Let us equate the prices on the left-hand sides of the two equations. Then, since the right-hand sides must also be equal, 10 Q = 1 + Q /2. Solving, Q = 6 is the equilibrium quantity. Now insert Q = 6 into the demand equation to nd the equilibrium price: P = 10 6 = 4. (Or we can obtain the same price by substituting Q = 6 into the supply equation: P = 1 + 6/2 = 4.) EXERCISE 2.1 As in the preceding paragraph, suppose the demand curve has the equation P = 10 Q and the supply curve is P = 1 + Q/2. Find the equilibrium by equating quantities rather than prices. A N S W E R : Rewrite both equations to put Q on the left-hand side. The demand curve becomes Q = 10 P and the supply curve becomes Q = 2( P 1). Setting the two right-hand sides equal leads to the condition 10 P = 2( P 1). Solving, P = 4 is the equilibrium price. To nd the equilibrium quantity, substitute P = 4 P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.1 EQUILIBRIUM: SUPPLY-DEMAND ANALYSIS 37 in the supply or the demand equation to obtain Q = 6. The answer is of course the same as before. Panel (b) of Figure 2.4 pictures the general linear demand equation, which can be written P = A B Q d . Here Qd is the quantity demanded, and A and B are positive constants. Geometrically, A is the intercept of the demand curve on the vertical price axis. Think of A as the choke price for demand, meaning that for any price P greater than or equal to A, purchases will be zero. In this linear equation, B is the slope of the demand curve. The general linear supply curve has the equation P = C + D Q s , where Qs is the quantity supplied. The positive constant C, the intercept of the supply curve on the vertical axis, is the choke price for supply. At any price P less than or equal to C, none of the good will be supplied. The positive constant D represents the slope of the supply curve. At equilibrium, the quantity demanded equals the quantity supplied: Qd = Qs (2.1) Since Q d = Q s at the equilibrium, we can drop the subscripts and just write Q in the equations for demand and supply: P = A B Q (Demand) P = C + D Q (Supply) Solving equations (2.2) algebraically, the solution is: Q = AC B+D and P = AD + BC B+D (2.3) (2.2) EXERCISE 2.2 What if the demand and supply curves are not straight lines? Suppose the demand curve is described by the equation Qd = 12 P 3 and the supply curve is Qs = P 2 . Find the equilibrium price and quantity. A N S W E R : Since at equilibrium Qd = Qs , the right-hand sides of the equations must be equal: 12 P 3 = P 2 . By inspection, P = 2 satises the equation. Checking the quantities demanded and supplied, Qd = 12 23 = 4 and Qs = 22 = 4. So the solution is P = 2, Q = 4. Let us now turn to the algebra of comparative statics. Shifts in either the demand curve or the supply curve can take many forms. One possibility is that the demand curve might shift parallel to itself: the intercept changes but the slope does not. Another possibility is that the slope changes in such a way that the curve rotates about an unchanged intercept on the vertical axis. EXERCISE 2.3 Start with the demand and supply equations of Exercise 2.1 in the form Q = 10 P and Q = 2( P 1). Now suppose the quantity demanded becomes twice as great at P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 38 2. WORKING TOOLS P D Demand curve Si Import supply curve Sh Homesupplycur ve S Aggregatesupplycur ve Price($ /Q ) P 0 P 1 F C Q i1 G E0 E1 Q h Q Q 01 1 Quantity Q Figure 2.5. Introduction of an Import Supply In the absence of imports, the equilibrium E 0 is at the intersection of the demand curve D and the home supply curve S h . The aggregate supply curve, labeled S , is the horizontal sum of S h and S i . The new equilibrium is E 1 . each price. Then the new demand equation is Q = 2(10 P ). (a) Does this change in demand represent a shift of the intercept, a change of the slope, or is it a more complicated type of change? (b) Find the new equilibrium price and quantity. A N S W E R : (a) The choke price for demand remains P = 10, so we have here a change in the slope only. (b) To determine the equilibrium, rst equate the righthand sides of the unchanged supply equation and the new demand equation, 2( P 1) = 20 2 P . Then solve this equation, obtaining P = 5.5, Q = 9. Compared with the previous solution ( P = 4 and Q = 6), here the equilibrium price and quantity have both increased. Notice that even though the new demand curve indicates that consumers will buy double the quantity at each given price, the new equilibrium quantity does not quite double. The explanation, of course, is that the equilibrium price has risen. An Application: Introducing a New Supply Source A more challenging problem is illustrated in Figure 2.5. Suppose a country that had previously barred imports of steel now permits them. The demand curve for steel is D. The home supply curve S h shows the amount of steel that domestic rms want to sell at each price. The import supply curve, which shows the quantities foreign rms want to sell, is S i. With no imports, the equilibrium E 0 is at the intersection of the D and S h curves. When imports are allowed, the new equilibrium E 1 is determined by the point where the demand curve intersects the aggregate supply curve that allows for both home supply and imports. This is the curve labelled S in Figure 2.5: it is the horizontal sum2 of the S h and S i curves. In the diagram, imports reduce the equilibrium price from P0 to P1 ; they raise the equilibrium quantity from Q to Q . There is one slightly tricky feature. At any price 0 1 2 The Greek letter , capital sigma, signies summation. P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.1 EQUILIBRIUM: SUPPLY-DEMAND ANALYSIS 39 below F, the choke price for import supply, no foreign steel enters the market. Therefore at prices below F the aggregate supply curve S is identical to the home supply curve S h . At prices above F, however, S diverges to the right of S h by the amount of imports. So the aggregate supply curve that allows for both home and import sources has a kink at point G (which is at the same height as point F). EXERCISE 2.4 Let demand be P = 300 Qd , and suppose the home supply curve is P = 60 + h 2 Qs . To nd the initial equilibrium with no imports ( E 0 in the diagram), set the h domestic demand equal to the domestic supply, 300 Qd = 60 + 2 Qs , and let Qd = h Qs . Numerically the E 0 solution is P0 = 220, Q0 = 80. Let the import supply curve i be P = 80 + 4 Qs . If imports are permitted, nd (i) the new equilibrium price, (ii) the amount sold by domestic rms, and (iii) the amount imported. A N S W E R : Note rst that the import choke price, 80, is lower than the original equilibrium price, P0 = 220. So foreign rms will want to sell in this market. The aggregate supply sums the amounts that foreign rms want to sell and the amounts that domestic rms want to sell. To determine this sum, put Q on the left-hand sides of both the foreign and the home supply equations. [Caution: Do not put P on the left side of the equations and then sum; that would be adding the prices, where what we want to do is to sum the quantities!] The home supply curve can be rewritten as Qh = ( P 60)/2. For imports, Qi = ( P 80)/4. The sum of the two is Q Qh + Qi = 3 P /4 50. Equating the right-hand side of this sum to the righthand side of the unchanged demand curve we have 3 P /4 50 = 300 P . Solving, at the new equilibrium the price is P1 = 200 (compared with the previous P0 = 220) and the quantity is Q = 100 (compared with the previous Q = 80). So the import 1 0 quantity has risen from zero to Q i1 = 30. The quantity supplied from home sources h falls from Q = 80 to Q1 = 70. 0 Taxes on Transactions Transaction taxes can take several forms. The two simplest are a unit tax (a xed dollar amount for each unit of the good sold) and a proportionate tax (a xed percent of the price). EFFECTS OF A PER-UNIT TAX A tax in the amount of T per unit sold creates a gap of T between the price paid by the buyers (the gross price P + ) and the price received by the sellers (the net price P ): P+ P + T (2.4) [Note: The symbol is used to emphasize that the equation is a denitional identity.] One result that can be derived from the algebra is that, regardless of whether the seller or instead the buyer is the one legally obligated to pay the tax, the results are the same. (If the seller has to pay the tax, he will charge enough extra to cover the tax; if it is the buyer, she will reduce the amount she is willing to pay by the same amount.) For convenience, lets assume it is the seller who has the legal obligation to pay the tax. P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 40 2. WORKING TOOLS P D P+ P P S F Price($ /Q ) S T G S 0 Q Q E S P P D D F S P P + Price($ /Q ) T G E D D Q 0 S D Q Q Quantity Q Quantity Panel(a) The Add-on Inter pretation Panel(b) The Take-awayInter pretation Figure 2.6. Effects of a Unit Tax Panel (a) depicts an add-on analysis, where the tax is regarded as shifting the supply curve SS upward by $T per unit. The intersection with the unchanged demand curve DD determines the equilibrium quantity Q and the gross price P + . Panel (b) depicts a take-away analysis, where the tax is regarded as shifting the demand curve DD downward by $T per unit. Here the intersection with the unchanged supply curve SS determines the same equilibrium quantity and the net price P . Regardless of which type of analysis is used, the equilibrium quantity falls from Q to Q . In comparison with the old equilibrium price P , the gross price P + is higher and the net price P is lower than before. Both panels of Figure 2.6 show an initial demand curve DD and supply curve SS. The equilibrium price is p and the equilibrium quantity is Q . Let government now impose a tax T = $2 on each unit sold. Sellers may think of this in either of two ways. First, a seller may regard the tax as raising unit cost by T = $2. This add on to cost interpretation is illustrated in Panel (a). Here the supply curve shifts up by the amount T; the new curve represents the quantity offered on the market at each gross price P + . Alternatively, a seller may think of the tax as reducing receipts by T = $2 per unit sold. This take away from receipts interpretation is illustrated in Panel (b). Here the demand curve shifts down by the same amount T; the new curve represents the net price (the after-tax price) P received for each possible quantity sold. In the add on picture of Panel (a), the intersection of DD with the new (upwardshifted) supply curve S S at point F generates the new solution values for quantity Q and for the gross price P + . The net price P is found in Panel (a) by simply moving downward from F to G along the original supply curve SS. In the take away picture of Panel (b), the intersection of the new (downwardshifted) demand curve D D generates the solution values for quantity Q and the net price P at point G . To nd the gross price P + we simply move upward from G to F . The locations of the points F and G are the same in both diagrams, and the solutions for Q , P + , and P are identical. When these solutions are compared with the original equilibrium at E, the unit tax reduces the quantity exchanged from Q to Q . However, care is required in describing the effect upon price. In Panel (a) the intersection point F occurs at a higher price than at E, but in Panel (b) the intersection point G occurs at a lower price. So does a unit tax raise price or does it reduce price? The answer: it does both! The gross price P + is P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.1 EQUILIBRIUM: SUPPLY-DEMAND ANALYSIS 41 higher than the original P , but the net price P is lower than P . In short, consumers pay more but sellers receive less. PROPOSITION: A unit tax on transactions reduces the equilibrium quantity sold. It raises the gross price P + (inclusive of tax) paid by consumers, but lowers the net price P (the net-of-tax amount) received by sellers. Algebraically, the demand and supply equations (2.2) and the tax identity (2.4) can be combined into a new system of three simultaneous equations: + P = A B Q (demand equation) P = C + D Q (supply equation) (2.5) + (tax identity) P P + T Skipping over the details, the algebraic solution is: Q= A (C + T ) B+D P+ = AD + B (C + T ) B+D P = ( A T ) D + BC B+D (2.6) When equations (2.6) are compared with to equations (2.3), where there was no tax, the algebra shows that (as in the diagram) Q must be less than Q . A tax on transactions reduces the quantity bought and sold. And it is also algebraically evident that the new gross price P + must be greater than the original price P , whereas the new net price P must be lower than P . This too conrms the geometrical result. Also, the new gross price that buyers pay rises by less than the full T, and the new net price that sellers receive falls by less than the full T. So buyers and sellers share the incidence of the tax. EXERCISE 2.5 Suppose that as before the original demand function is P = 300 Qd and the supply function is P = 60 + 2 Qs . A unit tax T = 15 is imposed. What is the effect of the tax in comparison with the previous no-tax equilibrium P = 220, Q = 80? A N S W E R : An easy way of solving the three-equation system (2.5) is to substitute the right-hand sides of the rst two equations into the third. This yields the single equation 300 Q = 60 + 2 Q + 15. The solution for quantity is then Q = 75. Substituting into the other equations gives P + = 225 and P = 210. So consumers pay $5 more per unit, while sellers receive $10 less. EXAMPLE 2.5 BEER TAXES AND DRINKING BY HIGH SCHOOL STUDENTS Although taxes on beer have risen in recent years, these increases have not kept up with ination. So the real (ination-adjusted) tax on beer has declined. Michael Grossman et ala . estimated how beer drinking by high school seniors would have responded in 1989 to a Federal excise tax increase of about 76 cents per six-pack (an amount calculated to adjust the Federal tax to the ination that had occurred since 1951). In the table, the Actual distribution gures were based upon a survey of high school students conducted at the University of Michigan. The Distribution after P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 42 2. WORKING TOOLS tax adjustment gures were calculated from an economic model of how prices would affect the drinking decisions of individuals in the various groups. Beer taxes and drinking by high school students, 1989 Category (# of drinking occasions in past year) Abstainers (none) Infrequent (19) Fairly frequent (1030) Frequent (more than 30) Estimate after tax adjustment 18.6% 46.1 24.7 10.6 100.0 Actual distribution 15.3% 44.4 27.1 13.2 100.0 Source: Adapted from Table 2 in Grossman et al. If the economic model is correct, higher beer taxes would have reduced drinking increasing the proportions of students in the abstaining and infrequent-use groups and decreasing the proportions in the heavier-drinking groups. The authors of the study claimed that these hypothesized tax increases would have been more effective than increasing the minimum drinking age to 21, a reform that by 1989 was adopted in all the states of the United States. a Michael Grossman, Frank J. Chaloupka, Henry Saffer, and Adit Laixuthai, Effects of Alcohol Price Policy on Youth, National Bureau of Economic Research, Working Paper #4385 (June 1993). EFFECTS OF A PROPORTIONATE TAX Since the same general principles apply as for a unit tax, the proportionate tax can be analyzed in more condensed fashion. The main difference is the way in which the demand or supply curves shift. If the proportionate tax is calculated as a percentage t added on to the sellers net price P (ordinary retail sales taxes are quoted this way), the tax identity (2.4) becomes: P + P (1 + t ) (2.7a) Alternatively, sometimes a tax is quoted as a percentage that the government takes away from the gross price P + . Denoting the percentage taken away by such a tax as (the Greek letter tau), the equation becomes: P + (1 ) P (2.7b) Any percentage of tax can be expressed either way. Simple algebra shows that t and are related by: = t /(1 + t ) or t = /(1 ) (2.8) So a tax of 25% quoted as a percentage added on to P is equivalent to a tax of 20% taken away from P + . Figure 2.7 resembles the preceding Figure 2.6. Once again Panel (a) represents the add on picture and Panel (b) the take away picture. (The graphs are constructed to represent an add on tax rate t = 100%, which implies a take away tax rate = 50%.) But whereas in Panel (a) of Figure 2.6 the supply curve SS was displaced upward parallel to itself, here it is displaced proportionately upward by the percentage t. Thus the vertical intercept shifts upward from C to C , where C = C (1 + t ). Moving to the right, the P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.1 EQUILIBRIUM: SUPPLY-DEMAND ANALYSIS 43 P A D S F Price($ /Q ) Price($ /Q ) P+ P C P C E S G S Q Quantity Q Q D S A P D P+ A P P D F E S G C S Q Quantity Q D D Q Figure 2.7. Effects of a Proportionate Tax As in Figure 2.6, panel (a) depicts an add-on analysis and panel (b) a take-away analysis. In panel (a) the supply curve SS is shifted upward by t = 100% to become S S . In panel (b) the demand curve DD is shifted downward by = 50% to become D D . In either case, the new equilibrium quantity Q is less than the no-tax equilibrium Q . As before, in comparison with the old equilibrium price P , the gross price P + is now higher and the net price P lower than before. new supply curve S S diverges increasingly from SS as the price rises. A similar pattern holds for the take away picture in Panel (b). Whereas in Figure 2.6 the demand curve was displaced downward parallel to itself, here the vertical intercept decreases from A to A , where A = A(1 ). And, moving to the right, D D converges upon the old DD the two necessarily intersect at the horizontal axis where price is zero. Algebraically, equations (2.5) remain valid except that the tax identity must be written in the form (2.7a) or (2.7b), depending upon whether the tax is quoted as an add on percentage t or a take away percentage . EXERCISE 2.6 Using the same supply and demand curves as in the previous exercise, suppose that an add on tax t = 100% is imposed. (This is equivalent to a take away tax rate of = 50%.) What is the effect of this tax in comparison with the no-tax equilibrium P = 220, Q = 80? P (1 + t ) = 2 P . So the gross price will be twice the net price. The quantity solution is Q = 36. The gross price is P + = 264, and the net price is P = 132. The quantity exchanged declines sharply in comparison with the no-tax equilibrium, as would be expected given such a steep tax. The gross price paid by buyers rises only moderately; the net price received by sellers falls drastically. So the incidence here is more heavily upon the sellers. A N S W E R : Start with equations (2.5), but replace the third equation with P + = An Application: Interdicting Supply In 1920 the Prohibition amendment to the United States Constitution made it illegal to produce or import alcoholic liquor. Soon thereafter a vast bootlegging industry P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 44 2. WORKING TOOLS developed. Despite costly police efforts, the interception of supplies from foreign or illegal domestic sources eventually became so ineffective that Prohibition was repealed in 1933. Instead, with the continuing aim of discouraging liquor consumption, the government imposed high liquor taxes. On the whole, these taxes have been effective. Although bootlegging continues, police efforts hold it to tolerable levels. And the liquor taxes raise large revenues for Federal and state governments. Currently, the United States is attempting to use the interdiction technique for narcotic drugs, leading to smuggling and bootlegging problems resembling those of the 19201933 Prohibition era. Some commentators have suggested that, following the precedent of alcoholic beverages, buying and selling narcotics should be legalized, but subject to heavy taxation. This normative policy question, which involves philosophical and moral issues as well as narrowly economic ones, is not addressed here. But from a positive point of view, one can ask about the relative effectiveness of interdiction versus taxes for discouraging usage. From the take away point of view of the preceding section, taxes intercept part of the price paid by buyers before the money reaches sellers, whereas interdiction intercepts part of the quantity produced by sellers before it reaches buyers. So, one might at rst think, perhaps a 50% take away tax would be as effective in reducing consumption as a 50% interdiction of supply. But this analogy is imperfect. In fact, a 50% interdiction rate if it could be achieved would more effectively reduce consumption than would a 50% tax. In dealing with transaction taxes, recall that it is essential to distinguish the gross price P + paid by buyers from the net price P received by sellers. With interdiction there is only one price, but the gross quantity Q + (the total manufactured) must be distinguished from the net quantity Q (the amount actually delivered to buyers).3 Call i the interdiction (interception) rate. Then the relation between the two is: Q Q + (1 i ) (2.9) Panel (b) of Figure 2.7 pictured a take away tax = 50%. Figure 2.8 shows a take away interception rate i = 50%. Without any attempt at interception, the equilibrium price and quantity are P and Q , where the supply curve SS intersects the demand curve DD at point E. Now consider interception from the point of view of the producers. First, since half their output will be intercepted and thus never reach any buyer, suppliers will be willing to supply any specied quantity Q + only at double the price. So, as shown in the diagram, the adjusted supply curve S S for manufactured quantities Q+ will be twice as high as SS throughout. But the story does not end there. Recall that the amount Q delivered to buyers is only half the Q + produced. So, from the buyers point of view, the supply curve is S S (a horizontal displacement of S S half-way to the vertical axis). Thus, 3 This analysis does not attempt to deal with the complicated delivery chain from grower to smuggler to wholesaler to retailer. P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.1 EQUILIBRIUM: SUPPLY-DEMAND ANALYSIS 45 P D P Price($ /Q ) S G F S Figure 2.8. Interdiction of Supply Here the government intercepts the fraction i = 50% of the amounts supplied before they are delivered to buyers. As suppliers require a price 1/ i = 2 times as high to produce any given quantity, the new supply curve S S is twice as high as the original SS. This S S curve pictures the produced quantity Q + at each price. Since the delivered quantity Q = (1 i ) Q + is just half the produced quantity, the effective supply curve S S to buyers is found by shifting S S inward by 50% toward the vertical axis. In comparison with the original equilibrium price P , the new equilibrium price P is higher. The quantity produced, Q + , is smaller than the original equilibrium quantity, Q , and the amount actually delivered, Q , is much smaller. P S S E S D S Q Q+Q Q Quantity interception has a kind of double whammy effect upon sellers incentives. First, interception increases the price suppliers must receive (if they are to stay in business) for any unit manufactured, and second, it reduces the amount delivered below the amount manufactured. Geometrically, rst SS shifts to S S and then S S shifts to S S . The interdiction equation system can be written: (demand equation) P = A B Q P = (C + D Q + )/(1 i) (supply equation) (2.10) (interdiction identity) Q Q + (1 i ) The only possibly unexpected element here is on the right-hand side of the middle equation. The 1 i in the denominator corresponds to the upward displacement from SS to S S in the diagram. For example, if i = 50%, at each Q+ the price P received by suppliers would have to be twice as high. EXERCISE 2.7 Use the same underlying supply and demand curves as in the previous exercise, but now assume an interception take away percentage i = 50%. What are the effects upon (i) the price P, (ii) the quantity manufactured Q+ , and (iii) the quantity delivered Q ? A N S W E R : Using the equation system (2.10), the demand equation remains as in the previous exercise, but now write it as P = 300 Q . The supply equation is modied by the expression 1 i in the denominator on the right-hand side, becoming P = (60 + 2 Q+ )/(1 i ). Assuming i = 50%, and skipping the algebraic details, the solutions Q+ = 40, Q = 20, and P = 280. Whereas a 50% take-away tax reduces consumption from 80 to 36, an interdiction rate of 50% would bring it farther down to Q = 20. Why does interdiction have this double whammy effect upon consumption? A tax that reduces the protability of output induces sellers to cut back, and in doing so P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 46 2. WORKING TOOLS they reduce their production costs. But with interdiction, suppliers suffer the costs of producing units that will be intercepted and will not reach consumers. The fact that interception has such a powerful discouraging effect may appear to favor the current interdiction policy as opposed to the tax alternative. Several important considerations, however, may cut the other way. Among them are: 1. A take away tax of 50% was compared with a take away interdiction rate of 50%. But it is far easier to enforce a tax rate of 50% than to achieve an interdiction rate of 50%. In fact, current liquor taxes are far above 50% on a take-away basis (that is, more than half of what the consumer pays for a bottle goes to the government rather than to producers),4 whereas current narcotic interdiction rates are believed to be only in the neighborhood of 20%. An interception rate of 50% is probably not feasible. 2. In contrast with interdiction, taxes generate revenues that might be used for antidrug education or other useful purposes. Recall, last, that even a fully satisfactory positive analysis would only partially resolve the normative issue of which policy to adopt. Among other things, social values are involved. Although some people regard drug use as a merely regrettable activity, for which a tax constitutes a sufcient penalty, others think that drugs are a moral evil to be fought without compromise. Price Ceilings and Price Floors Governments sometimes attempt to repress ination by price ceilings or freezes. In contrast, during the great depression of the 1930s in the United States, through what was called the National Recovery Administration, the U.S. government attempted to impose minimum wage-price controls (oors). Whether price ceilings or price oors can cure a general ination or cure a general depression are macroeconomic questions not considered here. Instead, the analysis will examine the effects of price controls on the markets for particular goods. In Figure 2.9, Panel (a) depicts an effective ceiling price at the level P . (To be effective, the ceiling must be lower than the equilibrium price P .) At price P the quantity demanded Q d exceeds the quantity supplied Q s so there is upward pressure on price. (Note the upward-pointing arrow.) The arrow, however, is blocked by the xed ceiling. If we can assume there are no dealings in illegal black markets, what quantity will be exchanged? A fundamental maxim of exchange is: It takes two to tango. That is, trade requires willing buyers and willing sellers. At the ceiling price the buyers want to buy Q d but the sellers want to sell only the smaller quantity Q s so Q s is the amount that will be traded. (Notice that the amount traded is not a compromise between what consumers want to buy and what sellers want to sell; it is always the smaller of the two.) The nal outcome is at point C in the diagram. The distance CH represents the shortage, the excess of the demand quantity over the supply quantity at the legal ceiling price. 4 According to the organization Americans for Tax Reform, in 2002 on average 60% of what was paid for a bottle of distilled spirits went to the government in taxes. P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.1 EQUILIBRIUM: SUPPLY-DEMAND ANALYSIS 47 P P D D S Floor Supplycur ve Price($ /Q ) Surplus J E K Supplycur ve S Price($ /Q ) P P P P Ceiling S 0 C E H Shortage Demandcur ve Demandcur ve S D Q 0 Qd Q Q s Quantity Panel(b): Aneff ectivepr icefloor Q D Qs Q Qd Quantity Panel(a): Aneff ectivepr iceceiling Figure 2.9. Ceilings and Floors In comparison with the unregulated equilibrium price P and quantity Q , panel (a) pictures an effective price ceiling P < P . The quantity exchanged falls to Q s , the supply quantity at price P . Because consumers seek to buy a larger quantity Q d at this price, there is a perceived shortage CH . Panel (b) pictures an effective price oor P > P . Here the quantity exchanged falls to Q d , again smaller than Q . An effective price oor thus creates a perceived surplus JK. Exception: If the price oor is supported, the amount Q s will actually be produced and the surplus will be absorbed by government purchases. EXAMPLE 2.6 POSTWAR SHORTAGES AND TREKKING During World War II, Germany and Japan had covered their huge scal decits largely by printing money. The inationary pressures generated were repressed by keeping prices frozen at low ceiling levels, enforced by severe penalties. After the war ended, Allied occupation authorities in both Germany and Japan continued the previous system of controls. But, given the huge accumulations of money stocks in the hands of the public, after a few years the control system broke down. The price ceilings had become so unrealistic as to paralyze legitimate trade. The shelves in retail stores were bare. In both Germany and Japan a pattern called trekking was observed. City-dwellers would leave town for the day and scour the nearby countryside for food sometimes making private black-market deals with farmers, sometimes bartering household goods, sometimes simply stealing. On one single day, it is reported, over 900,000 persons trekked from Tokyo to the countryside.a In 1948, with the approval of the Occupation authorities, Germany introduced the Erhard economic reforms, which reduced money stocks by a currency conversion from old marks to new marks. Shortly afterward, the price ceilings were abolished. Almost immediately, goods reappeared in the stores. Trekking abruptly ended. There was one unexpected consequence. The German state railroads suddenly faced a nancial crisis, owing to an immediate 40% decrease in short-haul passenger trafc. P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 48 2. WORKING TOOLS The sharp drop reected the huge amount of trekking to the countryside that had previously been taking place.b a Jerome B. Cohen, Japans Economy in War and Reconstruction (University of Minnesota Press, 1949), p. 378. b Lucius D. Clay, Decision in Germany (Doubleday, 1950), p. 191. Panel (b) of Figure 2.9 pictures an effective price oor P . At P the quantity Q s offered by sellers exceeds the quantity Q d desired by buyers, so there is downward pressure on price. But, as the blocked downward-pointing arrow in the diagram indicates, the legal oor prevents price from falling to its equilibrium level P . Once again, because it takes two to tango, the quantity traded is the lesser of Q d and Q s in this case, Q d . Note that although effective price ceilings and price oors have opposite effects upon price, they have parallel effects upon the quantity traded: in either case, the quantity exchanged is less than the equilibrium Q . With price ceilings, black-market dealings take place at illegally high prices; with price oors, black-market transactions involve illegally low prices. This picture changes when price oors are supported. Support takes the form of a buyer of last resort. In the United States, the Federal government has been such a buyer for several farm products. In Panel (b) of Figure 2.9, private buyers are only willing to buy the amount Q d at the high oor price P . Now suppose the government will buy any amounts left unsold. In the diagram this is the surplus amount FG. So with a supported oor no black market appears. Instead a problem of surplus disposal arises the buyer of last resort accumulates larger and larger unwanted holdings. CONCLUSION Effective ceilings hold down prices; effective oors keep them up. In either case, the quantity exchanged is less than in unregulated equilibrium. If, however, the oor is supported by a buyer of last resort willing to accumulate inventories, the quantity supplied will be greater than under the unregulated equilibrium. EXAMPLE 2.7 AGRICULTURAL PRICE SUPPORTS Since the 1930s the U.S. government has attempted to maintain parity prices for agricultural products. Parity means the relationship between agricultural and nonagricultural prices that obtained during the years 1910 and 1914, a period of farm prosperity. Throughout the 1950s and 1960s, high parity price oors were maintained by government purchases. A federal agency, the Commodity Credit Corporation (CCC), would buy any otherwise unsold quantities of supported crops at the support level usually at 90% of the parity price. The surpluses purchased by the CCC were mostly stored; the federal government hoped to sell them in years of small harvests. But the amount produced almost every year was greater than the amount consumers would purchase at the articially high supported prices. By 1960 the CCC held in storage as much wheat as that years entire crop. To reduce the cost of holding such huge stores, Congress passed food stamp and school lunch programs subsidizing food prices for some consumers. A variety of P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.2 FINDING AN OPTIMUM 49 supply management programs were introduced to reduce quantities produced. In addition, the price support levels were reduced. The table shows that, accordingly, in the 1960s government purchases were much smaller than in the previous decade. Yearly acquisitions of three supported crops by the commodity credit corporation, selected years Grain 1953 54 55 56 57 58 1963 64 65 66 67 68 Sorghum 40.9 110.1 92.6 32.5 279.5 258.0 125.1 66.8 85.0 0.3 9.1 13.7 Corn 422.3 250.6 408.9 477.4 268.1 266.6 17.9 29.1 11.2 12.4 191.0 34.4 Wheat 486.1 391.6 276.7 148.4 193.5 511.0 85.1 86.9 17.4 12.4 90.0 182.9 Source: Commodity Credit Corporation charts, November 1972, pp. 49, 75, 115. Over the years, political support for the policy of buying surpluses has declined. Instead, a variety of other techniques for maintaining farm prices have been increasingly used, the details varying from commodity to commodity. Generally speaking, these restrict either the number of acres that can be planted or the amount of product that can be sold. Such methods of supply management have been supplemented by other programs aimed at maintaining farm incomes, among them direct payments to farmers for acres not planted or for crops not sold.a a These programs are described in Chapter 2 of M. C. Hallberg, Policy for American Agriculture: Choices and Consequences, Iowa State University Press, 1992. See also Chapter 12 of M. C. Hallberg, Economic Trends in U.S. Agriculture and Food Systems since World War II, Iowa State University Press, 2001. 2.2 FINDING AN OPTIMUM Optimizing, nding the action that leads to the best outcome, is the second of the two major problem-solving methods used in microeconomics. Economists typically solve optimization problems by means of marginal analysis, a technique that does the work of the mathematical calculus without requiring any formal knowledge of calculus techniques. To nd the prot-maximizing level of output, for example, a rm should rationally balance its Marginal Revenue (the increment to receipts when it increases output) against its Marginal Cost (the added charges incurred in producing an extra unit). Optimization problems arise for all types of economic agents. Consumers choose how best to spend their incomes, resource-owners try to maximize income by choosing among different ways of employing their assets, and governments seek a preferred P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 50 2. WORKING TOOLS Table 2.2 Total, average, and marginal revenues Quantity (Q) 0 1 2 3 4 5 6 7 8 9 10 Price or average revenue (P = AR ) 10 9 8 7 6 5 4 3 2 1 0 Total revenue (R = PQ) 0 9 9 7 16 5 21 3 24 1 25 1 24 3 21 5 16 7 9 9 0 Marginal revenue (MR) balance between taxation and expenditure. This chapter mainly reviews the analytical tools for optimization decisions. The Logic of Total, Average, and Marginal Concepts Consider a rms revenue from sales. In Table 2.2 the rst column shows possible output quantities ranging from Q = 0 to Q = 10. (We will usually be treating variables as continuous, so that intermediate quantities like Q = 2.7 are also permitted.) The second column lists hypothetical prices at which these quantities can be sold. These two columns are the tabular equivalent of a standard demand curve. The third column is Total Revenue (or Revenue, for short), dened as price P times quantity Q: RPQ (2.11) The data corresponding to the third column are plotted in the upper diagram of Figure 2.10. Note that as quantity Q increases, Revenue R rst increases but eventually begins to decline as buyers become saturated with the rms product. Revenue is a total magnitude, whereas price P is an average magnitude. Specically, price P is denitionally identical to Average Revenue (AR), as follows obviously from the equation preceding: AR R / Q P (2.12) When Revenue is measured in dollars ($), Average Revenue or price is measured in dollars per unit quantity ($/Q). In Table 2.2, at quantity Q = 2 the Total Revenue is 16. P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.2 FINDING AN OPTIMUM 51 $ 25 24 21 TotalRe venue( R ) L 16 16 R 9 N M TotalRe venuecur ve 24 21 9 0 1 2 3 4 5 6 7 8 9 10 Q Quantity $/Q RevenueperUnit( ARor MR ) 10 AverageRe venue(demand)cur ve 6 2 Marginal Revenue curve MR 0 1 2 3 4 5 6 Quantity 7 8 9 AR Q 10 Figure 2.10. Geometrical Derivation of Average and Marginal Magnitudes The upper diagram pictures a Total Revenue R function, and the lower diagram the associated Average Revenue AR and Marginal Revenue MR functions. For the specic quantity Q = 4, Total Revenue is R = 24. The height of the AR curve in the lower diagram corresponds to the slope of the bold line ON in the upper diagram, so that AR = R / Q = 24 = 6 at Q = 4. The height of the MR curve at 4 Q = 4 corresponds to the slope along the Total Revenue curve. It is approximated by averaging the slopes of LN and NM . The slope of LN is (24 21)/1 = 3 and that of NM is (25 24)/1 = 1, the average being 2. Therefore, in the lower diagram, 2 is the height of the MR curve. Average Revenue at Q = 2 is 16/2 = 8, which corresponds to the price along the demand curve for that quantity. Marginal Revenue MR is shown in the fourth column of Table 2.2. Its denition is: MR R/ Q (2.13) P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 52 2. WORKING TOOLS where R and Q signify small changes in Revenue and in quantity.5 Like price, MR is measured in dollars per unit quantity ($/Q). WARNING A total magnitude (such as Revenue in the upper panel) should never be plotted on the same diagram as average and marginal magnitudes (such as Average Revenue and Marginal Revenue in the lower panel). The units of measurement are not the same. The vertical axis of the upper diagram of Figure 2.10 is scaled in dollars ($), whereas the lower diagram is scaled in dollars per unit quantity ($/Q). In Table 2.2, if the supplier sells two units instead of one, Revenue rises from 9 to 16. Over this quantity interval of size Q = 1, Marginal Revenue is MR R / Q = (16 9)/1 = 7. If output were increased further to Q = 3, over the next unit quantity interval MR would be 5, and so on. In numerically calculating Marginal Revenue, there is one tricky point. For an increase in output from say Q = 1 to Q = 2, the MR of 7 applies between Q = 1 and Q = 2 (rather than at Q = 1 or at Q = 2). (The jagged staircase in Table 2.2 suggests this.) At least as an approximation, then, MR = 7 applies best halfway between, at Q = 1.5. To nd the MR specically at Q = 2, the best estimate is to take the average of the MR of 7 over the lower interval (from Q = 1 to Q = 2) and the MR of 5 over the upper interval (from Q = 2 and Q = 3). Thus, as a good approximation, at Q = 2 the MR is about 6 (the average of 7 and 5). By similar reasoning, at Q = 3 the MR is about 4 (the average of 5 and 3). It is sometimes said that Marginal Revenue is the increment to revenue due to the last unit produced or the next unit that might be produced. The rst statement looks at the downward interval (so that, in terms of the numbers in the preceding paragraph, at Q = 2 the MR would be 7). The second statement looks at the upward interval (so that at Q = 2 the MR would be 5). Our recommended procedure is to average these two gures, yielding the result MR = 6 at Q = 2. When the increments R and Q are quite small relative to R and Q, the more precise approximation may make little difference, yet sometimes the disparity can be large. Since it is only trivially more difcult to do so, it is good practice always to use the better approximation. And in fact, for a straight-line demand curve like the one tabulated in Table 2.2, the recommended method always coincides with the calculus answer and so will be exactly correct.6 When the demand curve is not a straight line the recommended procedure will not be quite perfect, but it will almost always be more accurate than the alternatives. 5 Mathematical Footnote : For innitesimally small changes, Marginal Revenue becomes the calculus derivative: MR d R /d Q lim R/ Q Q 0 6 Mathematical Footnote: The demand-curve equation underlying Table 2.2 is P = 10 Q . Then Total Revenue is R = P Q = 10 Q Q 2 . Taking the derivative, Marginal Revenue is MR = R /d Q = 10 2 Q . At Q = 2, therefore, MR = 6. This exact answer is the same as shown by our recommended method of approximation. P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.2 FINDING AN OPTIMUM 53 EXERCISE 2.8 For the nonlinear demand curve P = 100 Q2 , compare the recommended method with the less precise methods for approximating MR at Q = 4. A N S W E R : Since Revenue = Price Quantity, the Total Revenue equation becomes R = (100 Q 2 ) Q = 100 Q Q 3 . Total Revenue R is 273 at Q = 3 and 336 at Q = 4. So between Q = 3 and Q = 4, the recommended method associates the revenue increment 336 273 = 63 with output Q = 3.5. Symbolically, the estimated Marginal Revenue at Q = 3.5 is R / Q = 63/1 = 63. Similarly, between Q = 4 and Q = 5, MR is (375 336)/1 = 39, which approximates the MR at Q = 4.5. The estimated MR at Q = 4 is found by averaging: (39 + 63)/2 = 51. (The exact calculus result at Q = 4 is MR = 52, close to the recommended approximation MR = 51.) In contrast, the less precise method of identifying Marginal Revenue at Q = 4 as the revenue increment from the last or fourth unit produced would lead to the poor estimate MR = 63 at Q = 4. Or saying that the MR at Q = 4 is the revenue increment from the next or fth unit would imply an even worse estimate: MR = 31. The recommended method is a much better approximation than either of the other two. What if the units of output are discrete rather than continuous, so that it is meaningless to calculate Marginal Revenue for fractions of units? In that case one cannot avoid having two different estimates for MR: one over the upward interval and the other over the downward interval. Which estimate should be used depends upon whether the decision to be made involves an upward or a downward choice. EXERCISE 2.9 Suppose that only exact integer amounts of output are possible. Imagine that the cost of producing remains constant at 6 per unit (so 6 is both the Marginal Cost and Average Cost at all levels of output). Using the data of Table 2.2, verify that Q = 2 is the best output to produce. A N S W E R : Starting from output Q = 2, the table indicates that over the upward interval (from Q = 2 to Q = 3) the Marginal Revenue is MR = 5. Since the cost of producing one more unit is 6, it is evidently unprotable to increase output. Over the downward interval Marginal Revenue is MR = 7. Then reducing output to Q = 1 would also be unprotable: it would reduce Revenue by 7 while reducing costs by only 6. So Q = 2 is the best amount to produce. The preceding exercise suggests the following general rule: RULE: When only discrete choices are possible, output is at an optimum when Marginal Revenue is less than Marginal Cost over the smallest allowable upward interval and Marginal Revenue is greater than Marginal Cost over the smallest allowable downward interval. EXAMPLE 2.8 PROFESSORS AND PUBLICATIONS Professors research results are usually reported in scholarly articles. Professors with many publications gain professional recognition and tend to receive higher salaries. P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 54 2. WORKING TOOLS Howard P. Tuckman and Jack Leaheya estimated the effect of article publication upon professors salaries in the 1970s. The table here compares the average and marginal salaries associated with varying numbers of published articles, in comparison with baseline salaries for professors with no publications. (Multiple authorship was disregarded, so that each coauthor received full credit for any published article.) The general relations between the tabulated average and marginal salary gures resemble those shown in the lower panel of Figure 2.10, taking number of publications as the quantity variable. In the data shown here, averaging over all professors the rst article was associated with a marginal salary gain of $543, whereas the marginal salary gain from the 35th article was only $49. (This declining pattern reects the Law of Diminishing Returns, to be discussed in Chapter 6.) Published articles and salary gains Number of articles 1 5 10 15 20 25 30 35 Average salary gain $543 295 227 194 174 160 149 150 Marginal salary gain $543 191 153 120 109 100 93 49 Source: Adapted from Tuckman and Leahey, Table 2. COMMENT The number of publications is necessarily discrete. The authors marginal estimates represent the upward interval interpretation of the marginal concept for discrete variables. The rst gure, $543, is the salary increment looking upward from zero to 1. This would be the relevant gure for a professor deciding whether or not to make the effort of producing a rst article. a Howard P. Tuckman and Jack Leahey, What Is an Article Worth? Journal of Political Economy, v. 83 (October 1975). How Total, Average, and Marginal Magnitudes Are Related When the variables are continuous rather than discrete, the relations among total, average, and marginal magnitudes are most easily interpreted in terms of geometry. The two main principles are: 1. The marginal magnitude is the slope of the total function. 2. The average magnitude is the slope of a ray from the origin to the total function. The rst principle is demonstrated in Figure 2.10. Corresponding to the data of Table 2.2, the parabola in the upper diagram shows Total Revenue R for each level of output Q. As Q rises from 4 to 5, R rises from 24 to 25, so the revenue increment is R = 25 24 = 1 between Q = 4 and Q = 5. Slope is dened as rise over run. Here the rise is 25 24 = 1 and the run is 5 4 = 1, so the slope is P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.2 FINDING AN OPTIMUM 55 R / Q = 1/1 = 1 in this range. Corresponding to the recommended approximation method described above, this slope of 1 is best associated with the in-between quantity Q = 4.5. (It would be wrong to say that the slope is 1 at point M, where Q = 5. Since M is the maximum of the parabola, the slope of the curve has to be zero there.) To approximate the slope specically at Q = 4, the recommended method averages the slopes at Q = 3.5 and at 4.5. From the Marginal Revenue column of Table 2.2, these two slopes are 3 and 1, respectively, so the recommended estimate of the MR at Q = 4 is 2. The second rule states that Average Revenue at any given output is, geometrically, the slope of a line that connects the origin to the point on the Revenue curve corresponding to the output level chosen. Look again at the upper diagram in Figure 2.10. At Q = 4, Total Revenue is R = 24. From the denition of Average Revenue, divide R by Q to obtain AR = 24/4 = 6. Now compare the ray ON . The slope of segment ON is the vertical distance or rise (24) divided by horizontal distance or run (4), yielding 6 once again. So the geometrical result is the same, as follows numerically from the denition Average Revenue R/Q. The lower panel of Figure 2.10 depicts the Average Revenue and Marginal Revenue curves that correspond to the Revenue function shown in the upper panel. Both AR and MR in this panel are falling throughout. MR is declining throughout because, in the upper panel, the R curve that relates revenue to quantity is always becoming (algebraically) less steep moving to the right. Thus the slope of the Total Revenue curve is initially positive, becomes zero at Q = 5 (where R reaches its maximum), and is negative for larger levels of Q. Similarly, Average Revenue AR also falls throughout, because the slope of the ray from the origin to a point along the Revenue curve declines steadily in moving to the right. (For example, OM is less steep than ON .) Note that at Q = 10 the line from the origin to the Revenue curve is at. Its slope is zero. This means that AR is zero at the output where the demand curve intersects the horizontal axis, which obviously must be true since Total Revenue is also zero there. However, as long as Total Revenue rises with increasing quantity, Marginal Revenue remains positive. But past the peak of the Total Revenue curve, the slope along the R curve becomes negative and so MR turns negative. Extending these ideas to general relations between total and marginal functions leads to the Propositions: PROPOSITION 2.1a: When a total magnitude is rising, the corresponding marginal magnitude is positive. PROPOSITION 2.1b: When a total magnitude is falling, the corresponding marginal magnitude is negative. Last, when Revenue reaches a maximum (or a minimum) the Revenue function is neither increasing nor decreasing; it is level. Drawing the obvious inference: PROPOSITION 2.1c: When a total magnitude reaches a maximum or a minimum, the corresponding marginal magnitude is zero.7 , 8 7 8 Mathematical Footnote: When dR/dQ < 0, the Total Revenue function R is increasing; when dR/dQ < 0, it is decreasing; when dR/dQ = 0, the function is stationary. Mathematical Footnote : As a technical qualication, Proposition 2.1c is valid only when the associated minimum or maximum is at. In the upper diagram of Figure 2.10, R has a at maximum at Q = 5: the Revenue curve is horizontal, and Marginal Revenue is MR = 0. But the Revenue curve also has minima at Q = 0 and Q = 10, P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 56 2. WORKING TOOLS When a total magnitude is at a maximum, it does not follow that either the corresponding average magnitude or the corresponding marginal magnitude is at a maximum. Indeed, as was just seen, when a total magnitude is at a maximum the associated marginal magnitude equals zero. And although the associated average magnitude will normally be positive, it will not be at its maximum. Since optimization consists of nding a maximum of some desired variable such as prot or utility, or a minimum of an undesired variable such as cost, Proposition 2.1c suggests how economists solve optimization problems. Suppose you were packing for a voyage for which you would be charged a unit fee proportional to weight carried (a continuous variable). The optimum number of pounds to pack would balance the marginal benet of another pound (or fraction thereof) against the additional fee you must pay. Similarly, a rms prots are maximized at the level of output where an additional unit neither increases nor decreases prot. The lower diagram in Figure 2.10 illustrates still another principle: PROPOSITION 2.2a: When the average magnitude is falling, the marginal magni- tude must lie below it. Think of the average weight of people in a room. If someone walks in and the average weight falls, the marginal weight (the weight of the person who just walked in) must have been less than the average weight.9 In Figure 2.10 each new unit lowers Average Revenue (AR is always falling); hence the Marginal Revenue curve MR lies always below it. Using similar reasoning: PROPOSITION 2.2b: When the average magnitude is rising, the marginal magnitude lies above it. PROPOSITION 2.2c: When an average magnitude is neither rising nor falling (at a minimum or maximum), the marginal magnitude equals the average magnitude.10 In Figure 2.11, the upper diagram shows a rms Total Cost curve C.11 To derive Marginal Cost MC from the Total Cost function shown, remember that MC is the slope of C. The slope along the cost curve in the upper diagram falls, moving to the right, up to point K. After that the cost curve becomes steeper. Correspondingly, in the lower diagram MC falls, reaches a minimum at point K , and then starts rising. The Average Cost AC at any output is given by the slope of a ray from the origin to the point on the Total Cost curve corresponding to that output: the vertical distance yet the curve is not at at those points; that is, MR = 0. In this book we will deal almost always with at minima or maxima, for which Proposition 2.1c holds. A careful reader will note that number of people is a discrete rather than a continuous variable. Nevertheless, the proposition certainly continues to hold true. A question at the end of the chapter asks how to reinterpret Propositions 2.1a,b and Propositions 2.1a,b,c when the underlying variable is discrete. Mathematical Footnote : Let us verify Proposition 2.2a of the text, and specically that MR is below AR when AR is falling. For AR to be falling it must be the case that: 0> d (AR) d ( R/ Q) Q (dR/dQ) R = = dQ dQ Q2 9 10 11 The inequality dictates that the last numerator must be negative. It follows that dR/dQ < R / Q , or MR < AR: Marginal Revenue is always less than Average Revenue. Similar proofs apply for Propositions 2.2b and 2.2c. In Figure 2.11 Total Cost is shown as positive even at an output of zero. The explanation is that xed costs (such as the rent on a factory building) must be paid even if nothing is produced. P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.2 FINDING AN OPTIMUM 57 $ Pointofsmallest slopealong C curve TotalCost( C ) L K C Lineofsmallest slopefromor igin tothe C curve Figure 2.11. Derivation of Average and Marginal Magnitudes from Total Function: Cost The lower diagram derives Average Cost AC and Marginal Cost MC from the Total Cost function C in the upper diagram. At the quantity where the slope along the Total Cost function is least, MC is at a minimum. Where the slope of the line drawn from the origin to the curve is least (point L in the upper diagram), AC is at a minimum. When AC is falling, MC lies below it; when AC is rising, MC lies above it. 0 Quantity Q $/Q MC CostperUnit( AC or MC ) AC L Pointof lowest AC K Pointof lowest MC 0 Quantity Q (cost C) at that point divided by the horizontal distance (output Q). Moving to the right along the Total Cost curve, the slope of the ray out of the origin falls until point L after which the slope begins to rise. So, in the lower diagram, AC falls until point L and rises after that. This means that AC is at its lowest value when output is L . (Note that if xed costs are positive, Average Cost AC C / Q is innite at the vertical axis where Q = 0.) In the upper diagram, anywhere to the left of L a ray from the origin to the cost curve is steeper than the slope of the cost curve itself. Since the slope of the ray is greater than the slope of the cost curve, AC is greater than MC for any output level in this range. This again conrms Proposition 2.2a: when AC is falling, MC lies below it. To the right of L, a ray from the origin to a point on the cost curve is atter than the cost curve itself at that point, so AC is less than MC. This conrms Proposition 2.2b: at those values of Q for which Average Cost is rising, Average Cost is less than Marginal Cost. P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 58 2. WORKING TOOLS Lastly, the ray from the origin to point L along the cost curve has the same slope as the cost curve itself at point L. This means that here Marginal Cost = Average Cost, conrming Proposition 2.2c. The following Example describes a policy error seemingly due to ignorance of marginal concepts. EXAMPLE 2.9 THE OIL ENTITLEMENT PROGRAM In 1973 and 1974 the Organization of Petroleum Exporting Countries (OPEC) drastically reduced petroleum production, causing the world price of crude oil to soar from about $2 to almost $12 per barrel (see the OPEC Example in Chapter 8). The U.S. government, concerned about its balance of payments, tried to reduce oil imports. However, American policy-makers also wanted to eliminate inequitable gains to those domestic producers of crude oil who were proting from the higher world prices. Unfortunately, the method chosen to achieve the second objective tended to defeat the rst.a To prevent domestic producers from reaping windfall gains, the price of domestic crude oil was frozen. (It was impossible, of course, to freeze the price of imported oil.) But some reneries, owing for example to vertical integration or to pre-existing contracts, had access to domestic crude while others did not. In the interests of equity the Entitlement Program was undertaken. The basic idea was that every rener was entitled to buy, at the low ceiling price, the nationwide average fraction of the (articially) cheap domestic oil. Reners having access to domestic crude had to compensate reners making more than average use of expensive imported crude. The unanticipated effect was to encourage imports of the high-priced foreign oil. From the point of view of the nation as a whole, the Marginal Cost of crude oil was the high-cost imported crude at $12 per barrel. Had all reners been required to pay this world price for imported crude oil, they would have wanted to import less oil. But under the Entitlement Program, each barrel imported entitled the importer to a great bargain: the right to obtain an equivalent amount of domestic crude at an articially cheap frozen price! So in effect, reneries were subsidized to make heavy use of high-cost imported crude.b a This is necessarily a very simplied discussion of the enormously complicated details of U.S. oil policy. In particular, the legal distinction between so-called new domestic oil and old domestic oil has been omitted here. b Many discussions of the oil entitlement program are available. See, for example, C. E. Phelps and R. T. Smith, Petroleum Regulation: The False Dilemma of Decontrol (Santa Monica, CA: RAND Corporation, 1977). Straight thinking about average and marginal concepts is also helpful in considering the tax implications of earning higher income. EXAMPLE 2.10 TAXES The table here shows the personal income tax schedule for single taxpayers, calculated from the Internal Revenue Services Form 1040 Instructions for the tax year 2003. For any Taxable Incomea in the rst column, the next columns show the tax at the lower end of the bracket and the marginal tax rate for additional dollars of income within the bracket. At an income of $28,400, for example, the tax is $3,910. This is the P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 2.2 FINDING AN OPTIMUM 59 sum of a tax rate of 10% paid on the rst $7000 of income and a rate of 15% paid on the remaining $21,400. The marginal tax on the next dollar earned would be 25%. The following fallacy is sometimes encountered. Suppose an employees taxable income is indeed $28,400 at the top of the 15% Marginal Tax bracket, so that her tax is $3,910. Her employer offers a raise of $100, but the worker refuses the raise because it would put her in a higher tax bracket! The worker may think that in moving up to a higher marginal tax rate (25% instead of 15%) she would be taxed the extra 10% on all her income, ending up worse off than before. This is false. The workers additional tax would be only 25% of $100, or $25. Accepting the raise would increase her after-tax income by $100 $25 = $75. The loss due to refusing the raise is one of the costs that arise from inability to use correct marginal reasoning. Personal income tax schedule for single taxpayers Taxable income $0 to $7000 $7000 to $28,400 $28,400 to $68,800 $68,800 to $143,500 $143,500 to $311,950 > $311,950 Tax at lower end of bracket $0 $700 (= $7000 10%) $3910 (= $700 + 0.15 $21,400) $14,010 (= $3910 + 0.25 $40,400) $34,926 (= $14,010 + 0.28 $74,700) $90,514 (= $34,926 + 0.33 $168,450) Marginal tax rate 10% 15% 25% 28% 33% 35% a Taxable income is earned income minus the exemptions, deductions, etc., provided in the tax law. An Application: Foraging When Is It Time to Pack Up and Leave?12 In the early history of humankind, foraging was a major economic activity. Human bands and tribes collected resources from the environment by hunting or shing or gathering fruits and vegetables. Some modern activities are logically analogous to foraging. Travelling salesmen, for example, might be said to be foraging for customers. A crucial choice for all foragers is how to distribute the available time over different sources of food and other usable resources. Imagine a human band roaming a desert, empty except for occasional resource patches in the form of oases. At any given oasis, living needs will gradually exhaust the available resources. So the band must eventually move on. The economic problem is just when to do so. Suppose all oases are equivalent and equally distant from one another. Figure 2.12 shows the total food yield y collectable from a given oasis, as a function of the stay time s that the band spends at that location. However, when the band moves on, a certain amount of dead time d occurs in travelling from one oasis to another. The Total Yield curve y(s) in Figure 2.12 is analogous to the Total Revenue curve of Figure 2.10. The main difference is that the curve emerges not from the origin but from a point (d,0) along the horizontal axis. This is in order to allow for the foragers dead time. 12 The analysis here is an adaptation of a result in Eric Charnov, Optimal Foraging, the Marginal Value Theorem, Theoretical Population Biology, 9 (1976), pp. 12936. P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 60 y 2. WORKING TOOLS y/t Yieldperpatch y (s ) Y Figure 2.12. Foraging Optimal Stay Time The optimal stay time s , at any single resource patch with yield y(s), occurs when the Marginal Yield in that patch equals the Average Yield (y/t) taken over the entire period dividing the yield per patch y by the overall time per patch t, where t = d + s . That is, the average time per patch includes not only the stay time s but the dead time d spent traveling from one patch to the next. 0 d t s t Timeperpatch If the group has a xed amount of time per season that can be devoted to foraging, it will want to maximize y/t, the Average Yield over all resource patches, where t is the sum of the dead time and stay time per patch. As with all average magnitudes, the Average Yield is shown geometrically as the slope of a line drawn from the origin to the curve. The maximum Average Yield is the slope of a line from the origin that is just tangent to the curve (at point Y ). As is consistent with Proposition 2.2c, when the average magnitude is maximized here the marginal magnitude equals the average magnitude. That is, at Y the Marginal Yield, the slope along the Total Yield curve, is equal to the Average Yield represented by the slope of the line OY from the origin to the curve. So the optimum stay time is characterized by the property that the Marginal Yield from remaining one more day in a particular resource patch equals the Average Yield over all patches, allowing for both stay time and dead time. The interpretation is that, having maximized average daily food intake over the entire season, it does not pay to stay at any particular oasis once its marginal yield has fallen below the average yield that the band is able to achieve overall. EXAMPLE 2.11 FORAGING CHOICES The Ache people of Paraguay obtain their food mainly by foraging. When encoun tered on a foraging expedition, food items typically require additional effort before actual capture. Animals must be pursued, fruits and berries have to be picked, tubers must be dug up, and so forth. So for each encounter a decision must be made: whether to devote the extra time and effort needed to actually acquire the item, or else pass it up in the hope of nding something more protable later on. For Ache foragers, calories can be taken as the value or yield associated with different food sources, to be measured against the cost in terms of time required for acquisition and preparation. If the Ache are choosing rationally, they should invest the time needed to acquire any food item whose marginal payoff (ratio of calories/hour) exceeds a certain cutoff level, passing up those with lower ratios. The cutoff level should be the average payoff achieved over all food types actually harvested or collected. P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 SUMMARY 61 Observing the Ache, the anthropologists Hillary Kaplan and Kim Hilla were able to classify 28 frequently taken food items in terms of the calories/hour ratio. As the table indicates, Ache foragers almost always invested the effort to take very high-ranking food items (high marginal yield per unit time) a group including honey, deer, and armadillo. The average rank of these foods was 11.6 (rank 1 being best). Relatively lower-ranking items such as palm nuts might or might not be acquired, depended upon circumstances. And nally, many possible food sources with very low calorie/hour ratios (not shown in the table) were never taken at all. Ache food choices Average rank (calories/hour) 11.6 15.2 No. of items Items almost always taken Items sometimes taken 14 14 Source: Interpreted visually from p. 175 of Kaplan and Hill. a Hillary Kaplan and Kim Hill, The Evolutionary Ecology of Food Acquisition, in Eric Alden Smith and Bruce Winterhalder, eds., Evolutionary Ecology and Human Behavior (1992). SUMMARY On the intermediate level there are two main techniques of economic analysis: nding an equilibrium, and nding an optimum. Equilibrium price and quantity are geometrically determined by the intersection of a supply curve and a demand curve. Changes in demand or supply are shown by shifts in these curves. An increase in demand (more of the product is desired at each price) raises both the equilibrium price and quantity. An increase in supply (more of the product is offered at each price) raises price but lowers the quantity sold. A tax on transactions reduces the quantity bought and sold. The tax raises the gross price (the price a buyer pays) but reduces the net price (the price a seller receives). The volume of transactions always decreases. If a price ceiling or a price oor is effective, the quantity bought and sold is the smaller of the quantities demanded and supplied at that price. The market is not in equilibrium. An effective price ceiling necessarily leads to upward pressure on price, and an effective price oor to downward pressure on price. The typical consequence will be black markets or other attempts to evade the price controls. The solutions to optimization problems depend upon the relations among total, average, and marginal magnitudes. Comparing marginal and total magnitudes: 1. When the total magnitude is rising, the marginal magnitude is positive. 2. When the total magnitude is level, the marginal magnitude is zero. 3. When the total magnitude is falling, the marginal magnitude is negative. Comparing marginal and average magnitudes: 1. When the average magnitude is falling, the marginal magnitude is below the average magnitude. 2. When the average magnitude is level, the marginal magnitude equals the average magnitude. P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 62 2. WORKING TOOLS 3. When the average magnitude is rising, the marginal magnitude is above the average magnitude. QUESTIONS The answers to daggered questions appear at the end of the book. 1. Which of the following are optimization problems? Which are equilibrium problems? [Note: You need not give the actual answers to the questions, but you might think about them.] a. Is it more protable for a business to offer occasional special sales at reduced prices, or to stick with moderate prices year-round? b. Would a gold discovery in Hawaii raise apartment rents on the island? c. If the punishment for murder were made more severe, would there be fewer murders? d. As a military commander, should I attack now when the enemy doesnt expect it or wait for my reinforcements, even though the enemy will then be alerted? e. Over the year, why is the price of strawberries more variable than the price of potatoes? f. If my wife and I have had three girl babies in a row, should we give up or try again for a boy? For Review 2. Is supply-demand analysis the key tool for equilibrium or for optimization problems? For what class of problem is the relation among total, average, and marginal quantities the key tool? 3. In what sense is price a ratio of quantities? 4. Explain why market equilibrium is determined by the intersection of the supply curve and the demand curve. 5. How does an increase in demand shift the demand curve? How does an increase in supply shift the supply curve? Does an increase in demand affect the equilibrium price and quantity in the same direction? What about an increase in supply? 6. In the analysis of a $T per unit tax, we shifted the demand curve downward by $T to nd the new equilibrium. Would the same result have been achieved if instead the supply curve were shifted upward by $T ? Explain. 7. Draw supply and demand diagrams, with upward sloping supply curves and downward sloping demand curves, to illustrate the following possibilities: a. A large demand increase may have little effect on equilibrium price. b. A demand increase may raise price substantially, while an equal supply decrease would hardly affect price. c. A small demand decrease may produce a large drop in equilibrium quantity. d. Supply changes may have no effect on the monetary values of total sales. 8. In each of the following cases, state whether an excise tax will raise the (gross) price paid by consumers, or reduce the (net) price received by sellers, or both. a. Supply curve slopes upward and demand curve slopes downward. b. Supply curve horizontal, demand curve slopes downward. c. Supply curve vertical, demand curve slopes downward. d. Supply curve vertical, demand curve horizontal. 9. Suppose the government pays a $5 per unit subsidy on sales of ags. What would be the effect on the quantity exchanged? On the gross and the net price? P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 QUESTIONS 63 10. a. b. c. What is an effective price ceiling or price oor? Why do effective oors and ceilings both decrease the quantity traded? What happens, however, if a price oor is supported by government purchases of any amounts unsold in the market? 11. Starting from the Total Revenue function, show how the Average Revenue function is derived. Show how the Marginal Revenue function is derived. 12. Starting from the Total Cost function, show how the Average Cost function and the Marginal Cost function are derived. 13. The Lackawanna Social Club, which has 20 resident members, keeps a refrigerator stocked with soda. Soda cans are obtained from a local distributor for 30 cents per can. Each member has free access to the refrigerator and can consume as many cans as he likes. At the end of each month, the total cost of the soda is divided equally among the members. What is the marginal cost per can to the club? To a member? 14. In terms of the general relations among total, average, and marginal quantities, which of the following statements are necessarily true, and which are not? a. When the total function is rising, the marginal function is rising. b. When the total function is rising, the marginal function is positive. c. When the total function is rising, the marginal function lies above it. d. When the marginal function is rising, the average function is also rising. e. When the average function is falling, the marginal function lies below it. f. When the marginal function is neither rising nor falling, the average function is constant. 15. In the application on interdicting supply, suppose a tax rate of 50% and an interdiction rate of 20% are about equally easy to enforce. Which would have a bigger effect upon consumption? For Further Thought and Discussion 1. In the year 302, the Roman emperor Diocletian commanded that there should be cheapness. His edict declared: Unprincipled greed appears wherever our armies, following the command of the public weal, march, not only in villages and cities but also upon all highways, with the result that prices of foodstuffs mount not only fourfold and eightfold, but transcend all measure. Our law shall x a measure and a limit to this greed. a. b. Why do you think Diocletian found food prices higher wherever he marched with his armies? What result would you anticipate from the command that there should be cheapness? 2. Suppose that the supply curve for gold is very steep (positively sloped, but almost vertical). a. Would a $T tax tend to have a relatively large or a relatively small effect upon the quantity exchanged in the market? Would there tend to be a relatively large or a relatively small effect upon the gross price paid by buyers? Upon the net price received by sellers? b. Explain in terms of the underlying economic meaning. 3. Analyze correspondingly the case where the demand curve is very steep (negatively sloped, but almost vertical). P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 64 2. WORKING TOOLS 4. a. b. If the price of gasoline rises as a result of a reduction in petroleum supplies, what effect would you anticipate on the price of automobiles? Upon the relative price of small, light cars versus large, heavy cars? What assumptions underlie the method of comparative statics? Will these assumptions ever be met in the real world? 5. a. b. 6. During World War II, the British government imposed a ceiling price on bread. Explain why there was upward pressure upon the price of bread. What consequences would you anticipate, given continuing enforcement of the ceiling? To alleviate the upward pressure on the bread price, the British government took fresh bread off the market; all bread sold had to be at least one day old. Would you expect this regulation to achieve the desired effect? 7. Owing to congestion, Gregory Peck International Airport wishes to limit the number of daily airplane departures to one hundred. (The airlines are eager and willing to provide two hundred ights a day.) It is proposed to auction off the rights to use the terminal, thus in effect imposing departure fees on the airlines. What are the likely consequences? 8. The table below gives a partial tabulation of a demand function. Estimate Marginal Revenue at Q = 3. Quantity 0 3 6 Price 30 20 12 9. The following is part of a price schedule, showing the quantity discounts offered by a printing shop. Does something peculiar happen as the size of your order approaches the upper limit in a given price range? Explain in terms of Marginal Revenue to the printing shop. Can you think of a more sensible way for the printing shop to offer quantity discounts? Size of your order 110 units 1120 units 2150 units Over 50 units Your price ($) .50 each .40 each .35 each .30 each 10. In Example 2.8 (PROFESSORS AND PUBLICATIONS), why are the average and marginal gures inconsistent in the last two rows of the table? 11. In a recent book, the philosopher John Searle stated: During the Vietnam War . . . a high ofcial of the Defense Department . . . went to the blackboard and drew the curves of traditional microeconomic analysis; and then said, Where the two curves intersect, the marginal utility of resisting is equal to the marginal disutility of being bombed. At that point they have to give up . . . I knew then that we were in serious trouble, not only in our theory of rationality, but in its application in practice. Searle here questions the applicability of rational analysis to warfare. Leaving aside that larger issue, show that the high ofcial is applying marginal reasoning incorrectly. (Or perhaps the philosopher misunderstood what he said.) [Hint : Does the intersection P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 QUESTIONS 65 of the two curves indicate the point where the enemy must give up, or does it indicate something else?] 12. What happens to equilibrium price and quantity if both supply and demand increase? 13. In the application to introducing a new supply source (as in Figure 2.5), what would happen if the initial equilibrium price P0 were below the import choke price F ? 14. Show how the incidence of a per-unit tax on transactions depends upon the slopes of the supply curve and demand curve. 15. a. b. In the early 20th century, there were many local opera and theatre companies and other local providers of musical entertainment. With the rise of mass media and duplicative technologies (such as television, radio, and recordings), many of these local services disappeared. What do you think happened to the demand for the services of performers with extraordinarily high charm or talent (the Luciano Pavorrotis, Britney Spearses, and Tom Cruises of their day)? What do you think happened to the equilibrium price of the services of the most exceptional individuals? How do you think the price of the services of performers of somewhat less talent changed? Near the turn of the millennium, duplicative and transmission technology (the Internet, CDs) led to a further development: easy acquisition and duplication of music without paying the supplier. Assume that such piracy is cheap but not costless to consumers. Based on supply/demand analysis, what effect do you think this development had on the demand for the services of the very highest talent performers? Of performers with somewhat less talent? P1: JZP/... P2: JZP/... 0521818648c02.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:21 66 P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 II PREFERENCE, CONSUMPTION, AND DEMAND 67 P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 68 P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 3 Utility and Preference 3.1 3.2 The Laws of Preference 70 Utility and Preference 72 Cardinal versus Ordinal Utility 73 Utility of Commodity Baskets 77 3.3 3.4 3.5 Characteristics of Indifference Curves 79 More on Goods and Bads 83 An Application: Charity 85 The Sources and Content of Preferences 86 SUMMARY 90 QUESTIONS 90 EXAMPLES 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Transitivity and Age 70 Income and Happiness? 75 Preferences for Brides among the Kipsigis 76 Cultures and Preferences 82 Charity and Income 86 Are Stepmothers Wicked? 87 Legacies 88 Modern Art and the Taste for Innovation 89 69 P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 70 3. UTILITY AND PREFERENCE As explained in the previous chapter, there are only two main methods of microeconomic analysis. The rst is nding an optimum: whats the best thing to do? The second is nding the equilibrium: when everyones actions are taken into account, whats the overall result? Here in Part Two of the book, we apply the rst of these methods to analyze the optimum of the consumer. Specically, what is the best bundle of goods for a consumer to purchase? People in a market economy face two fundamental choices: how to earn an income, and how to spend it. Part Two deals with how income is spent, taking earnings (income) as given. Part Four will analyze the decisions that generate income for example, whether or not to work overtime. 3.1 THE LAWS OF PREFERENCE The economist thinks of the individual as aiming to maximize utility. The logic of utility analysis is the central topic of this chapter. Theories or models are pictures that simplify reality. Irrelevant details are stripped away to concentrate on essentials. The economists picture (theory) of preferences is based on two axioms: 1. The Axiom of Comparison: A person can compare any two baskets A and B of commodities. Such a comparison must lead to one of the three following results: he or she (i) prefers basket A over B, or (ii) prefers basket B over A, or (iii) is indifferent between A and B. 2. The Axiom of Transitivity: Consider any three baskets A, B, and C. If a consumer prefers A to B, and also prefers B to C, he or she must prefer A to C. Similarly, a person who is indifferent between A and B, and is also indifferent between B and C, must be indifferent between A and C. Each of these axioms simplies reality. The Axiom of Comparison does not permit a person to say I just cant decide, even though that does sometimes happen. As for the Axiom of Transitivity, the Example that follows provides some indication as to when the axiom might or might not be valid. EXAMPLE 3.1 TRANSITIVITY AND AGE The psychologists Hinton Bradbury and Karen Rossa asked children of various ages, and also some adults, for their color preferences among square patches of red, green, and blue offered in a variety of sequences. In a fraction of cases transitivity was violated. A child choosing red over green, and then green over blue, might next time choose blue over red. As the table shows, the proportion of intransitive choices declined notably with age. Intransitivity and age Number of subjects 39 33 23 35 40 % Intransitive choices 83% 82 82 78 68 Age 4 5 6 7 8 P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 3.1 THE LAWS OF PREFERENCE 71 9 10 11 12 13 Adults 52 45 65 81 81 99 57 52 37 23 41 13 Source: Adapted from Bradbury and Ross, Table 1. COMMENT At very low ages, transitivity failures might arguably be due to the limited reasoning abilities of young children. As another possible explanation, what appear to be intransitivities may only reect that fact that younger persons are still exploring their needs and tastes. Dont knock it until youve tried it is a dangerous maxim, but has a degree of validity. Young children have more to learn, so it makes sense for them to be more strongly inclined toward experimenting with novelties. So supposing that Margie has chosen red over green and then chosen green over blue, she can try out blue only by violating transitivity, by choosing blue over red next time. Although the tabulated percentages of intransitive choices steadily decrease with rising age, there is one exception: the sudden sharp increase at age 13. Perhaps the onset of puberty opens up new types of novelties calling for exploration. a Hinton Bradbury and Karen Ross, The Effects of Novelty and Choice Materials on the Intransitivity of Preferences of Children and Adults, Annals of Operations Research, 23(1990), 141159. The economists laws of preferences are not purely academic. Someone who violates them can be exploited by a clever swindler. Take the Axiom of Transitivity. Suppose Isaac prefers specic quantities of apples to bananas, and bananas to cherries, but (intransitively) also prefers cherries to apples. Imagine he initially has only cherries. The swindler offers him bananas in exchange for a small fee x. Since Isaac prefers the bananas to cherries, he is willing to make the exchange and pay the fee. Now holding bananas, Isaac would be willing to pay another fee y to obtain apples in place of the bananas. Last, holding only apples, he would be willing to pay a third fee z to obtain cherries instead. But now Isaac is back where he started, with cherries, but poorer by the dollar amount x + y +z! The Axiom of Comparison and the Axiom of Transitivity taken together lead to the: PROPOSITION OF RANK ORDERING OF PREFERENCES: A consumer can consistently rank all baskets of commodities in order of preference. This ranking is called the preference function. EXERCISE 3.1 Jane prefers basket A, consisting of one beer and one taco, to either (i) basket B, consisting of two beers alone, or (ii) basket T, consisting of two tacos alone. Comparing the last two baskets, suppose she would rather have two beers than two tacos. Do these facts indicate that the Axiom of Comparison and the Axiom of Transitivity apply for Jane, at least among the three combinations described? If they do apply, what is her rank ordering of preferences? P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 72 y 3. UTILITY AND PREFERENCE QuantityofCommodity y Figure 3.1. Alternative Consumption Baskets B A C D Points A, B, C, and D represents different combinations, or baskets, of commodity X and commodity Y. If X and Y are both goods, then basket A is preferred to any of the other marked points. 0 x QuantityofCommodity x A N S W E R : As to the Axiom of Comparison, yes, the stated facts show that Jane can compare all three consumption baskets. As to the Axiom of Transitivity, the answer again is yes. Transitivity would tell us that if she prefers the mixed basket over two beers, and two beers over two tacos, she should prefer the mixed basket over two tacos. And we are told that she does. Her rank ordering is clearly rst A, then B, then T. Suppose now you are choosing among combinations of two commodities X and Y. The amounts x and y are scaled along the axes in Figure 3.1.1 Four possible baskets are represented by the points A, B, C, and D. The Laws of Preference tell us only two things about this situation: (1) You can rank all four baskets; and (2) If, for example, you prefer basket A over B and prefer B over C, then you must also prefer A over C. Since A contains more of both X and Y, and we usually think that more is preferred to less, we might expect a consumer to denitely prefer basket A over basket D. But more is preferred to less is not an axiom of preference. The assertion is obviously false for commodities that are bads such as garbage, pollution, risk, and exhausting labor. More is preferred to less is not an axiom; instead, it is the dening characteristic of what economists call a good. DEFINITION: A good is a commodity for which more is preferred to less; a bad is a commodity for which the reverse holds. 3.2 UTILITY AND PREFERENCE The term utility was introduced by the British philosopher Jeremy Bentham. Bentham declared: Nature has placed mankind under the governance of two sovereign masters, pain and pleasure. . . . The principle of utility recognizes this subjection. . . . By the principle of utility is meant that principle which approves or disapproves of every action whatsoever, according to the tendency which it appears to have to augment or diminish the happiness of the party whose interest is in question.2 1 2 Capital letters X and Y are used here to designate commodities, while lowercase letters x and y indicate particular quantities of each. J. Bentham, An Introduction to the Principles of Morals and Legislation (1823 edition), Chapter 1. P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 3.2 UTILITY AND PREFERENCE 73 The modern economic theory of choice does not require us to agree with Bentham that humans seek only to gain pleasure and avoid pain. That is a question for psychology or perhaps philosophy. For economics, it is sufcient to say that the Axiom of Comparison and the Axiom of Transitivity Laws of Preference of the preceding section do generally describe actual behavior. What modern economists call utility reects nothing more than rank ordering of preference. The statements Mary prefers basket A over basket B and Basket A has higher utility for Mary than basket B mean the same thing. They both lead to the empirical prediction: If Mary is offered a choice between A and B, other things equal Mary will choose basket A. Conversely, if Mary is observed to choose A over B, economists infer that basket A has higher utility for her than basket B. DEFINITION: Utility is the variable whose relative magnitude indicates the direc- tion of preference. In nding his or her preferred position, the individual is said to maximize utility. Cardinal versus Ordinal Utility Early economists thought that utility, like length or temperature, could be measured quantitatively. They would have regarded it as perfectly reasonable to construct a diagram like the upper panel of Figure 3.2, where an individuals utility is shown as a function of the amount consumed. Some economists even believed it possible to add up these util numbers interpersonally: 5 of John Does utils could be added to 7 of Richard Roes to give a total of 12 utils for the pair. On this basis, it was thought that correct public policies how severely to punish crime, whether the rich should be taxed more heavily than the poor could be scientically chosen by summing the utils of everyone involved. (This seems to be what Bentham meant in recommending that public policy ought to aim at the greatest good of the greatest number, a noble-sounding though hardly meaningful expression.) In deciding on length of jail terms, for example, Bentham would weigh the criminals util loss from imprisonment against the util loss to prospective victims of the additional crimes he might commit if freed earlier. Economists today generally believe that comparing or summing the utilities of different people is meaningless, and cannot be used as a scientic basis for public policy. A stronger case can be made that utility can be measured for a single individual. First, however, what does it means for a variable to be quantitatively measurable? Measurability does not require a unique way of scaling. Temperature can be measured, but a thermometer can be scaled to show degrees in Fahrenheit or else in Celsius. What makes temperature quantitatively measurable is that the Fahrenheit and Celsius scales differ only in zero point and unit interval: 32 Fahrenheit is 0 Celsius, and each degree up or down of Celsius corresponds to 1.8 degrees up or down of Fahrenheit. Similarly, altitude could be measured from sea level or from the center of the earth (shift of zero-point) and in feet or meters (shift of unit interval). Quantitatively measurable variables such as temperature and altitude are cardinal magnitudes. The crucial property is that, regardless of shift of zero point and unit interval, the relative magnitudes of differences remain the same. Consider altitude: the height difference between the base and the peak of Mount Everest is greater than the height difference between the ground oor and roof of any manmade building. This remains true whether we scale altitude in feet or in meters and whether we measure from P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 74 3. UTILITY AND PREFERENCE U 6 5 AmountofUtility(utils) 4 TotalUtility 3 2 1 c TU Figure 3.2. Cardinal Utility: Total and Marginal The Total Utility curve TU in the upper diagram is a cardinally measurable utility function. Marginal Utility in the lower diagram can be derived from Total Utility, as explained in Chapter 2. As consumption rises, Total Utility increases but at a decreasing rate, and so Marginal Utility is positive but declining. 0 1000 2000 3000 4000 QuantityofConsumption U/C UtilityperUnitofConsumption MarginalUtility MU c 0 1000 2000 3000 4000 QuantityofConsumption sea level or from the center of the earth. Looking at the upper panel of Figure 3.2, which pictures a cardinal utility function for an individual, it does not matter where we place the zero point or what unit interval is chosen for U. Regardless of these specications, utility rises by more between 1,000 and 2,000 units of consumption than it does between 2,000 and 3,000 units.3 3 Mathematical Footnote : Two utility scales U and U are cardinally equivalent if measurements along the two scales are related by the linear equation: U = a + bU , for b > 0 The constant a here represents the shift of zero point, and the constant b the change in unit interval. Consider three quantities U1 , U2 , and U3 along the U scale, where the difference U3 U2 exceeds the difference U2 U1 . Then U3 U2 also exceeds U2 U1 , as can be veried by direct substitution. Thus for all cardinally equivalent scales, the ranking of differences is the same. P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 3.2 UTILITY AND PREFERENCE 75 Utility in the upper diagram of Figure 3.2 is a total function of consumption C. The corresponding Marginal Utility function, following the discussion in Chapter 2, is the slope or rate of change of the Total Utility function, as shown in the lower panel of Figure 3.2. Since the Total Utility function as drawn in the upper panel rises throughout, Marginal Utility is always positive. But since the Total Utility curve increases at a decreasing rate, the Marginal Utility curve is falling as consumption increases. This property is called diminishing Marginal Utility.4 In commonsense terms, youd probably get more of a thrill from your rst million dollars than from your tenth. One possible way of measuring cardinal utility is by asking people How happy are you? Such surveys tend to conrm that Marginal Utility is positive, and that peoples preferences are consistent with the principle of diminishing Marginal Utility. EXAMPLE 3.2 INCOME AND HAPPINESS? In a study by Richard Easterlin in 1994, American respondents were asked to rate themselves on a happiness scale.a As shown in Table 1, life satisfaction was reported as rising sharply with income. Table 2 is derived from a 1984 survey by the same author comparing satisfaction scores for 24 different nations, as related to per capita GNP.b The second study shows that, across different nations, greater average per capita incomes once again were associated with higher reported levels of satisfaction. Table 1: Relative income and life satisfaction in the United States, 1994 Total household income (thousands) Less than $10 $1020 $2030 $3040 $4050 $5075 Greater than $75 Very happy 16 21 27 31 31 36 44 Pretty happy 62 64 61 61 59 58 49 Not too happy 23 15 12 8 10 7 6 Source: Adapted from Table 1 in Easterlin (2001). Table 2: Absolute income and life satisfaction (across nations), 1984 GNP per capita < $2,000 $2,0004,000 $4,0008,000 $8,00016,000 Number of nations 1 3 6 14 Median satisfaction score 5.5 6.6 7.0 7.4 Source: Estimated visually from Easterlin (1995), Figure 3.4. 4 Mathematical Footnote: Let utility be a function of consumption c. Since U = a + bU , and b is positive, positive Marginal Utility according to the U scale (dU /dc > 0) implies positive Marginal Utility according to the U scale (dU /dc = bdU /dc > 0). Note that a change in zero point a does not affect Marginal Utility at all, and a change in unit interval b changes it only by the same positive multiplicative constant everywhere. Diminishing Marginal Utility according to the U scale (d 2 U /dc 2 < 0) similarly implies diminishing Marginal Utility according to the U scale. P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 76 3. UTILITY AND PREFERENCE COMMENT Both tables suggest that utility, as measured by reported satisfaction, consistently rises with income. That is, the Marginal Utility of income is positive. There is also an indication of diminishing marginal utility. In Table 2, for example, a comparison of the second and third rows shows that a doubling of per capita GNP is associated with only a small rise in national satisfaction level, from 6.6 to 7.0 an improvement of only about 6%. a Richard A. Easterlin, Income and Happiness: Towards a Unied Theory, The Economic Journal, v. 111 (July 2001). b Richard A. Easterlin, Will Raising the Incomes of All Increase the Happiness of All? Journal of Economic Behavior and Organization, v. 27 (1995). Another possible indicator of utility is expected life span. It seems reasonable that, other things being equal, people who expect to live longer are happier. And we know that people do generally try to live longer. Life expectancy is a biological measure of wellbeing. Another biological measure is what students of evolution call reproductive success (RS): the offspring/parent ratio from one generation to the next at corresponding phases in the life cycle. (Thus, a population with RS = 2 would double in size each generation.) Evolutionists argue that the bodily form and the biochemistry and behavior of all living beings can be explained by the assumption that natural selection operates to maximize each organisms reproductive success in competition with all the others. Notice that maximizing reproductive success does not mean simply living as long as possible, or having as many offspring as possible; the point is to have the maximum number of offspring surviving into the next generation. So, in a sense, reproductive success is what Mother Nature (that is, biological evolution) uses as its utility function for natural species. Does this biological utility measure have any relevance for modern human beings? That question will be taken up when the sources and content of peoples preferences are examined later on in the chapter. But it is worth noting here that a utility scale can be analytically useful even if the organism involved does not consciously maximize it. Birds do not design their superb eyesight, or bats their excellent hearing. Mother Nature, by selecting these patterns for survival, is doing the designing. Yet if postulating that living organisms maximize reproductive success permits accurate predictions of bodily shape or of behavior, one can say that reproductive survival RS serves as a utility function. Similarly, human preferences may be described by utility functions even if individuals are unaware of pursuing any denite plan or goal. EXAMPLE 3.3 PREFERENCES FOR BRIDES AMONG THE KIPSIGIS The anthropologist Monique Borgerhoff Mulder studied the marital practices of the Kipsigis people of Kenya in the period 19401973.a In this polygynous society men had to buy wives. The bridewealth required to obtain a wife was generally a very substantial expenditure, around one-third of an average mans wealth. The bridewealth was paid in the form of cows, goats, and (after 1960) Kenyan shillings. Early-maturing women commanded higher prices. The explanation offered by the author was that a man purchasing such a bride could anticipate higher reproductive success (RS). Not only is an early-maturing woman able to commence bearing P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 3.2 UTILITY AND PREFERENCE 77 children earlier, but she is likely to be in better health to begin with. The table here classies 130 reported bridewealth payments (in cow-equivalents) into upper, middle, and lower price groups divided between early-maturing and late-maturing women. The rst row, for example, shows that of the 46 cases where high prices were paid, 32 were on behalf of early-maturing women. The bottom row indicates that of the 42 brides for whom low prices were paid, 28 were on behalf of late-maturing women. Bridewealth payments among the Kipsigis (cow equivalents) Early-maturing women High price Average price Low price 32 19 14 Late-maturing women 14 23 28 Source: Estimated visually from Figure 5 in Borgerhoff Mulder. a Monique Borgerhoff Mulder, Early Maturing Kipsigis Women have Higher Reproductive Success than Late Maturing Women and Cost More to Marry, Behavioral Ecology and Sociobiology, v. 24 (1989). For many purposes, however, it is not necessary to measure preferences cardinally. Instead, an ordinal concept of utility sufces. Under ordinal utility, a person may prefer basket A to basket B, and basket C to D, but need not be able to say I prefer A over B more than I prefer C over D. If Total Utility is only an ordinal magnitude, whether Marginal Utility is positive or negative can still be determined, but not whether Marginal Utility is rising or falling. That last step would involve comparing utility differences. As will be seen shortly, ordinal utility sufces for analyzing most consumption choices. Utility of Commodity Baskets Figure 3.3 pictures a cardinal function U (x , y ) for two goods, X and Y. The quantities x and y are scaled along the two axes. If utility is cardinal, its magnitude (in utils) can also be quantied as the height above the base plane. When x = x 1 and y = y 2 , for example, utility is the height T T . If the quantity of Y is held constant at y = y 1 , how utility varies with x is shown by the curve PQR lying on the utility surface. If Y is held constant at y = y 2 instead, there is a similar curve STU; or if Y is held constant at y = y 3 , we see the curve BVG. Each curve is shown as always rising (Total Utility increases as x increases); the Marginal Utility of X is therefore positive throughout. (X is a good rather than a bad.) Similarly, the rising curves OPB, WQV, and ARG show that the Marginal Utility of commodity Y is also always positive. Typically, consumer preferences for goods are interdependent. (Your desire for another pound of butter varies with how much bread you will be eating.) In the illustration here, the Marginal Utility of X at the point T (i.e., when x = x 1 and y = y 2 ) is shown by the slope at point T along the curve STU. This is not necessarily the same as the Marginal Utility of X at the point V (where x = x 1 as before, but y = y 3 ), which is the slope at V along BVG. So the Marginal Utility of X may depend on the quantity of Y, and vice versa.5 5 Mathematical Footnote: Where Utility U (x , y ) is a function of amounts consumed of both X and Y, the Marginal Utilities are dened as partial derivatives: MU x U / x and MU y U / y . In general, the Marginal Utility P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 78 3. UTILITY AND PREFERENCE G U V T R B y y3 V Q S W A x T Qu ant x2 of X y2 ityo fY P y1 0 x1 Qua ntity Figure 3.3. A Cardinal Total Utility Function of Two Goods Utility is measured up from the base plane; the horizontal axes x and y represent quantities consumed of commodities X and Y. The curves OA, PR, SU, and BG along the surface show how Total Utility changes as x increases, holding y constant (at a different level for each curve). Similarily the curves OB, WV, and AG show how Total Utility changes as y increases, holding x constant. The cardinal utility function of Figure 3.3 is pictured again in Figure 3.4. But now a different set of curves are drawn on the surface: CC, DD, and EE are contours connecting points of equal height on the utility hill. These contours are therefore curves of constant utility, also called indifference curves. Figure 3.5 pictures the same utility function again, but with the third vertical dimension suppressed. The indifference curves, contours of equal heights on the now invisible utility hill, are shown in two dimensions as in a topographic map. The arrows in the diagram indicate the preference directions. (By assumption, X and Y here are both goods, so as indicated by the arrows more is preferred to less applies here to both X and Y.) The indifference curves, together with the preference directions, are all that are needed to determine how a consumer ranks baskets of goods. The geometrical step of deleting the vertical utility dimension of Figure 3.4 corresponds to the shift from cardinal utility to ordinal utility. In terms of ordinal utility the only meaningful comparisons concern how baskets of commodities are ranked.6 Two possible cardinal preference scales, U and U , are used to label the indifference curves of Figure 3.5, but the two scales are equivalent in the ordinal sense. Why? Because they give the same answers (i) as to which baskets are equal in utility (whether they lie along the same indifference curve) and (ii) as to how baskets that are unequal in utility should be ranked (what are the preference directions). of each commodity will be a function of both x and y ; that is, the cross-derivative 2 U / x y will not ordinarily be zero. Mathematical Footnote: If the two utility scales are only ordinally equivalent, all we can say is that U = F (U ) and dU /dU = F (U ), where F (U ) > 0. Nevertheless, the positive derivative dU /dU always preserves rankings of magnitudes. So if U 1 > U 2 , then the same holds true on the U scale: U1 > U2 . 6 P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 3.3 CHARACTERISTICS OF INDIFFERENCE CURVES 79 G E E D D C C E y E D C x D C Qu ant ityo fY Q t uan ityo fX 0 Figure 3.4. Cardinal Utility and Indifference Curves The surface here is the same as in the preceding diagram, but the curves along the surface (CC, DD, EE) are contours that connect points of equal heights (levels of utility). The projections of these curves onto the base plane (the dashed C C , D D , E E ) are indifference curves. 3.3 CHARACTERISTICS OF INDIFFERENCE CURVES If X and Y are both goods, commodities for which more is preferred to less, then indifference curves drawn on x,y axes have four crucial properties. y C DE F Preference Directions Quantityof Y F (U=4, U =120) E (U=3, U =20) D (U=2, U =19) C (U=1, U =0) 0 x Quantityof X Figure 3.5. Indifference Curves and Preference Directions: Ordinal Utility Here the cardinal (vertical) scaling of utility has been stripped away, leaving the indifference curves. These indifference curves, together with the preference directions, provide all the information needed to rank alternative consumption baskets in terms of ordinal utility. P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 80 y 3. UTILITY AND PREFERENCE S Quantityof Y Preference Directions Figure 3.6. Properties of Indifference Curves The preference directions indicate that every point in the + region is preferred to A, whereas A is preferred over every point in the region. It follows that any indifference curve through A must have negative slope. Also, there can be only one indifference curve through A, because intersecting indifference curves violate transitivity of preference. T + A R U2 Q U1 0 x Quantityof X 1. Negative slope: In the ordinal-utility diagram of Figure 3.6, each point corresponds to a particular basket of goods X and Y. Given the preference directions, starting with the basket represented by some point A, the consumer would prefer all points to the northeast (above and to the right) of A. Similarly, the consumer would prefer point A to all points that lie southwest (below and to the left) of A. It follows that all points indifferent to A must lie either southeast of A (like points R and Q) or else northwest of it (like points S and T ). Thus an indifference curve passing through point A cannot lie within either the + or the region shown in Figure 3.6. So any indifference curve cutting through A must necessarily have negative slope, like curves U1 or U2 in the diagram.7 2. Indifference curves never intersect: Assume tentatively that two indifference curves such as U1 and U2 do actually intersect at point A. This leads to a contradiction. Indifference curve U1 states that the consumer is indifferent between baskets A and Q. Indifference curve U2 states that the consumer is indifferent between A and R. By transitivity, the consumer must therefore be indifferent between Q and R. But R represents more of both commodities than Q. Since X and Y are both goods, more is preferred to less, and the consumer must prefer R over Q. But these two implications contradict one another. So the initial assumption is invalid; indifference curves cannot intersect. 3. Coverage of indifference curves: An indifference curve passes through each point in commodity space. In other words, between any two indifference curves another can always be drawn. The real number system has a corresponding property. Between any two numbers such as 17.4398 and 17.4399 there is always another 7 Mathematical Footnote: In terms of calculus, along any indifference curve utility U(x,y) is constant. So: 0 = dU U / x d x + U / y d y Then the slope along the indifference curve is: dy dx = U U / x U / y Since U / x and U / y are both positive (X and Y are both goods with positive Marginal Utilities), the slope dy/dx is negative. P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 3.3 CHARACTERISTICS OF INDIFFERENCE CURVES 81 y y Quantityof Y A B Convexindiff erence curve Quantityof Y Concaveindiff erence curve C D 0 x Quantityof X Panel(a) ConvextoOr igin 0 x Quantityof X Panel(b) ConcavetoOr igin Figure 3.7. Convexity and Concavity Between two goods, indifference curves must have negative slope. Curvature may be convex to origin as in panel (a), or concave to origin as in panel (b). The convex case is normally observed, even though concavity would not necessarily violate the laws of preference. number such as 17.43987 larger than the rst and smaller than the second. The coverage property is equivalent to the Axiom of Comparison, which says it is always possible to compare any baskets of commodities. It follows that any basket must lie on some indifference curve.8 (A diagram can only show a selection of the indifference curves; to show them all, the picture would have to be solid black.) 4. Indifference curves are convex to the origin: The two panels of Figure 3.7 show the curvatures dened as convex and concave to the origin. The convex curve of Panel (a) represents the standard shape. A curve is convex if the straight line that connects any two points on it lies above the curve. For example, if the line segment BC in Figure 3.7(a) were plotted it would lie above the indifference curve. Correspondingly, a curve is concave if the straight line that connects any two points on it lies below the curve. In contrast with the previous three properties (negative slope, nonintersection, and coverage), convexity cannot be proved from the postulates of rational choice. Rather, it is based on the well-established empirical principle of diversity in consumption, as will be discussed in Chapter 4. As a commonsense justication for convexity, suppose Panel (a) of Figure 3.7 represents Sallys preferences for food X and entertainment Y. At point A she has plenty of entertainment but little food. To get a bit more food, we would expect her to be willing to sacrice a fair amount of entertainment Y. The diagram shows her as just willing to move from A to B, giving up (say) 3 units of entertainment Y for just 1 unit of food X. At B her consumption is more diversied. Therefore, she should be less willing than before to give up entertainment for more food. This time she might be willing to give 8 Psychological experiments indicate that below a certain threshold sensations cannot be distinguished from one another. This suggests that indifference curves in actuality have some width. So indifference curves are an idealization rather than a precise picture of reality. But this is no more disturbing than the fact that the lines of Euclids geometry, having length but no breadth, similarly could not ever actually be drawn in the real world. P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 82 3. UTILITY AND PREFERENCE up only 2 units of Y for 1 unit of X. Last, from C to D, perhaps she is willing to give up only 1 unit of her now scarce entertainment Y for 1 unit of food X. Thus, the picture in Panel (a) of Figure 3.7 seems to t normal patterns of preference. EXERCISE 3.2 (a) John claims that the two equations xy = 100 and x + y = 20 are both valid indifference curves for him. Can this be correct? (b) What about the curves corresponding to the equations xy = 100 and xy = 200? A N S W E R : (a) No. The curves corresponding to the two equations xy = 100 and x + y = 20 intersect at x = 10, y = 10. This violates the condition that his indifference curves cannot intersect (property 2). (b) The curves xy = 100 and xy = 200 do not intersect, and so satisfy property 2. You can use algebra or plot the functions to satisfy yourself that both curves have negative slope (property 1) and are convex toward the origin (property 4). So these two curves could both be valid indifference curves for the same person. (Since we are dealing with only two curves, property 3 coverage is not relevant here.) EXAMPLE 3.4 CULTURES AND PREFERENCES In a pioneering study, a team of two anthropologists and an economist used an ingenious technique to elicit indifference curves for human subjects of different cultural backgrounds.a The experimental subjects (all were Cornell University students or their spouses) came from the United States, France, Turkey, Chile, India, Cameroon, and Egypt. The experimenters asked subjects to express preference ratios between alternative combinations, of shirts and (pairs of) shoes. For example, a subject might indicate a 7:4 preference ratio for the combination 4 shirts + 2 shoe-pairs as against another combination, 3 shirts + 0 shoe-pairs. Each subject expressed preference ratios between 1,176 paired combinations. From these reports a computer was programmed to generate a best t pattern of indifference curves. Although the computed indifference curves were almost always negatively sloped and convex in curvature, as would be expected, striking individual and cultural differences appeared. One male subject, for example, displayed a tilt toward shirts. That is, on a graph with shirts on the horizontal and shoes on the vertical axis, his indifference curves were quite steep. (He was very reluctant to give up shirts for more shoes.) Other individuals were much more balanced. In one case not only was the slope more like 1:1 (the subject was willing to exchange approximately one shirt per shoe-pair), but the indifference curves showed very little convexity they were almost (though not quite) straight lines. Thus, for this individual shirts and shoes were (almost) perfect substitutes. Turning to cultural differences, for the Americans the indifference curves tended to be more convex at low levels than at high. For small numbers of these clothing items, there was a strongly preferred ratio (close to 1:1). But when in a position to acquire relatively ample quantities, the American subjects were willing to tolerate a wider spread of ratios so that combinations such as 4,2 or 3,3 or 2,4 were all almost equally preferred. A Chilean female subject, on the other hand, displayed such a strongly preferred ratio (again near 1:1) that divergence in either direction led to P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 3.4 MORE ON GOODS AND BADS 83 r U4 U3 U2 U1 Mean return r on assets is a good, but riskiness of return s is a bad. The preference directions are therefore north and west (up and to the left), so the indifference curves slope upward. MeanRetur n Figure 3.8. Portfolio Preferences: Indifference Curves between a Good and a Bad Preference Directions 0 s RiskinessofRetur n one commodity or the other (whichever was the more plentiful) becoming a bad for her. a John M. Roberts, Richard F. Strand, and Edwin Burmeister, Preferential Pattern Analysis, in Paul Kay, ed., Explorations in Mathematical Anthropology (M.I.T. Press, 1971). 3.4 MORE ON GOODS AND BADS An important application of utility theory is to portfolio selection how a person should balance wealth over assets such as stocks, bonds, and real estate. Portfolios have two main characteristics: (i) a desired feature in the form of average percent yield r and (ii) an undesired feature in the form of riskiness s. Figure 3.8 shows an investors preferences over portfolios offering differing combinations of r and s. Note that the preference directions here are up and to the left. For the good feature r, more is preferred to less. But for the bad feature s, less is preferred to more. Given these preference directions, it is easy to see that the indifference curves must have positive slope. Everyday experience also tells us that a commodity can be a good up to a point of satiation, beyond which it becomes a bad. Figure 3.9 pictures such a situation. Commodity Y , let us say shirts, is always a good. But commodity X (think of it as amounts of cake to be eaten in a short time period) is rst a good and then a bad.9 Last, having more or less of some commodities can sometimes leave a person entirely indifferent. Amounts of such a neutral commodity neither add to nor detract from utility. In the indifference-curve picture of Figure 3.10, Y is a good but X is a neuter commodity. 9 In Roughing It, Mark Twain describes a visit with the Mormon leader Brigham Young. After a harrowing day dealing with recriminations and jealousies among his multiple spouses, Young supposedly said to his visitor: My friend, . . . dont encumber yourself with a large family . . . Take my word for it, ten to eleven wives is all you need. Presumably, Brigham Young found that, after the 11th, wives became a bad. [Note: This was probably a ctionalized account.] P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 84 3. UTILITY AND PREFERENCE Y Zone1 Preference Directions Zone2 Preference Directions U3 U2 Shirts U1 0 X Cake Figure 3.9. Satiation In Zone 1 both commodities, X and Y, are goods, so the indifference curves have negative slope. Zone 2 is the region of satiation for Y; in this region the preference directions are north and west (up and to the left), and the indifference curves have positive slope. In this region an individual would have to be paid to eat another piece of cake. EXERCISE 3.4 For each of the following possible algebraic utility functions, indicate whether each commodity is a good, a bad, or a neuter: (a) U = xy; (b) U = x / y; (c) U = 2xy/ y. A N S W E R : (a) Since U = xy rises as either x increases or y increases, both X and Y are goods. (b) Here U rises with x but falls as y increases, so X is a good and Y is a bad. (c) Here y cancels out, and the utility function becomes U = 2x . So X is a good, but Y is a neuter commodity (utility does not depend at all upon y). y Preference Direction Figure 3.10. A Neuter Commodity U4 Quantityof Y U3 U2 U1 Y is a good, but X is a neuter commodity. The consumer does not care about having more or less of X. The only preference direction is up, and so the indifference curves are horizontal. 0 x Quantityof X P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 3.4 MORE ON GOODS AND BADS 85 Preference Direction Preference Direction U1 U2 U3 U4 45 Line F 1,000 AlterIncome 1,000 F AlterIncome U1 Zone2 U2 U3 U4 45 Line preference Directions M M C E 0 EgoIncome Panel(b) BenevolentPref erences 1,000 Zone1 E 0 500 1,000 EgoIncome Panel(a) NeutralPref erences Figure 3.11. Preference and Utility If Ego preferences are as pictured in panel (a), Alter income is a neuter commodity for me. Then I would never give charity to him. If panel (b) pictures Ego preferences, I may give charity, but only to someone poorer than myself. (Alter income is a good for me below the 45 line, but it is a neuter commodity for me above the 45 line.) An Application: Charity The following observations can be made about charity: (1) Not everyone contributes. (2) But a great many people do. (3) Almost always, contributors donate to persons poorer than themselves. Can we construct an indifference-curve picture consistent with these observations? Figure 3.11 has axes Egos Income and Alters Income (where Ego is the person whose indifference curves are being described and Alter is any other person). Since we are dealing solely with Egos preferences, Alters feelings are not involved in the picture. Imagine rst that Ego is completely unconcerned with Alters well-being. For Ego, Alters Income is a neuter commodity. This is the situation pictured in Panel (a) of Figure 3.11. Since Egos Income is surely a good for Ego, the only preference direction is to the right. On these axes Egos indifference curves are vertical. With preferences as pictured in Panel (a), would Ego ever give charity to Alter? Suppose Ego is initially at point E in Panel (a) with an income of 1,000 units while Alter has an income of zero. Imagine that Ego can transfer income to Alter, dollar for dollar. In the diagram, this means Ego can move to any point along the line EMF with slope 1. But any such movement from point E must evidently put Ego on a lower indifference curve, and hence would not be undertaken. Panel (b) of Figure 3.11 pictures a more interesting situation. Suppose Ego is benevolent, but only to people poorer than herself. The points where Alter is poorer than Ego all lie below the dashed 45 line (Zone 1 in the diagram). In this zone Alters Income is a good for Ego. Since Egos Income is of course always a good for Ego, the preference directions are north and east up and to the right. Both commodities are goods, and the indifference curves have their usual negative slopes. So an Ego initially at E would now transfer some income to Alter, specically an amount just enough to attain point P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 86 3. UTILITY AND PREFERENCE C along the line EMF. Why? Because C is the point along EMF where Ego can get onto her highest attainable indifference curve (U3 ). In contrast, suppose the initial situation is in Zone 2 of Panel (b), at some point above and to the left of point M along the line EMF. Since this range is above the 45 line, here Alter is richer than Ego. So Ego would be unwilling to transfer any income to Alter. As pictured, Ego is not actually malevolent to Alter. If she were malevolent her indifference curves in Zone 2 would have positive slope. (Alters income would be a bad for Ego.) But Egos indifference curves in the diagram are vertical in Zone 2, meaning that in this range Alters income is merely a neuter commodity for Ego. EXAMPLE 3.5 CHARITY AND INCOME If people make charitable contributions mainly to recipients poorer than themselves, giving will be positively correlated with income. The table here extracts some data from a study of charitable contributions in 1994. Notice that the percentage of families making some contribution does indeed rise quite steadily with income. The average dollar amount in each bracket (taking into account the zero contributions of those not participating) also increases. As a percentage of family income, however, the rise is quite slow until very high income brackets are reached. Charitable giving in 1994 selected income levels a Average contribution, $ 209 474 779 1,846 3,546 27,491 244,586 960 Average as % of income 1.36 1.37 1.44 1.71 2.09 4.15 4.88 2.14 Family income $10,00019,999 $30,00039,999 $50,00059,999 $100,000124,999 $150,000199,999 $500,000999,999 > $1,000,000 Overall % contributing 64 80 84 92 96 97 100 75 Source: Data selected from Table 1 of Paul G. Schervish and John J. Havens, Wealth and the Commonwealth: New Findings on Wherewithal and Philanthropy, Nonprot and Voluntary Sector Quarterly, v. 30 (March 2001). 3.5 THE SOURCES AND CONTENT OF PREFERENCES Why do people want some things and not others? Why are our desires for some goods easily satiated, for others not? How and why do tastes vary with age, ethnic origins, and circumstances? Preferences are not always difcult to explain. It is easy to predict that iced drinks will be more popular in Georgia than in Alaska, that baby diapers will not be a big merchandising item in a retirement community, that pickled herring will sell best in Jewish neighborhoods and soul food in Harlem. But what are the bases for these commonsense judgments? On the most fundamental level, human beings resemble other animals who seek (and so can be said to have preferences for) survival and comfort. We like to keep our skins intact, our body parts connected up, and our blood temperatures close to 98.6 F. P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 3.5 THE SOURCES AND CONTENT OF PREFERENCES 87 Physical considerations such as these broadly explain human desires for food, shelter, and protection against injury. As already mentioned, evolutionary biologists contend that natural selection has shaped all our preferences, with the ultimate goal of maximizing reproductive success: Instead of a disorganized list of items that we may care to invest ourselves in, such as children, leisure time, sexual enjoyment, food, friendship, and so on, Darwins theory says that all of these activities are expected to be organized eventually toward the production of surviving offspring. Robert Trivers, Social Evolution, 1985, p. 21. On the other hand, it is not immediately clear how evolutionary considerations translate into specic likes or dislikes for three-piece suits or Levis, pizza or sushi, split-level houses or mobile homes. Cultural and accidental elements are also involved. Biological factors are particularly relevant for interpersonal attitudes, why we incline to help some people and refrain from helping others. The leading fact here is that people are especially keen to help their own children. This of course is consistent with the evolutionary need to maximize reproductive success. Organisms that help their own offspring rather than others offspring have left more descendants over the generations. So it is not surprising that, other things being equal, people are especially inclined to aid and support their own biological offspring. EXAMPLE 3.6 ARE STEPMOTHERS WICKED? In fairy tales such as Cinderella, stepmothers have a bad reputation. Might that possibly have some factual basis, at least in terms of statistical averages? Anne Case, I-Fen Lin, and Sara McLanahan compared food consumption in families with various patterns of biological and nonbiological children.a Concentrating upon the mother (the parent mainly responsible for food purchases and preparation), in a regression analysis they examined how family status related to family food expenditures. Some of the results are shown in the table. Food consumption at home, 19721985, as related to family structure (mean = $4,305) Variable Child with adoptive mother Child with stepmother Child with foster mother and father Adjustment of mean (dollars) 204 274 365 Source: Extracted from Table 1 of Case, Lin, and McLanahan. These data indicate, for example, that holding constant other important variables such as family income and family size replacing a single biological child with an adopted child is on average associated with a reduction of $204 on family food expenditures. With two adopted children in place of two biological children the difference would become $408, and so on. The distinctions among the three different types of nonbiological children also make sense. On average we are not surprised that a nonbiological parent committing herself to formal adoption is likely to be more intensely concerned with that child than someone who remains merely a stepmother, and this consideration holds with P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 88 3. UTILITY AND PREFERENCE even greater force when the comparison is with foster children (where parental care is in effect a hired service). Apart from the fact that statistical averages paint an unjust picture of the many deeply loving and self-sacricing nonbiological parents, a number of other considerations may also be involved. One is that families with nonbiological children are liable to have a number of other problems for example, expenses connected with divorce and noncustodial child care that may make it difcult for them to spend as much on childrens food. Another is that aggregating food expenditures at the family level does not reveal possible differential treatment of biological and nonbiological children, and this is after all the crucial point (as brought out in the Cinderella story). And nally, the authors suggest, in view of the current problem of child obesity it is conceivable that lower expenditures on food may in many cases be on balance benecial so that the nonbiological mothers might be actually helping rather than slighting the children concerned. a Anne Case, I-Fen Lin, and Sara McLanahan, Household Resource Allocation in Stepfamilies: Darwin Reects on the Plight of Cinderella, American Economic Review, v. 89 (May 1999). The data in Example 3.6 suggest, without being necessarily fully convincing, that stepmothers slight children in their care. How about stepfathers? Suggestive evidence comes from England. In a sample of 29 babies fatally battered by male parents, 15 of the men involved (52%) were stepfathers even though overall, fewer than 1% of such babies lived with their stepfathers. Thus the relative risk of fatal battery was over 15 times as great for stepfathers as compared with birth fathers!10 (Lest this give the wrong impression, it must be remembered that such child killings remain very rare. The great preponderance of stepfathers and stepmothers are loving and concerned parents.) Biological inuences upon parental choices may be reected in subtler ways, as the following Example indicates. EXAMPLE 3.7 LEGACIES Debra S. Judge and Sarah Blaffer Hrdya studied the legacies left in their wills by 1,538 male and female testators in Sacramento for the period 18901984. The table here illustrates some of their results for male and female testators who left both a surviving spouse and children. Percent allocations Male testator % to spouse % to children Total 69.8% 21.7% 91.5% Female testator 42.4% 47.6% 90.0% Apart from the obvious fact that decedents of both sexes left 90% or more of their estates to their immediate families spouses or children the feature of the table calling for explanation is that men left relatively more to their spouses, women relatively more to the children. The authors suggest a biological explanation. Since 10 Martin Daly and Margo Wilson, Homicide (New York: Aldine de Gruyter, 1988), pp. 8990. The fatality data are attributed to a study by P. D. Scott published in 1973. P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 3.5 THE SOURCES AND CONTENT OF PREFERENCES 89 men remain fertile longer than women, widows are less likely than widowers to be still of reproductive age. So a male testator could allocate wealth to his widow with considerable condence that she will use the money only for the benet of their joint biological offspring. But a widower is quite likely to remarry and have additional children with a new spouse. So when a woman leaves a legacy to her husband, the resources he inherits might well be converted to the benet of the offspring of a later wife, possibly at the expense of her own offspring. COMMENT Although the biological explanation for leaving inheritances to offspring is plausible, it is not the only possibility. Arguably, it might be that the determining factor is not relatedness but rather simple propinquity, the fact that people get to love and identify with the children with whom they live until maturity. If people were forced to bring up one anothers offspring rather than their own, perhaps decedents would leave their estates to their adoptive rather than to their birth children. And mothers giving relatively more to children than fathers do may similarly only reect the fact that mothers spend more time with their children, hence are more closely bonded to them. a Debra S. Judge and Sarah Blaffer Hrdy, Allocation of Accumulated Resources among Close Kin: Inheritance in Sacramento, California, 18901984, Ethology and Sociobiology, v. 13 (1992). Biologically founded preferences, such as benevolence toward ones children, are quite stable and permanent. In contrast, the kinds of tastes reected in fashions are notoriously volatile. When it comes to skirt lengths or dance styles or popular songs, what is in this year is almost sure to be out next year. Somewhat intermediate between the two are long-lived cultural trends. Among these are, in the eld of dress, the last centurys movement toward light and informal attire, and in art, the movement away from realism and toward abstraction. In accordance with the analysis of Chapter 2, such changes in tastes increase the demand for some commodities, whose prices therefore tend to rise, while reducing the demand for other commodities, whose prices tend to fall. EXAMPLE 3.8 MODERN ART AND THE TASTE FOR INNOVATION Beginning in the latter half of the 19th century, new artistic movements such as impressionism and expressionism began to displace traditional representational styles in both critical and popular esteem. David W. Galenson and Bruce A. Weinberga interpreted this development as a general increase in the demand for innovation, in turn associated with the ongoing drastic changes in technology, fashions, and morals that were taking place within society at large. An increase in the demand for artistic innovation would imply a comparative fall in the value that art purchasers placed upon pictorial works reecting maturity and experience as opposed to novelty and shock value. Table 1 documents this change in the light of the ages at which French artists, born in various 19th-century cohorts, found their paintings achieving peak market values. The rst cohort, born in the 1820s, received highest prices for paintings that were executed at the rather mature age of 46.6 years. But for the cohort born 60 years later, artists on average received their highest prices for paintings produced at the remarkably low age of 27.0 years. P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 90 3. UTILITY AND PREFERENCE Ages at which French artists paintings achieved peak market value Birth period 18201839 18401859 18601879 18801900 Peak age 46.6 37.0 28.8 27.0 Source: Adapted from Galenson and Weinberg, Table 4. a David W. Galenson and Bruce A Weinberg, Creating Modern Art: The Changing Careers of Painters in France from Impressionism to Cubism, American Economic Review, v. 91 (Sept. 2001). SUMMARY In choosing a preferred consumption basket, a person is said to maximize utility. Preferences over different baskets of goods are assumed to obey two fundamental laws: (1) the Axiom of Comparison (a person can compare all possible pairs of consumption baskets) and (2) the Axiom of Transitivity (a person who prefers basket A to B, and prefers B to C, will prefer A to C ). These two laws together imply that a person can rank all conceivable consumption baskets in order of preference. If differences in utility, moving from one basket to another, can be measured, then utility is said to be a cardinal magnitude and Marginal Utility can be dened. Commonsense evidence indicates that, beyond a certain level, the Marginal Utility associated with income generally or with any commodity in particular begins to decline. But for many purposes in economics it sufces to merely ask whether the consumer prefers one basket over another, without measuring the size of the difference. If so, an ordinal concept of utility is being used. Indifference curves require only ordinal utility. Each indifference curve connects baskets that the consumer views as equally desirable. Between pairs of goods, indifference curves have four properties: (1) each has a negative slope; (2) they do not intersect; (3) some indifference curve goes through each point; (4) each indifference curve is convex (a straight line connecting any two points on an indifference curve lies above the curve). More is preferred to less is the dening characteristic of a commodity that is a good. For a bad, less is preferred to more. Human preferences, and notably our desires to help our own offspring, are in part the outcome of the evolved history of the human species. But a host of historical and cultural and accidental factors, not yet fully understood, are also involved in generating our tastes and desires. QUESTIONS The answers to daggered questions appear at the end of the book. 1. Bill is offered a choice between a ski trip to Aspen and four cases of Cutty Sark whiskey. Which of the following possible responses violate the laws of preference? a. Theyre so different, I cant choose. For Review P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 QUESTIONS 91 b. c. I dont care, you choose for me. Whichever I choose, I know Ill be sorry. 2. Name a commodity that is a good for many people, but is a bad for you. Name a commodity that is a good for you, but only up to a point; after that it becomes a bad. 3. Draw possible indifference maps between the following: a. Two goods. b. A good and a bad. c. A good and a neuter. d. A good and a commodity that is a good up to a point, but then becomes a bad. 4. What do modern economists mean by the term utility? 5. Given a cardinal (quantitatively measurable) Total Utility function, show how a corresponding Marginal Utility function is derived. 6. What can be said about the Marginal Utility function if Total Utility is given only in ordinal terms? 7. What are the four essential properties of indifference curves between two goods? Explain the justication for each of the four properties. 8. Which of the following requires only ordinal utility, which requires cardinal utility, and which requires interpersonal comparability of cardinal utilities? a. Indifference curves can be drawn. b. A Marginal Utility function can be used to see numerically how Total Utility changes as consumption of a good increases. c. It can be determined which person is most desirous of receiving a particular prize. 9. In suppressing the cardinal dimension of the utility hill so as to picture preferences only in terms of indifference curves, why is it necessary also to indicate the preference directions? For Further Thought and Discussion 1. Why isnt it possible to give an exact meaning in utility terms to the expression greatest good of the greatest number? 2. An example of an ordinal measure is the military rank system. A sergeant has more authority than a private, a lieutenant more than a sergeant, and so on. Give another example of an ordinal scale of magnitude. 3. Since you probably would not want to eat pickles and ice cream together, does it follow that your indifference curves between these two goods are concave rather than convex? 4. For His Income and My Income regarded as goods, what shape for the indifference curves would correspond to the Golden Rule (Love thy neighbor as thyself)? 5. In surveys of income and happiness (see Example 3.3), a puzzling discrepancy has been noted. Although higher income is associated with higher reported happiness at a moment in time, this conclusion does not seem to hold for comparisons over time. Even though wealth has risen over the years in the United States all across the scale, so that both rich and poor have higher incomes than before, reports on happiness do not average higher than before. The most natural explanation of this paradox is that happiness is more powerfully affected by relative income status than by absolute income. The poor consume more than before, but are still on the bottom of the heap and so still feel just as unhappy. How would you draw the preference map to picture this situation? 6. In Example 3.4 on Cultural Differences, sketch patterns of indifference curves with the preferences described, putting shirts on the horizontal axis and shoes on the vertical axis. P1: JZP/... P2: JZP/... 0521818648agg2.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:23 92 3. UTILITY AND PREFERENCE 7. An economics student offered dessert tells his friend and classmate, The Napoleon would increase my utility more, but the fresh fruit is better for me, so Ill take the fresh fruit. Does this comment reect an accurate understanding of utility theory? 8. How could a condence man exploit someone whose preferences violate the Axiom of Comparison? The Axiom of Transitivity? P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 4 4.1 Consumption and Demand The Optimum of the Consumer 94 The Geometry of Consumer Choice 94 Optimum of the Consumer (Cardinal Utility) 97 Optimum of the Consumer (Ordinal Utility) 100 4.2 4.3 Complements and Substitutes 104 The Consumers Response to Changing Opportunities 107 The Income Expansion Path 107 The Engel Curve 110 Price Expansion Path and Demand Curve 112 4.4 Income and Substitution Effects of a Price Change 115 An Application: How Can the Giffen Case Come About? How Likely Is It? 117 4.5 4.6 From Individual Demand to Market Demand 118 An Application: Subsidy versus Voucher 120 SUMMARY 122 QUESTIONS 124 EXAMPLES 4.1 4.2 4.3 4.4 4.5 4.6 4.7 Smart Ants 100 Prisoners of War: Tea versus Coffee 102 Rats 106 How Much Are Christmas Gifts Worth? 109 Luxuries versus Necessities in a P.O.W. Camp 111 Was Bread a Giffen Good? 118 But Do Vouchers Really Help? 122 93 P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 94 4. CONSUMPTION AND DEMAND This chapter analyzes consumer decisions. Your choice among different consumption bundles, if you are rational, will depend upon your preferences (what you want to do) and your opportunities (what you are able to do). And, in a market economy, opportunities will in turn depend upon your income and upon the prices you face. Individual consumption choices respond to all three of these variables: preferences, incomes, and market prices. 4.1 THE OPTIMUM OF THE CONSUMER1 The Geometry of Consumer Choice Dealing for simplicity with only two goods, Figure 4.1 shows the baskets of goods X and Y that a consumer with a given income can afford (the shaded triangle). The upper boundary of the shaded area, the budget line KL, shows the baskets attainable by a person who spends all of his or her income on the two goods X and Y. Suppose that Marys income is I = $100 and that the market prices are Px = $2 and P y = $1. Spending all of her income on X, Mary could buy x = 100/2 = 50 units. This would put her at point L in the diagram. At the other extreme she could buy y = 100/1 = 100 units of good Y (point K ). More generally she could afford any combination of X and Y lying on her budget line the straight line between points K and L. Prices are usually quoted in terms of money. But it is useful to pierce the veil of money to focus upon the underlying real magnitudes. Think of prices and incomes as measured in terms of some standard real good, what economists call a numeraire say, corn. Then the prices Px and Py represent amounts of the numeraire (corn) that must be paid to obtain a unit of X or of Y. Similarly, income I is the total amount of the numeraire good available for spending. If a person spends all of his or her income on goods X and Y, the following equation holds: Px x + P y y = I (4.1) Unless indicated to the contrary, it will be understood that the variables x and y cannot be negative. Symbolically: x 0, y 0. On this understanding, equation (4.1) is the algebraic equivalent of the budget line KL in Figure 4.1. At the vertical intercept (where x = 0), point K corresponds to buying I / P y units of Y. Similarly, at the horizontal intercept (where y = 0), point L corresponds to buying I / Px units of X. Allowing also for the possibility that some income might not be spent, equation (4.1) becomes an inequality : Px x + P y y 1 (4.1 ) This inequality, again on the understanding that x and y cannot be negative, is the algebraic equivalent of the consumers opportunity set (the shaded region in Figure 4.1). If X and Y are both goods for the consumer (if the preference directions are to the north and east, as shown in Figure 4.1), the individual would clearly prefer baskets along the budget line KL to any in the interior. On the other hand, points in the interior 1 The optimum of the consumer is sometimes rather carelessly referred to as the equilibrium of the consumer. Such wording blurs the distinction between the two key analytical concepts of microeconomics: nding an equilibrium versus nding an optimum. An optimum is the best possible action available to a decision-maker. In contrast, an equilibrium represents a balance of the actions of many independent decision-makers, for example, the balance between the overall forces of supply and demand in a market. Individual consumer choice is an optimization problem, not an equilibrium problem. P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 4.1 THE OPTIMUM OF THE CONSUMER 95 y Preference Directions I/Py K Figure 4.1. Optimum of the Consumer The shaded region OKL is the consumers market opportunity set; it is bounded by the horizontal and vertical axes and the budget line KL. The optimum is the point on the budget line KL that lies on the highest attainable indifference curve (point C on indifference curve U2 ). Quantityof Y Q C y S U3 R U2 U1 L I/Px Quantityof X x 0 x might become relevant if other constraints limited the available choices for example, rationing in wartime (as will be discussed in Chapter 5). The slope of the budget line KL, dened as rise over run (see Chapter 2), is the vertical intercept of the line KL ( I / P y ) divided by the horizontal intercept ( I / Px ). Since an increase in x is associated with a decrease in y, the sign is negative: Slope of budget line y x I I / Py Px I / Px Py (4.2) In the notation here, x and y represent small changes in x and y. (The vertical bar with subscript I signies that the slope is measured along a curve or line where income I is held constant.)2 EXERCISE 4.1 Suppose the price of apples is Pa = 10, the price of beer is Pb = 2, and Sams income is I = 100. (a) If Sam consumes only these two goods, what is the equation of his budget line? With beer on the vertical axis, what are the intercepts? What is the slope? (b) What would happen if, with income unchanged, the price of apples were halved? (c) What if, with the original prices unchanged, income doubles? A N S W E R : (a) The equation of the budget line is 10a + 2b = 100. The vertical b- intercept is 100/2 = 50; the horizontal a-intercept is 100/10 = 10. The slope is 50/10 = 5. (b) If Pa is halved, the equation of the budget line becomes 5a + 2b = 100. The a-intercept becomes 20 instead of 10; the b-intercept is unchanged. Geometrically, the budget line swings out to the right from the unchanged vertical intercept, with a new atter slope equal to 50/20 = 2.5. (c) If income doubles while the original prices are unchanged, the equation of the budget line becomes 10a + 2b = 200. Both intercepts double. Geometrically, the budget line retains the old slope 100/20 = 5 but shifts outward parallel to itself. 2 Mathematical Footnote : In terms of calculus, the derivative dy/dx replaces the ratio y / x of nite increments. Along the straight line P x x + P y y = I , with income I held constant, standard calculus techniques show that the derivative is d y /d x = P x / P y . (In this case the derivative is the same as the slope dened in terms of nite increments, as always holds for a straight line.) P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 96 y 4. CONSUMPTION AND DEMAND Preference Directions K Quantityof Y C Figure 4.2. Concave Indifference Curves and Corner Solution If the indifference curves have the usual negative slope but are concave to the origin, the best attainable position along the budget line KL must be a corner solution, at one or the other axis. Here the optimum of the consumer, C on the y-axis, lies on indifference curve U4 . U2 U3 U4 L Quantityof X x T U1 Now we want to locate the consumption basket that maximizes utility. In Figure 4.1, along the budget line KL the consumer attains the highest indifference curve U2 at point C the consumption basket containing x units of commodity X and y units of commodity Y. Although there are baskets preferred to (on a higher indifference curve than) C , any such bundle lies above the line KL; it would therefore require spending more than the income I available. And the points Q and R along KL, though attainable, lie on a lower indifference curve. At the optimum point C the indifference curve U2 is tangent to the budget line. For less desired combinations such as Q and R along KL, the indifference curve cuts through (and so is not tangent to) the budget line. As described in Chapter 3, convexity is one of the essential features of indifference curves. That is, a line connecting any two points on an indifference curve lies above the curve, so the curve bulges toward the origin. Convexity is not a necessary inference from the Laws of Preference, but is founded upon the empirical principle of diversication in consumption. Suppose indifference curves were not convex but concave, as in Figure 4.2 Again there is a tangency between the budget line KL and indifference curve U2 (at point T ). But now the tangency is not the optimum for the consumer. Indeed, T is the least preferred basket attainable along the budget line KL: a consumer who moves in either direction from T can get onto higher indifference curves such as U3 or U4 . In Figure 4.2 the true optimum is at C , where all of the available income is spent on the single good Y. Such an outcome is called a corner optimum, as opposed to the interior optimum C in Figure 4.1 At a corner solution you would devote all your income to purchasing one good, buying none of the other. But people never limit themselves to consuming only a single good they diversify their consumption. That is why, on observable empirical grounds, concave indifference curves must be rejected. Consider, however, the following situation. Suppose you like Beluga caviar (it is a good for you), but its so expensive you feel you cant afford to buy any. In Figure 4.3, suppose that X is caviar and Y is everything else. The diagram illustrates how, with indifference curves of normal convex curvature, the consumer can still attain a corner optimum at C where consumption of X is zero. The upshot is that convex indifference curves are consistent both with interior solutions, as in Figure 4.1, and with corner solutions, as in Figure 4.3. In contrast, if indifference curves were concave, only corner solutions would be possible. P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 4.1 THE OPTIMUM OF THE CONSUMER 97 y Preference Directions If indifference curves are convex to the origin, the optimum of the consumer may be either in the interior or at a corner. Here the optimum along the budget line KL is the corner solution C . Quantityof Y Figure 4.3. Convex Indifference Curves and Corner Solution K C U3 U2 U1 0 x L Quantityof X CONCLUSION The optimum of the consumer is the point on the budget line that touches the highest attainable indifference curve. With convex indifference curves, the optimum can be an interior solution where positive amounts of both commodities are bought. Or it can be a corner solution: the budget line reaches the highest attainable indifference curve along an axis, so that one of the commodities is not bought at all. Optimum of the Consumer (Cardinal Utility) This section interprets the optimum of the consumer in terms of Marginal Utility (MU ). Recall that, as discussed in Chapter 3, one can speak of larger or smaller MU only when utility is a cardinal variable. In addition, diminishing Marginal Utility is assumed: for any good X, as the amount of X increases, MUX falls (refer back to Figure 3.2).3 If two goods X and Y are consumed in positive amounts, the consumer is at an interior optimum when the following Consumption Balance Equality is satised: MU y (when y > 0) MUx (when x > 0) = Px Py Consumption Balance Equality (interior solution) (4.3) The explanation is immediate. For any good, Marginal Utility divided by price is Marginal Utility per dollar spent. At the optimum, the last dollar spent on X must yield the same satisfaction as the last dollar spent on Y. EXERCISE 4.2 An apple costs 50 cents and a nectarine costs 25 cents each. Mary initially buys 10 apples and 5 nectarines. At this point suppose her Marginal Utility for an apple is 3 units of utility (utils) and for a nectarine is 1 util. Is Mary at an optimum? (Assume she is willing to accept fractional quantities.) 3 Mathematical Footnote : Marginal Utility corresponds to the derivative dU /d x . The assumption here is that dU /d x > 0, but d 2 U /d x 2 < 0. That is, Marginal Utility is a positive but decreasing function of x. P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 98 4. CONSUMPTION AND DEMAND A N S W E R : For an interior optimum, her Marginal Utility per dollar spent must be equal for the two goods. In terms of equation (4.3), 3/0.50 = 6 exceeds 1/0.25 = 4. So her MUa / Pa for apples exceeds her MUn/ Pn for nectarines; hence Mary is not at an optimum. She should shift some of her spending from nectarines to apples. Giving up one nectarine means a sacrice of 1 util, but that leaves 25 more cents to spend on apples. At a price of 50 cents, the extra 25 cents buys half an apple, yielding 3/2 = 1.5 additional utils in place of the 1 util sacriced. What about the possibility of a corner solution? Suppose that commodity Z is Beluga caviar, whose price is so high that its MUz / Pz remains lower than MU y / P y even for the very rst unit of caviar bought. At such a corner optimum a Consumption Balance Inequality holds, as shown in Equation (4.3 ): MU y (when y > 0) MUz (when z = 0) < Pz Py Consumption Balance Inequality (corner solution) (4.3 ) If (4.3 ) is satised, at the optimum the consumer will be consuming only the numeraire good Y. EXERCISE 4.3 For Andrew, the Marginal Utility of bread is MUb = 30 b. The Marginal Utility of wine is MUw = 40 5w. (That Andrews MUb depends only on the quantity b, and his MUw only on the quantity w, is a special assumption made for illustrative purposes only.) (a) Suppose the prices are Pb = 1 and Pw = 5, and his income is I = 40. Find the consumption optimum for Andrew. (b) What if his income were instead I = 10? A N S W E R : (a) Here the budget equation (4.1) is b + 5w = 40. Any interior solution must satisfy the Consumption Balance Equality (30 b)/1 = (40 5w)/5. Solving the two equations simultaneously, the solution is b = 25, w = 3 (an interior solution). (b) Now the budget equation becomes b + 5w = 10. Solving simultaneously with the Consumption Balance Equality leads algebraically to b = 20, w = 2. But a negative consumption quantity is economically impossible. The best Andrew can do is move to the corner solution, where he sets w = 0, allowing him to buy b = 10 units of bread. Consider now three commodities X, Y, and Z. For an interior solution it is simple to add an additional equality to the Consumption Balance Equality: MU y ( y > 0) MU y (z > 0) MUx (x > 0) = = Px Py Pz Consumption Balance Equality (interior (4.4) solution,three goods) But now suppose that, at the optimum, commodities X and Y are bought but Z is not. P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 4.1 THE OPTIMUM OF THE CONSUMER 99 b Crusoes opportunity set, the shaded region, is bounded by his Production-Possibility Curve for producing combinations of sh and bananas for his own consumption. His consumption optimum is the tangency point C (an interior solution). QuantityofBananas Figure 4.4. Consumption Optimum for Robinson Crusoe Q C U U ProductionPossibilityCur ve f 0 Q QuantityofFish Then an equality holds as between commodities X and Y but an inequality with regard to Z: Consumption Balance Equality/Inequality (4.4 ) (mixed solution, three goods) MU y ( y > 0) MU y (z = 0) MUx (x > 0) = > Px Py Pz This is the condition for a mixed interior/corner solution. Marginal Utility per dollar is equalized for the two commodities X and Y that are consumed in positive amounts: MUx / Px = MU y / P y . Commodity Z is not bought at all, because even for the very rst unit that might be consumed, MUz / Pz is less than MUx / Px = MU y / P y . Generalizing these results: ANALYTIC OPTIMUM PRINCIPLE (CARDINAL UTILITY): For all goods consumed in positive quantities, at the optimum the Consumption Balance Equality holds (Marginal Utility per dollar is the same for each). For any good not consumed at all, its Marginal Utility per dollar must be smaller, even for the very rst unit, than the Marginal Utility per dollar of the goods consumed in positive quantities. A digression: The analysis so far has dealt only with market opportunities. But even an individual isolated from markets needs to choose among alternative possible consumption baskets. Figure 4.4 shows how Robinson Crusoe might choose among differing combinations of sh and bananas. In the absence of markets, Robinsons opportunity set (the shaded region) is bounded not by a market budget line but by the ProductionPossibility Curve shown in the diagram. The Production-Possibility Curve will be taken up in more detail in Chapter 13, but note that its curvature represents a kind of diminishing returns in production. (As Robinson tries to catch more sh, he has to sacrice increasing amounts of bananas, and conversely if he tries to produce more bananas.) The diagram illustrates an interior solution where Robinsons optimum is at the tangency point C . P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 100 4. CONSUMPTION AND DEMAND EXAMPLE 4.1 SMART ANTS Ant colonies, like some primitive foraging tribes (see Example 2.11), must meet their nutritional needs without dealing in markets. Ants do not go through rational thinking processes or, at least, we humans do not give them credit for doing so. Instead, as explained in the preceding chapter, efcient patterns of behavior tend to be selected for evolutionary survival by Mother Nature. The biologist Adam Kay studied the foraging choices of the ant species Dorymyrmex smithi.a These ants forage for proteins and carbohydrates as nutrients. In the experiment six colonies were provided with a certain amount of 6% casein solution each day for free, to see if that would affect their foraging choices between sources of casein (a protein) and sources of sucrose (a carbohydrate). A control group of six colonies were treated the same way except that, as a kind of placebo, plain water replaced the 6% casein solution. The rst data column shows the average choices of the control group, which can be taken to represent the normal foraging pattern for these ants. (The foraging options were controlled so that the ants could go to casein sources, to sucrose sources, or to sources representing a 50:50 mixture of the two nutrients.) The last column shows the choices of the groups receiving the casein supplement. As can be seen, under normal conditions the ants divided their efforts fairly evenly between sucrose (carbohydrate) and casein (protein). But given the casein supplementation, they chose to devote more effort to seeking sucrose. COMMENT The ants behavior was consistent with diminishing Marginal Utility. The free casein supplement reduced the Marginal Utility of protein relative to carbohydrate, so they shifted their foraging effort away from casein and toward sucrose. Ant choices proteins versus carbohydrates collected (% of total) Only water provided Sucrose only Mixture Casein only 20% 48% 32% Casein supplement provided 48% 37% 15% Source: Estimated visually from Kay, Figure 2. a Adam Kay, The Relative Availabilities of Complementary Resources Affect the Feeding Preferences of Ant Colonies, Behavioral Ecology, v. 15 (1993). Optimum of the Consumer (Ordinal Utility) The preceding analysis assumed cardinal (measurable) utility. But, as indicated in the preceding chapter, in economics the weaker assumption of ordinal utility usually sufces. The crucial idea is to think in terms of the ratio at which a person is just willing to substitute a small amount of Y for a small amount of X in his consumption basket. This ratio is called the Marginal Rate of Substitution in Consumption (MRSC ). The P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 4.1 THE OPTIMUM OF THE CONSUMER 101 y l/3 Quantityof Y Figure 4.5. Marginal Rate of Substitution in Consumption (MRSC ) and the Price Ratio (Px /Py ) At point A, MRSC , the absolute value of the indifference-curve slope, is approximated by the ratio AD/DB = 5/2. The price ratio Px / P y is the absolute value of the budget-line slope. In the diagram, this slope is AD/DG = 5/3. Since the two slopes are unequal, point A cannot be an optimum for the consumer. A 5 G D 2 B U l =5 x +3 y l/5 Quantityof X x expression just willing to substitute Y for X means a substitution of Y for X that leaves the consumer indifferent. So MRSC is dened as: MRSC y x (4.5) U The vertical bar with the subscript U indicates that the ratio is evaluated holding utility constant. Since constant utility is what denes an indifference curve, MRSC corresponds to the slope at a specied point along an indifference curve. Because MRSC is dened as positive whereas normal indifference curves have negative slope, the ratio on the right-hand side of (4.5) is preceded by a minus sign.)4 In Figure 4.5, suppose Ellen is initially at point A, holding the basket x = 3, y = 15. Consider the alternative basket x = 5, y = 10 represented by point B. Since baskets A and B lie on the same indifference curve, they are equally preferred. In moving from A to B, the change in Y is y = 5 and the change in X is x = +2. The ratio 5/2, the slope of the line connecting points A and B, therefore approximates (after reversing the sign) Ellens MRSC in the neighborhood of points A and B. (The smaller the changes considered, the better the approximation.) MRSC represents the ratio at which the consumer is willing to substitute Y for X. To nd the consumption optimum, one must also know the ratio at which the market permits the two goods to be traded. That rate of exchange is the price ratio Px / P y . Returning to Figure 4.5, suppose the prices are Px = 5 and P y = 3. Then it is possible to exchange 5 units of Y in the market for 3 units of X. But Ellen was willing to give up 5 units of Y for 2 units of X. So, although she was willing to move from A to B, the market permits a movement to point G on a higher indifference curve. Ellen should therefore make the trade. In fact, it is always possible to make an advantageous exchange, one way or the other, whenever there is any discrepancy between MRSC and Px / P y between the rate at which the consumer is willing to make such substitutions and the rate at which the market permits trades. This principle can be expressed as the Substitution 4 Mathematical Footnote : The denition of MRSC in the text is expressed in terms of nite changes Using calculus this ratio becomes the derivative d y /d x |U . x and y. P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 102 4. CONSUMPTION AND DEMAND t t K C Tea Tea K U0 U1 U2 U2 U1 U0 0 Coffee Panel(a) EnglishPr isoners L c 0 Coffee Panel(b) FrenchPr isoners C c L Figure 4.6. Coffee versus Tea in a P.O.W. Camp English and French P.O.W.s had differing tastes for tea versus coffee. An efcient smuggling system equalized the price ratio Pc / Pt in the two sectors of the camp. At these prices the English optimum C involved relatively heavy consumption of tea, whereas the French optimum C was more heavily weighted toward coffee. Balance Equation, which holds for any interior optimum: MRSc = Px / P y Substitution Balance Equation (interior optimum) (4.6) Equation (4.5) was an identity, a denition of MRSC , as indicated by the identity sign (). But equation (4.6) is a conditional equality, and so the equals (=) sign is used.5 The relation between MRSC and the price ratio in (4.6) is not determined by denition. Rather, it is the condition that must obtain at an interior optimum.6 EXAMPLE 4.2 PRISONERS OF WAR: TEA VERSUS COFFEE As a prisoner of war in Germany and Italy during World War II, the economist R. A. Radford found that highly active markets functioned in the camps.a Cigarettes generally served as the numeraire (or standard good), so that prices for other goods were quoted in terms of cigarettes. A shirt might cost 80 cigarettes, washing services 2 cigarettes per garment, and so forth. In the section for British prisoners, tea was preferred to coffee. In the French section, coffee was preferred to tea. The two panels of Figure 4.6 illustrate the situations of typical British and French prisoners. Owing to an efcient smuggling trade between the sections, the coffee-tea price ratio Pc / Pt was about the same for both groups of prisoners. But for the British prisoners, the tangency point C (where 5 6 In this text, as in scientic writing generally, the ordinary = sign can optionally be used for identities when no confusion is likely to arise. Mathematical Footnote : Equation (4.6) is derived easily from equation (4.3), the Consumption Balance Equality in terms of Marginal Utilities. After simple transpositions, the left-hand side of equation (4.3) can be written as the ratio of Marginal Utilities and the right-hand side as the ratio of prices. Since MRSC equals the ratio MUx /MUy , making that substitution immediately yields equation (4.6). P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 4.1 THE OPTIMUM OF THE CONSUMER 103 MRSC = Pc / Pt ) was well over toward the tea axis; for the French prisoners the optimum C lay toward the coffee axis. a R. A. Radford, The Economic Organization of a P.O.W. Camp, Economica, v. 12 (1945). For corner solutions, the Substitution Balance Equation becomes an inequality instead. If the consumer buys none of commodity X, it must be that: MRSc < Px / P y when x = 0 Substitution Balance Inequality (4.6 ) (A corresponding equation holds if the consumer buys none of the other commodity, Y.) Summarizing: ANALYTIC OPTIMUM PRINCIPLE (ORDINAL UTILITY): If the optimum of the consumer is an interior solution along the budget line, with positive amounts of both commodities bought, then MRSC , the Marginal Rate of Substitution in Consumption, must equal the price ratio Px / Py . This corresponds to the geometrical tangency of the budget line and indifference curve. But when the best attainable position along the budget line is at a corner (along one of the axes), it will generally be impossible to set MRSC equal to Px / Py . Reducing consumption of one or the other commodity to zero brings MRSC and Px / Py as near to equality as possible. A more intuitive terminology is sometimes useful to avoid the awkward expression Marginal Rate of Substitution in Consumption. Suppose Y stands for the numeraire commodity (e.g., corn) serving as standard of value. Then the MRSC between X and Y can be interpreted as good X s Marginal Value MVx in terms of the numeraire commodity. Thus MVx is the consumers marginal willingness to pay for X, in units of the numeraire good Y. Recall that, by denition, the numeraire good Y has price PY 1. Then for any nonnumeraire good X, in Marginal Value terminology the Substitution Balance Equation and Inequality become: MVx = Px MVx < Px when x > 0 when x = 0 Substitution Balance Equation (interior optimum) Substitution Balance Inequality (4.7) The consumer will increase purchases of any good X as long as its Marginal Value MVx exceeds its price Px , both measured in terms of the numeraire good Y. If equality can be achieved, the individual is at an interior solution. But if MVx remains less than Px even when x = 0, the optimum is along the Y axis (corner solution). EXERCISE 4.4 Edgars preferences are represented by the Marginal Rate of Substitution MRSC = 2 y/x . His income is I = 180. The market prices are Px = 3 and Py = 1. (a) What is his optimal consumption basket? (b) Express the result in terms of Marginal Value (MV ). A N S W E R : (a) The Substitution Balance Equation (4.6) provides one of the equations needed: MRSC = 2 y/x = Px / Py , or 2 y = 3x /1. The consumption optimum must P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 104 4. CONSUMPTION AND DEMAND also satisfy the budget equation Px x + Py y = I ; this becomes here 3x + y = 180. When these two equations are solved simultaneously, the solution is x = 40, y = 60. (b) Since Py = 1, equation (4.7) can be written MVx = 2 y/x = Px , or 3x = 2 y. Substituting Px x into the budget equation above leads to 2 y + y = 180. The solution is the same as before: y = 60, x = 40. An important implication of the analysis is that, despite differences of tastes, at interior solutions everyone ends up with the same MRSC or, equivalently, the same Marginal Value MVX . In our P.O.W. example the French prisoners preferences inclined toward coffee and the British prisoners preferences toward tea. Nevertheless, once each group adapted to the ruling prices, on the margin a French prisoner was no more willing than an English prisoner to give up a unit of tea for a unit of coffee. Thus, even though utility is subjective, as a result of trade the objective price ratio between two goods in the market measures the marginal preference ratio for everyone consuming both goods. 4.2 COMPLEMENTS AND SUBSTITUTES Certain commodities go well together and tend to be consumed in combination: bread and butter, shoes and socks, CD players and CD discs. Such pairs of goods are called complements. Other commodity-pairs go poorly together and tend to be used to the exclusion of one another: for example, butter and margarine, shoes and sandals, CDs and DVDs. Such pairs are called substitutes or anticomplements. (Pairs of goods that are on the borderline, neither complements nor anticomplements, are said to be independent in consumption.) Consider two commodities that consumers might regard as perfect substitutes. A person may be completely indifferent between 2 nickels and 1 dime, 20 nickels and 10 dimes, 200 nickels and 100 dimes, and so on. Then the preference map will look like Panel (a) of Figure 4.7: the indifference curves are parallel straight lines. For two goods that are close but not quite perfect substitutes, such as Jonathan apples and Granny Smith apples, the indifference curves would be almost linear, as in Panel (b). The observable characteristic of close substitutes is that a small change in relative prices brings about large changes in relative consumption. Suppose Roger has the preferences pictured in Panel (b), and initially faces a steep budget line like SS in the diagram. The steep budget line means that Granny Smith apples are expensive compared to Jonathan apples. Rogers best consumption bundle is S , where he mostly buys inexpensive Jonathan apples. An only moderately atter budget line such as FF in the diagram (representing a slightly lower relative price of Granny Smiths) leads him instead to the drastically different consumption bundle F , where he now chooses mostly Granny Smith apples. The extreme opposite case is perfect complementarity. Here the consumer wants to buy goods in some xed ratio (for example, one left shoe for each right shoe). Panel (a) of Figure 4.8 shows the right-angled indifference curves implied by perfect complementarity. The slope of the dashed line through the elbows represents the desired ratio of the two commodities. (For right and left shoes this would be 1:1, or a slope of 45 .) Moving away from the extreme case, when two goods are strong though not perfect complements examples include bagels and cream cheese, electricity and electric appliances, and roads and automobiles the indifference map would be as in P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 4.2 COMPLEMENTS AND SUBSTITUTES 105 j S n 40 JonathanApples 30 Nickels S F 20 F U2 15 Dimes Panel(a) PerfectSubstitutes U3 d 0 10 20 0 U1 U2 U3 g U1 S F GrannySmithApples Panel(b) CloseSubstitutes Figure 4.7. Substitute Commodities The indifference curves of Panel (a) are parallel straight lines, indicating that the two commodities (nickels and dimes) are prefect substitutes. If the price ratio in the market, represented by the slope of the budget line, differs from the slope of the indifference curves, the consumer will go to a corner solution. In Panel (b) the indifference curves have a slight degree of normal convex curvature, indicating that the two commodities (Granny Smith apples and Jonathan apples) are close, though not perfect, substitutes. A relatively small change in the price ratio (from the slope of line SS to the slope of line FF ) causes a relatively large change in consumption (from S to F ), though not a total switch from one good to the other. Panel (b). If two goods are complements, then large changes in price ratios lead to only small shifts in relative quantities bought. In Panel (b), along the steeper budget line SS , the optimum solution S differs little from the optimum F along the much atter budget line FF . EXERCISE 4.5 Suppose Evelyns Marginal Rate of Substitution in Consumption between wine and bread is MRSC = w/b. For another commodity pair, roses and daisies, it is MRSC = (r /d )2 . Which pair are closer substitutes in Evelyns utility function? A N S W E R : Plotting a few points, you can verify that the indifference curves for wine versus bread are more tightly curled, as in Figure 4.8(b), whereas for roses versus daisies the indifference curves are relatively at, as in Figure 4.7(b). Evelyn nds roses and daisies to be closer substitutes for one another than wine and bread. The Examples that follow provide clues as to when commodities are likely to be complements, or conversely to be substitutes. P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 106 4. CONSUMPTION AND DEMAND l S 1:1Ratio ElectricalAppliances a LeftShoes U3 U2 F S F U3 U2 U1 U1 r RightShoes Panel(a) PerfectComplements 0 0 e S Electricity Panel(b) StrongComplements F Figure 4.8. Complementary Commodities The right-angled indifference curves of Panel (a) indicate that the two commodities (right shoes and left shoes) are perfect complements. A change in the price ratio has no effect on the quantity ratio chosen, which will always be 1 : 1 at the best attainable elbow point. In Panel (b) the indifference curves are nearly, but not quite, right-angled: the commodities (electricity and electrical appliances) are strong, though not perfect, complements. Here a relatively large change in the price ratio (from the slope of line SS to the slope of line FF ) induces only a relatively small change in the quantity ratio (from S to F ). EXAMPLE 4.3 RATS A team of psychologists and economists investigated how rats responded to changes in price ratios of desired goods.a In the rst experiment, the rodents were given unlimited amounts of water and rat chow. They could obtain two other commodities root beer and Collins mix by pressing one of two levers. A rats income was the total number of lever presses allowed per day. The price was the number of presses required per milliliter of uid. The experimenters varied the price ratio by increasing one price and simultaneously reducing the other in such a way that each rat remained approximately on the same indifference curve. Root beer and Collins mix proved to be substitutes for these rats: just as in Figure 4.7, Panel (b), the consumption ratio shifted substantially when the price ratio changed even by a small amount. In a second experiment, unlimited food and water were no longer provided, but instead became the two commodities bought by pressing the appropriate lever. When the price ratio between water and rat chow was varied (again holding real income approximately constant), the picture was more like Figure 4.8, Panel (b): the consumption ratio remained about the same. So food and water were strong complements. COMMENT When unlimited amounts of water and rat chow are provided, root beer and Collins mix are not essential nutrients for the rats. Since the proportions consumed P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 4.3 THE CONSUMERS RESPONSE TO CHANGING OPPORTUNITIES 107 seemed hardly to matter, the rats responded mainly to the relative prices of the two uids. In contrast, water and food are both essential to life. Forced to choose between these essentials, the rats, despite changing price ratios, probably could not diverge much from the physiologically necessary proportionality between water intake and food intake. a J. H. Kagel, H. Rachlin, L. Green, R. C. Battalio, R. L. Basmann, and W. R. Klemm, Experimental Studies of Consumer Demand Behavior Using Laboratory Animals, Economic Inquiry, v. 13 (March 1975). 4.3 THE CONSUMERS RESPONSE TO CHANGING OPPORTUNITIES If preferences do not change, the optimum of the consumer can vary only in response to changes in opportunities. A persons market opportunities depend on two elements: (1) his or her income and (2) commodity prices. This section examines how optimal consumption choices vary in response to changes in income only. (Among other applications, this question could be important in studying what would happen if the government were to redistribute income from some people to others.) The Income Expansion Path Consider a simplied world of only two commodities X and Y. In Figure 4.9 the consumers original optimum is at point Q, where the budget line KL is tangent to indifference curve U0 . (Point Q here corresponds to point C in Figure 4.1.) If income rises from I to I while prices are held constant, the budget line shifts outward parallel to itself, from KL to K L . (The slope of the budget line, Px / P y , is the same for KL and K L .) The new optimum position is at point R, where the budget line K L is tangent to the higher indifference curve U1 . And a further increase in income from I to I shifts the budget line further outward to K L , with the optimum at the tangency position S on indifference curve U2 . More generally, as income varies while prices and tastes remain unchanged, an entire curve is traced out connecting all the different optimum positions like Q, R, and S. This curve is the Income Expansion Path (IEP). Each different price ratio generates a different Income Expansion Path. In particular, Figure 4.9 shows how a smaller ratio Px / P y (implying atter budget lines) would be associated with a new Income Expansion Path (IEP ) that lies below the original one. EXERCISE 4.6 Williams Marginal Rate of Substitution in Consumption is MRSC = y/x . The market prices are Px = 5 and Py = 1. (a) What is the equation of his Income Expansion Path, and what does the curve look like? (b) How would the Income Expansion Path change if the price of X fell to Px = 4? A N S W E R : (a) From the Substitution Balance Equation (4.6), MRSC = y/ x = Px / P y = 5/1 = 5. So the equation for the Income Expansion Path is y = 5x , which is a ray out of the origin with slope 5. (b) With Px = 4, the equation of the Income Expansion Path would be y = 4x (a atter ray out of the origin, with slope 4). P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 108 4. CONSUMPTION AND DEMAND y l /Py K Quantityof Y l /Py K IEP IEP S l /Py K Q U0 0 l /Px R U2 U1 L L l /Px Quantityof X L l /Px x Figure 4.9. Derivation of the Income Expansion Path As income increases from I to I to I , with prices Px and P y held constant, the budget line shifts outward from KL to K L to K L . The tangency dening the consumer optimum correspondingly shifts from Q to R to S. The Income Expansion Path (IEP) shows all the optimum consumption bundles for the consumer as I varies, with prices remaining the same. For a smaller price ratio Px / P y (the corresponding atter budget lines are not shown in the diagram) the IEP lies further down and to the right, as indicated by the dashed IEP curve. What shapes are possible for the Income Expansion Path? Consider Figure 4.10. In both panels the original optimum is at point Q, where indifference curve U0 is tangent to budget line KL. Now let income increase, so that the budget line shifts to K L . In Panel (a) the new tangency point R lies northeast of Q : the Income Expansion Path has positive slope. This means that, given increased income, the consumer would buy more of both X and Y. When this holds, X and Y are both said to be superior goods. In Panel (b) the new tangency R lies northwest of Q, meaning that at higher income the consumer chooses more Y but less X. Here Y remains a superior good. But X, whose consumption falls when income rises, is an inferior good. Since Y would be called superior in the situation of either Panel (a) or Panel (b), it is convenient to have a terminology that distinguishes the two cases. For the situation of Panel (a), X and Y can be termed normal superior goods. For the situation of Panel (b), where X is inferior, the partner good Y might be called ultrasuperior. Less of the inferior good being purchased, once income rises, means that the amount spent upon the ultrasuperior partner exceeds the increase of income. Last, a third type of curve (not shown in Figure 4.10) could be drawn for the case where Y is inferior and X ultrasuperior. In that third diagram the slope of the Income Expansion Path would again be negative, but the upward utility direction along the Income Expansion Path (as shown by the arrowhead) would point to the southeast rather than northwest. CONCLUSION For two goods X and Y, a positively sloped Income Expansion Path indicates that consumption of both goods rises as income grows. Then X and Y are called normal P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 4.3 THE CONSUMERS RESPONSE TO CHANGING OPPORTUNITIES 109 y K K IEP Quantityof Y K V R Q T U1 U0 0 L Quantityof X Panel(a) Xand Ynor mal L x Quantityof Y y IEP R K Q U1 U0 0 L L Quantityof X Panel(b) Xinf erior, Yultr asuperior x Figure 4.10. Income Expansion Paths: Superior and Inferior Goods The outward shift of the budget line (from KL to K L ) represents an increase in income I, with prices held constant. In Panel (a) the Income Expansion Path (IEP) points north and east. Here both X and Y are normal superior goods. In Panel (b) the IEP points north and west; here X is an inferior good, and Y is an ultrasuperior good. superior goods. If instead the Income Expansion Path has negative slope, one of the goods must be inferior. The other good must of course be superior, but more specically may be called ultrasuperior because more than 100% of the increment of income now goes to purchasing it. EXERCISE 4.7 (a) Georges preferences are described by the condition MRSC = y/x . Are goods X and Y both normal for him, or is one of them inferior? (b) What if his preferences are given by MRSC = y? A N S W E R : (a) When MRSC = y/ x the Substitution Balance Equation (4.6) is y/ x = Px / Py . Solving for y, the equation of the Income Expansion Path is y = Px x / Py . Since Px and Py are both positive constants, the IEP has positive slope, as in Panel (a) of Figure 4.10. Then X and Y are normal superior goods. (b) If MRSC = y, the equation for the IEP becomes y = Px / Py . So the Income Expansion Path is a horizontal line on x,y axes. This means that 100% of any income increase will be spent on good X. Here X is a superior good. Good Y, while not inferior, is just on the borderline of being so. EXAMPLE 4.4 HOW MUCH ARE CHRISTMAS GIFTS WORTH? Would you rather get a gift of $20 in cash, or two neckties that cost $10 each? Economic analysis suggests that cash is better. You can use the cash to buy the two ties, if you like, but you dont have to. Perhaps you are already satised with the ties you now own. If so, your marginal willingness to pay for additional ties could be less than the store price. P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 110 4. CONSUMPTION AND DEMAND x Quantityof X Superiorgood Inferiorgood(f orl > I ) 0 I Income i Figure 4.11. Engel Curve For any good X , the Engel Curve shows the quantity purchased as a function of income. For a superior good, the Engel Curve has positive slope. An inferior good has negative slope; however, a good cannot be inferior over the entire range of income. Joel Waldfogel surveyed 86 economics students about their holiday gifts.a The students were asked how much they would have been willing to pay in cash for the gifts received, in comparison with their guess as to how much the donors had actually paid. On average, givers had paid a total of $438.20, whereas as recipients the students would have been willing to pay on average of only $313.40 for those items about 71.5% as much. In Figure 4.10, Panel (a), the vertical axis represents cash and the horizontal axis represents noncash gifts; both commodities are assumed to be normal superior goods. If the pregift optimum was at point Q, a cash gift would move the recipient to the vertically higher point V. The cash gift would in effect increase income; the recipient would likely want to spend some of the cash to move to the tangency optimum point R. (This could mean, for example, spending $10 of the $20 gift on one tie but using the remaining $10 to buy something else.) But the gift in noncash form, assuming it is nonreturnable, moves the recipient from point Q to point T which is less preferred than point R. COMMENT Does that mean that donors should always give cash? Not necessarily! A noncash gift may signal that the donor cares enough to devote time and thought to what the recipient desires or needs. Even if the choice itself misses the mark, the recipient may value the expression of concern that lies behind it. a Joel Waldfogel, The Deadweight Loss of Christmas, American Economic Review, v. 83 (December 1989), pp. 13281336. The Engel Curve The Income Expansion Path shows how consumption baskets (combinations of goods) change as income rises of falls. The Engel Curve pictures the effect of income changes upon a single good X.7 Two possible Engel Curves are shown in Figure 4.11. The 7 Ernst Engel (18211896), German statistician. P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 4.3 THE CONSUMERS RESPONSE TO CHANGING OPPORTUNITIES 111 c Figure 4.12. Food versus Cigarettes in a P.O.W. Camp After a halving of cigarette and food rations, the typical P.O.W. was forced from an initial position like Q to a less preferred outcome Q . Under these circumstances it was observed that Pf / Pc , the price of food in terms of cigarettes fell. Since Pf / Pc = MRSC at the consumers optimum, we know that MRSC (the absolute value of the slope of the indifference curve) must have been less at lower incomes. That is, cigarettes were relatively more preferred at lower levels of income. c Cigarettes f Q Q c f 0 Food U U f upward-sloping curve represents a superior good (the quantity bought always increases as income rises). The hill-shaped curve shows a good that is initially superior, but beyond a certain level of income becomes inferior. Lower-quality cuts of meat, for example, might be a superior good for poorer people but an inferior good for the wealthy. [Note : a good X cannot be inferior over its entire range, as that would require positive purchases of X even when income I is zero which is impossible.] EXAMPLE 4.5 LUXURIES VERSUS NECESSITIES IN A P.O.W. CAMP Goods mostly bought by wealthy people are commonly called luxuries. Goods whose consumption does not vary very much between rich and poor are sometimes termed necessities even if, strictly speaking, they are not essential for life. On these denitions, standard food items like bread or breakfast cereals are necessities. Although richer people can afford to and generally do buy more bread than poorer people (that is, bread is usually not an inferior good), the proportion of the budget spent on bread tends to fall as income rises. In the prisoner-of-war economy described above, R. A. Radforda made interesting observations about necessities and luxuries. As the Germany economy worsened toward the end of the war, the Allied prisoners suffered severe privation. In August 1944 rations for food and cigarettes were cut in half from an already low level. Unexpectedly, after the rations were reduced, the price of food, as measured in terms of cigarettes, fell. Thus cigarettes proved to be more of a necessity (by the standard denition above) than food. COMMENT Figure 4.12 shows the implied shape of prisoners indifference curves between cigarettes C and food F. At point Q , where income is very low, the indifferencecurve slope (Marginal Rate of Substitution in Consumption) MRSC = c/ f is less than at the higher income level (point Q ). a R. A. Radford, The Economic Organization of a P.O.W. Camp, Economica, v. 12 (1945). P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 112 K 4. CONSUMPTION AND DEMAND I/Py PEP Quantityof Y Figure 4.13. Derivation of the Price Expansion Path A fall in the price of good X (with income I and the price of the other good Y held constant) tilts the budget line outward (from KL to KL to KL ). The optimal consumption bundle shifts from Q to R to S. The Price Expansion Path (PEP) connects all such optimum positions; the arrowhead on the PEP curve indicates the direction of utility improvement. x Q R S U2 U0 U1 L Quantityof X L 0 L Price Expansion Path and Demand Curve The previous section dealt with changes in income. This section discusses changes in price. More specically, how does the consumers best choice respond when a specic price Px changes, holding income and prices of other goods constant? In Figure 4.13 the optimum is initially at Q where the budget line KL is tangent to indifference curve U0 . Now let the price of X fall. The intercept of the budget line along the vertical Y-axis is unchanged at I / P y . But since the intercept of the budget line with the horizontal X-axis is I / Px , the budget line swings outward to a new position like KL . The consumers new optimum is at point R where KL is tangent to a higher indifference curve U1 . A further decline in Px leads to further outward tilting of the budget line, to the position KL ; here the optimum is at S on the still higher indifference curve U2 . The curve connecting all the optimum positions like Q, R, and S is called the Price Expansion Path (PEP). Just as there was a different Income Expansion Path for each different price ratio Px / P y , there is a different PEP for each possible level of income. EXERCISE 4.8 Roberts Marginal Value for good X (his marginal willingness to pay in terms of the numeraire commodity Y ) is given by MVx = y. His income is I = 120. (a) What is the equation for his Price Expansion Path and what is its shape? (b) How would his Price Expansion Path change if income increased to I = 150? A N S W E R : (a) The Substitution Balance Equation (4.7) here becomes MVx = y = Px . The budget line is Px x + Py y = I , or (since Py 1) Px x + y = 120. The two equations need to be combined into a single equation involving x and y (since the Price Expansion Path is drawn on x,y axes). Eliminating Px between the two equations, the Price Expansion Path is y(x + 1) = 120. This Price Expansion Path has a yintercept of 120. Like the Price Expansion Path of Figure 4.13, it slopes down from the y-intercept; unlike that curve, it never curls up again but approaches (without ever intersecting) the horizontal axis. (b) If income is I = 150, the equation of the Price Expansion Path becomes y(x + 1) = 150. The intercept on the y-axis is higher and the curve shifts generally to the right. P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 4.3 THE CONSUMERS RESPONSE TO CHANGING OPPORTUNITIES 113 y K Quantityof Y Figure 4.14. Price Expansion Path: Giffen Case The Price Expansion Path (PEP) can have a segment where it curls back up and to the left (the circled region): less of X is purchased as its price declines. In this range X would be called a Giffen good. PEP 0 x Quantityof X Leaving aside the details of verication, here are some properties of the Price Expansion Path: 1. As price Px falls, income I held constant, the consumer attains higher utility. In Figure 4.13, the arrowhead indicates the direction of increasing utility along the Price Expansion Path. 2. When the Price Expansion Path slopes downward, as in the range between Q and R in Figure 4.13, the consumer responds to a fall in Px by choosing more X but less of the numeraire good Y. Where the Price Expansion Path has a positive slope, as in the range between R and S in the diagram, reducing Px induces the consumer to buy more of both X and Y. 3. Point K in Figure 4.13 is associated with a price Px so high that the consumer buys none of good X at all. (This is the choke price for X.) The Price Expansion Path must also lie everywhere below the dashed horizontal line at height K in the diagram. 4. The Price Expansion Path may even have a section that curls upward and to the left (the circled region in Figure 4.14), in which a lower Px causes the consumer to buy less of good X ! When this condition applies, the commodity is called a Giffen good8 for this consumer. The Giffen property can only hold over a limited range. With negatively sloped indifference curves and positive preference directions, the Price Expansion Path cannot move up and to the left very long and still enter regions of higher utility. Most important of all, the data summarized by the Price Expansion Path can be replotted to show the relation between price Px and the quantity of X bought. This is the consumers demand curve for X, as shown in Figure 4.15. Panel (a) pictures the normal (non-Giffen) situation. Panel (b) pictures a situation where the Giffen property holds over a limited range corresponding to the limited range in which the Price Expansion Path curls up and to the left in Figure 4.14. 8 Sir Robert Giffen, British statistician and economist (18371910). P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 114 4. CONSUMPTION AND DEMAND Px Px d Priceof X Priceof X d d d x x Quantityof X Panel(b) TheGiff enCase 0 x1 x2 Quantityof X 0 Panel(a) TheLa wofDemand Figure 4.15. Demand Curves: The Law of Demand versus the Giffen Case Panel (a) pictures a negatively sloped individual demand curve, satisfying the Law of Demand: as the price falls, more of X is purchased. In Panel (b) the demand curve has the exceptional Giffen property. In the small circled region (corresponding to the circled region in Figure 4.14) more of X is bought as Px rises. The Giffen property can hold, if at all, only over a limited range of prices. EXERCISE 4.9 In the preceding exercise, given the individuals Marginal Value MVx = y and income I = 120, the Price Expansion Path equation y(x + 1) = 120 was derived. What is the individual demand curve associated with this Price Expansion Path? Is X a Giffen good? A N S W E R : The derivation of the Price Expansion Path in Exercise 4.8 used the Sub- stitution Balance Equality y = Px and the budget equation Px x + y = 120. To derive the demand curve, which is a relation between x and Px , starting from the same two equations, y needs to be eliminated. Omitting the algebraic details, the result is Px (x + 1) = 120, or x = 120/ Px 1. This is the equation of the demand curve for good X. Since this demand curve has negative slope throughout, X is not a Giffen good. The Giffen condition violates the Law of Demand, that a lower price always induces consumers to buy more. So the Law of Demand does not follow strictly from the pure logic of rational consumer choice. Like convexity of indifference curves, its justication is empirical observation. Giffen goods are rarely if ever encountered in the real world. Figure 4.16 shows how a change in income affects the demand curve. If X a normal superior good, higher income shifts the demand curve to the right (more of X is desired at each price). If X is an inferior good, higher income shifts the demand curve to the left (less is desired at each price). P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 4.4 INCOME AND SUBSTITUTION EFFECTS OF A PRICE CHANGE 115 Px d d Figure 4.16. The Demand Curve: Effect of Income Changes If X is a superior good (whether normal or ultrasuperior), a rise in income implies larger purchases of X at each price Px the demand curve shifts to the right (from dd to d d ). If X is an inferior good, as income increases less is purchased at any given price; the demand curve shifts to the left (from dd to d d ). Priceof X d Higherincome superiorgood d Higherincome inferiorgood d x 0 Quantityof X d EXERCISE 4.10 For the individual of Exercise 4.9, how would the demand curve shift if income rose from I = 120 to I = 150? A N S W E R : With I = 120 the demand equation was Px ( x + 1) = 120, or equivalently x = 120/ Px 1. With I = 150, the same technique yields x = 150/ Px 1. With increased income the demand curve has shifted to the right. This shows that X is a superior good. 4.4 INCOME AND SUBSTITUTION EFFECTS OF A PRICE CHANGE The effect of price changes upon consumer demand may be separated into two components. 1. A fall in Px increases the consumers real income. He or she could buy the same bundle of goods as before, and have something left over. If X is a superior good, the consumer will use some of the excess to buy more X. This is called the income effect of the fall in Px . 2. Furthermore, at the lower Px the Substitution Balance Equation tells us that even if real income or utility had remained the same, more X would have been purchased. This is called the pure substitution effect of the price change. Continuing to think in terms of a fall in price, Figure 4.17 pictures the Hicks9 decomposition of the income and substitution effects. Suppose Harriet is at an initial optimum position Q on indifference curve U0 . When Px falls, the new optimum is at S on her higher indifference curve U1 . Now, keeping the lower price Px , imagine taking away just enough income to leave Harriet on the old indifference curve U0 . This leads to the dashed budget line MN parallel to KL and just touching indifference U0 at point R. Since Q and R are on the same indifference curve, real income is unchanged. So 9 Sir John R. Hicks, contemporary British economist. P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 116 4. CONSUMPTION AND DEMAND y K Quantityof Y Q M S R U1 U0 0 xQ L xR xS N Quantityof X L x Figure 4.17. Income and Substitution Effects: Hicks Decomposition A fall in price Px , with income and P y held constant, shifts the budget line from KL to KL so that the consumption optimum changes from Q to S. Because S lies on a higher indifference curve, there has been an increase in real income. The income effect of the price change can be separated from the pure substitution effect by constructing an articial budget line MN parallel to KL and tangent to the original indifference curve U0 . At the tangency point R, utility is the same as at Q. The income effect of the price change is therefore x S x R and the pure substitution effect of the price change is xR xQ . this procedure isolates the pure substitution effect of the price change. The increased purchases of X due to the substitution effect alone is the distance xR xQ . The income effect of the price change is the movement from R to S. The increased amount of X purchased due to the income effect is x S x R . So the overall change from Q to S has been divided into two movements: from Q to R (the pure substitution effect) and then from R to S (the income effect). Notice that, in the case pictured, the two effects reinforce one another. A price reduction increases consumption of X for two reasons: the pure substitution effect makes X a better buy for Harriet (in comparison with the numeraire good Y ), and the income effect has enriched her so that she can now buy both more X and more Y. Looking at the substitution effect alone, it is important to note that the quantity change and price change are in opposite directions. Why? Because the pure substitution effect involves movement along an indifference curve, and indifference curves have negative slopes. The direction of the income effect can go either way, depending upon whether X is an inferior good or a superior good. In Figure 4.17, X was a superior good. Had X been inferior instead (so that a rise in income would decrease consumption of X), point S would lie to the northwest of R instead of to the northeast. The income effect and substitution effect would then no longer reinforce one another. As before, the pure substitution effect would be the positive difference x R x Q . But now the income effect would be a negative difference x R x S . Even with a negative income effect the Law of Demand would continue to hold if the new optimum S were to the right of the original P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 4.4 INCOME AND SUBSTITUTION EFFECTS OF A PRICE CHANGE 117 m Meat K M R Q S 0 Bread b L N L Figure 4.18. Conditions for a Giffen Good At the initial high bread price the budget line is KL and the optimum is at Q. A fall in the price of bread shifts the budget line to KL . The consumer is sufciently enriched to prefer buying less bread and more meat at point R. The movement from Q to R consists of a small substitution effect (Q to S) and a large negative income effect (S to R). For this Giffen result to occur, bread must be strongly inferior. optimum Q. Conceivably, however, such an abnormal (negative) income effect could be so great that S along the higher indifference curve U1 lay to the left of Q. This would mean that a reduction in price reduced the quantity bought. This is the underlying explanation for the Giffen case. An Application: How Can the Giffen Case Come About? How Likely Is It? Giffen goods violate the Law of Demand. Here is an example commonly given. Suppose poverty forces you to live mainly on bread (the cheapest source of calories) and to consume little meat (a desired but more expensive food). Since you spend most of your income on bread, a fall in the bread price makes you richer in real terms. But when you are richer you can afford to buy more meat instead, so your consumption of bread might fall! Referring back to Figure 4.17, which illustrated the decomposition of the income and substitution effects of a price change, a Giffen good must have the following properties: 1. It must be inferior, so that the income effect of a price change is negative. 2. It must account for a large fraction of the budget. This makes the perverse income effect large in magnitude. (It has to be large if it is to overcome the pure substitution effect.) These properties are illustrated in Figure 4.18. Initially the consumer chooses a mixed basket along budget line KL indicated by point Q. When the price of bread Pb falls, the budget line swings outward to KL . At the new optimum position R the individual chooses less bread! Although the pure substitution effect here is (as always) in the normal direction involving movement from Q to S along the articial dashed budget line MN the income effect from S to R is perverse in direction and sufciently large in magnitude to overwhelm the substitution effect. P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 118 4. CONSUMPTION AND DEMAND EXAMPLE 4.6 WAS BREAD A GIFFEN GOOD? Some historians have suggested that bread was a Giffen good for English rural laborers at the end of the eighteenth century. A study by Roger Koenker casts doubt on this claim.a In the late eighteenth century, the limited transportation network in Britain meant that prices differed considerably across communities. These differences, as well as changes over time, provided data for estimating the demand for bread. The demand function of a typical English rural laborer household was estimated as follows: Quantity of bread = 0.40 + 0.41 Family size + 0.024 Weekly expenditures 0.35 Bread price + 0.57 Meat price Here bread quantity was measured in loaves per week, bread price in pence per loaf, and meat price in pence per pound. Weekly spending (in pence per week) was used as the measure of overall income. The negative coefcient (0.35) for bread price shows that bread was not a Giffen good for these consumers. Indeed, the positive coefcient for weekly spending (income) suggests that both bread and meat were normal superior goods. (As the text showed, although an inferior good can be a Giffen good, a superior good cannot be.) The positive coefcient on the meat price means that an increase in the price of meat increased consumption of bread, suggesting that bread and meat were substitutes. Consumers, buying less meat in response to the higher meat price, bought more bread. COMMENT Recall that a persons demand for a good can have the Giffen property only over a limited range of prices. So averaging over different individuals and averaging over time could mask any Giffen effects: some individuals, in some periods, might still have been Giffen consumers. But if the Giffen effect is so easily lost by averaging, it is unlikely to be substantively important. a Roger Koenker, Was Bread Giffen? The Demand for Food in England circa 1790, Review of Eco- nomics and Statistics, v. 59 (1977). 4.5 FROM INDIVIDUAL DEMAND TO MARKET DEMAND The market demand curve shows the aggregate quantity demanded by all consumers together, as a function of the price. Geometrically, the market demand curve is obtained by summing the individual demand curves horizontally, as Figure 4.19 illustrates. Suppose there are only two consumers, whose individual demand curves are d1 and d2 . At price Px the rst consumer will buy x1 units and the second consumer will buy x2 units. The total quantity demanded is then x 1 + x 2 , which corresponds to point A on the market demand curve. Repeating this process for every possible price generates the entire market demand curve D. More generally, with N consumers: N X i =1 xi (4.8) P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 4.5 FROM INDIVIDUAL DEMAND TO MARKET DEMAND 119 Px Priceof X Px A d2 D d1 x1 x2 x1 + x 2 x, X 0 Quantityof X Figure 4.19. Individual and Aggregate Demand Here d1 and d2 are the demand curves for two individuals. If these are the only two potential purchasers of the good, the overall market demand curve D is the horizontal sum of d1 and d2 . The market demand X is the sum of the demands of all N consumers in the market, where i indexes the consumers from 1 to N. (The uppercase letter X here symbolizes the aggregate market quantity.) Note that the market demand curve in Figure 4.19 has a atter slope than each of the individual demand curves. If price falls, the overall increase in the market quantity will ordinarily be much greater than the increase in the purchases by any single consumer. The percentage increase in X along the aggregate demand curve D, however, need not exceed the percentage increase along the individual demand curves. (This point will be considered further when the concept of elasticity is taken up in the next chapter.) An implicit assumption of the foregoing analysis is that all consumers are charged the same price Px . If they pay different prices, a market demand curve in the ordinary sense cannot be constructed. CONCLUSION The market demand curve is the horizontal sum of the individual demand curves. EXERCISE 4.11 Adams demand curve for commodity X is x A = 10 2 Px . Bettys demand is xB = 10 3 Px . They are the only two consumers in the market. What is the market demand curve? Compare the slopes along the individual demand curves with the slope of the market demand curve. A N S W E R : Remember that it is the quantities demanded that must be summed (not the prices). So the market demand equation is X = x A + xB = 20 5 Px . Since demand curves are drawn with price on the vertical axis, the slope (rise over run) P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 120 4. CONSUMPTION AND DEMAND Y K Y AllOtherGoods AllOtherGoods K K K S Q R Q U1 U0 0 e0 e1 L Education Panel(a) EffectofaSubsidy L E U1 U0 0 e0 e L L E Education Panel(b) EffectofaVoucher Figure 4.20. Subsidy versus Voucher In Panel (a) a subsidy to consumers of education reduces its price; the budget line shifts from KL to KL . At the new optimum R, the quantity of education purchased will be greater (unless it is a Giffen good in this range, which is highly unlikely). In Panel (b), the voucher amount KK is a gift of income that is spendable only on education. The budget line shifts to the right, from KL to K L , except that the consumer cannot consume in the range between K and K (because the full amount of the voucher would not then be spent on education). The new optimum at S will involve buying more education, so long as it is not an inferior good. is Px / x . Specically, Adams demand equation implies that a quantity change of, say, x A = 1 is associated with a price change of Px of 1/2. So the slope of Adams demand curve is 1/2, the slope of Bettys demand curve is 1/3, and the slope of the market demand curve is 1/5. Thus, as in the diagram of Figure 4.19, the market demand curve is atter than either of the individual demand curves. 4.6 AN APPLICATION: SUBSIDY VERSUS VOUCHER Governments often try to encourage people to consume more of a particular good, for example, education. One method is to subsidize producers or consumers of education. (Free public education is of course an extreme kind of subsidy.) Here we shall explore a much-disucssed alternative, vouchers. In Figure 4.20, E represents education and Y represents all other goods. Panel (a) shows the effect of a subsidy. The original (unsubsidized) tangency optimum is at Q on indifference curve U0 . A subsidy acts like a reduction in price; it rotates the budget line from KL outward to KL . The new optimum is at R on indifference curve U1 . Apart from the unlikely possibility that education is a Giffen good, the subsidy will increase the amount of education consumed. In the diagram, the increase is the distance e 1 e 0 on the horizontal axis. Panel (b) of Figure 4.20 shows the effect of a voucher. The initial optimum Q on indifference curve U0 is the same as before. A voucher is a gift of income spendable only P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 4.6 AN APPLICATION: SUBSIDY VERSUS VOUCHER 121 z K Figure 4.21. Corner Solution and Voucher The initial optimum is the corner solution at K; no education is purchased. A voucher gift of income in the amount KK leads to a new optimum at K . (The consumer would prefer a corner solution at point K , but this is unattainable.) The voucher leads to increased consumption of education, provided only that education is a good rather than a bad for this individual. AllOtherGoods K K U2 U1 U0 e 0 e0 L L Education on the voucher good here, education. The distance KK on the vertical axis represents the amount of the voucher, so the consumers budget line shifts outward from KL to K L . But since the gift can only be spent on education, the consumer is not allowed to move to any point on the dashed segment K K . Therefore the effective new budget constraint is the kinked line KK L . In Panel (b) the new optimum is at S on indifference curve U1 , with increased consumption of education (e > e 0 ). So far a subsidy appears to differ little from a voucher. The subsidy works through a price change, the voucher through an income change. But the voucher has an especially strong effect upon those consumers who would otherwise have chosen little or no education. In Figure 4.21 the individual is initially at a corner solution at point K on indifference curve U0 , spending nothing on education. Even a large subsidy, swinging the budget line outward from point K, may have little or no effect upon the amount of education chosen. But the voucher moves the entire budget line outward to K L (of which only the solid range K L is effective). The new optimum is at K . The consumer would prefer K to K , but K is not available since the voucher amount can be spent only on education. At K the individual spends the entire voucher amount on education, and spends just as much on other goods as before. CONCLUSION For persons who had previously not consumed the voucher commodity at all (or who consumed an amount less than the voucher provides), vouchers almost always increase consumption. The only exception would be where the voucher commodity was regarded as a bad rather than a good; in that case, the voucher would remain unused. For either subsidies or vouchers, this analysis is incomplete in at least two respects. First, the market price of the good was assumed to remain constant throughout. If a voucher or subsidy were to increase the desired consumption of education, for example, the enlarged demand by beneciaries of the subsidy or voucher would tend to raise its price thus possibly reducing the purchases of those not beneting from the subsidy or voucher. Second, the taxes collected to nance the subsidy or voucher would reduce P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 122 4. CONSUMPTION AND DEMAND the spendable income of some or all consumers. So these other individuals might spend less on the commodity. A full analysis needs to take these secondary effects into account. EXAMPLE 4.7 BUT DO VOUCHERS REALLY HELP? Low-income housing has been subsidized in the United States since the 1930s. At rst the subsidy mainly took the form of public housing projects. Since the early 1980s, vouchers have been increasingly used. For families who receive them, vouchers are a big help. But not all eligible families are granted vouchers. If the voucher program raises the price of housing, those low-income households who do not receive vouchers could end up worse off. A study by Scott Susin suggests that this indeed occurred.a He found that vouchers conferred a very large benet upon recipients. But, allowing for the consequent rise in housing prices, the cost imposed upon nonsubsidized poor households was even greater. As shown in the table, the average annual benet covered 69% of the rental cost for the 1.3 million households receiving vouchers. But low-income families that did not get vouchers faced an increase of about 16% in their housing expense. Benets and costs of housing vouchers (1993) Households receiving vouchers Average monthly rent % effect on housing cost Number of households Annual benet $537 69% 1.3 million +$5.8 billion Low-income unsubsidized households $443 +16% 9.6 million $8.2 billion Source: Adapted from Susin, Table 9 (p. 145). This adverse effect might have been avoided by reforming the voucher program to spread the benet more widely, instead of providing very large per-family benets to a small fraction of low-income families. a Scott Susin, Rent Vouchers and the Price of Low-Income Housing, Journal of Public Economics, v. 83 (2002). SUMMARY The optimum of the consumer involves the interaction of preferences (indifference curves) with market opportunities (budget line). The consumers optimum occurs where the budget line bounding the opportunity set touches the highest attainable indifference curve. This solution can be either an interior optimum (both goods are consumed) or else a corner optimum (only one good is consumed). In an interior solution the budget line is tangent to an indifference curve. In a corner solution the highest attainable indifference curve meets the budget line along one or the other axis. Analytically, the budget equation for an individual with income I, who can buy good X at price Px and good Y at price Py , is: Px x + P y y = I P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 SUMMARY 123 The cardinal concept of utility allows the Marginal Utilities of goods to be dened. If goods X and Y are bought but good Z is not, the optimum of the consumer can be expressed as the Consumption Balance Equation/Inequality: MU y ( y > 0) MU X (x > 0) MUz (z = 0) = > Px Py Pz Using the more general concept of ordinal utility, the rate at which the consumer is willing to substitute one good for the other (the slope along the indifference curve) is compared to the rate at which the market permits such exchanges (the price ratio). The Marginal Rate of Substitution in Consumption (MRSC ) is the slope of the indifference curve, with sign adjusted to be positive. If both goods X and Y are consumed, then the Substitution Balance Equation holds: MRSC = Px / P y If good X is consumed but good Y is not, the Substitution Balance Inequality holds: MRSC > Px / P y Suppose good Y is the numeraire commodity with price xed at P y = 1. Then the Marginal Rate of Substitution between X and Y can be expressed, in a more intuitive terminology, as the Marginal Value of X in terms of Y , symbolized as MV X . Goods that are strong complements, such as bread and butter, tend to be consumed together. Consequently, a large change in the price ratio between them causes only a small change in the ratio in which they are consumed. Close substitutes, such as Dell and HP computers, tend to be consumed to the exclusion of one another. Consequently, even a small price shift may lead to a big change in the ratio in which they are bought. As income increases, with prices held constant, the budget line shifts parallel to itself and outward from the origin. The optimum positions attained, for given prices Px and Py , are shown by the Income Expansion Path (IEP). If both X and Y are normal superior goods, the Income Expansion Path has positive slope. The data described by the Income Expansion Path can also be plotted as an Engel Curve showing how the quantity of X bought varies with income. As price Px falls, with I and Py held constant, the budget line tilts outward while retaining the same intercept on the y-axis. The optimum positions attained are represented by the Price Expansion Path (PEP). Since a fall in Px , with I and Py held constant, implies an increase in real income (higher utility), a price change has both a pure substitution effect and an income effect upon consumption of X. The substitution effect shows that, as Px falls, a consumer always buys more of X. The income effect can go either way: it is positive for a superior good, and negative for an inferior good. Market demand is aggregated from individual demands by summing, at each price, the quantities bought by all the consumers. The slope of the market demand curve is always atter than the slopes of the individual demand curves. Government may attempt to increase consumption of a good by means of a subsidy or a voucher. A subsidy works like a reduction in price in inducing consumers to purchase more of the good. A voucher works like an increase in income, except that the enlarged income can be spent only on the voucher good. A voucher is therefore particularly P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 124 4. CONSUMPTION AND DEMAND effective for consumers who would otherwise have bought very little of the good, or none at all. QUESTIONS The answers to daggered questions appear at the end of the book. 1. What is the meaning of the expression the optimum of the consumer? 2. In a situation with just two goods, how does the amount of income affect the shape of an individuals market opportunity set? How do the prices of the two goods affect the shape? For Review 3. a. b. c. What is the budget line? What is its equation? What determines the slope of the budget line? 4. What is the geometrical condition for the optimum of the consumer? (Distinguish between a corner solution and an interior solution.) 5. If indifference curves were concave, why would the consumers optimum never be in the interior? 6. a. b. What is the Consumption Balance Equation that expresses the optimum of the consumer? Relate this to the Substitution Balance Equation. Do the equations hold for an interior solution, a corner solution, or both? 7. Explain the relation between Marginal Value and Marginal Rate of Substitution. What are the differences between them? 8. Give examples of pairs of goods that are strong complements, versus pairs that are close substitutes. What observable market characteristic distinguishes them? 9. Characterize a normal good, an inferior good, and an ultra-superior good. Give examples of each. For two goods, which of the above must they be if the Income Expansion Path has positive slope? What can you say if the Income Expansion Path has negative slope? 10. Prove that if X and Y are goods rather than bads, the Income Expansion Path never points down and to the left. 11. a. b. A positively sloped Income Expansion Path implies what shape for the Engel Curve? What can you say about the Engel Curve for an inferior good? 12. Show how an individuals demand curve can be derived from the Price Expansion Path. 13. Is there a utility-increasing direction along the Income Expansion Path? Along the Price Expansion Path? 14. What does the Law of Demand say about the shape of the Price Expansion Path? 15. How does the Hicks decomposition separate the income effect and the substitution effect of a price change? 16. Using the Hicks decomposition, show that the Giffen condition (a price decrease reduces consumption of the good) can hold only for an inferior good. 17. How is the market demand curve derived from knowledge of individuals separate demand curves? Can individual demand curves be determined from knowledge of the market demand curve? 18. As compared with a simple subsidy, the voucher scheme is particularly effective for consumers who would otherwise have chosen little or none of the commodity. Illustrate and explain. P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 QUESTIONS 125 19. In Exercise 4.11, we can rewrite Adams demand equation as P x = 5 (x A /2) and Bettys as P x = (10/3) (x B /3). Can we conclude that the price in the market demand curve for a given quantity x is the sum of Adams demand price at x and Bettys demand price at x , P x = (25/3) (5x /6)? For Further Thought and Discussion 1. a. b. Describe an experiment that might reveal an individuals Marginal Rate of Substitution in Consumption between two goods. Describe how an experiment might reveal Marginal Utility for either good. 2. Why is diminishing Marginal Utility necessary if the Consumption Balance Equation is to express an optimum? Why is decreasing Marginal Rate of Substitution in Consumption necessary if the Substitution Equivalence Equation is to express an optimum? Is decreasing Marginal Utility also necessary? 3. a. b. Why can the Giffen condition hold only over a limited range of the Price Expansion Path? Could the Price Expansion Path ever circle around and rejoin itself at its starting point on the y-axis? How does a change in the price of a good tend to shift the position of the Income Expansion Path? How does a change in income tend to shift the position of the Price Expansion Path? 4. a. b. 5. Let an individuals demand curve cut the vertical price axis at some nite choke price Pxo . Show the equivalent situation in terms of the individuals indifference curves and o budget line. Must the consumers optimum then be a corner solution at price P x ? 6. I think I could be a good woman if I had ve thousand a year Becky Sharp, in Thackerays Vanity Fair. Can you give an economic interpretation? 7. Consider a pair of commodities such as bread and butter, which are strong complements, versus another pair such as butter and margarine, which are close substitutes. Which pair is more likely to have a member that is an inferior good? Explain. 8. Why is the income effect of a price change usually small compared to the substitution effect? 9. Since 1900, real income has increased tremendously, yet the average number of children per family has decreased. Consider the following possible explanations, and illustrate in terms of market opportunity sets and indifference curves of families between number of children and all other goods. a. Children are an inferior good; since were richer now, we want fewer of them. b. Children are not an inferior good; however, it has become more expensive to bear and raise children. c. Children are not an inferior good, nor have they become relatively more expensive. What has happened is that tastes have changed; couples today want smaller families than couples did in 1900. 10. In the comparison of subsidy versus voucher in the text, the price of the good was assumed to remain unchanged. Would it be correct to anticipate some change of price? In which direction is this likely to go? Show the effect upon the market opportunity set. 11. Still another consideration is that government spending on subsidies or vouchers must ordinarily be nanced by taxes, say on income. Show the effects upon a consumers market opportunity set of a tax-nanced subsidy and of a tax-nanced voucher. P1: OBM/JzG 0521818648c04.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:17 126 4. CONSUMPTION AND DEMAND 12. The following is sometimes given as an example of a Giffen situation. A person with only $100 available must make a 1,000-mile train trip. He prefers rst-class travel to coach travel, but his rst priority is to complete his trip. Suppose rst-class travel costs 20 cents per mile and coach costs 5 cents per mile. Then it can be veried that he will travel 333 1/3 miles in rst class and 666 2/3 miles in coach. Now let the price of coach travel rise to 10 cents per mile. Then the traveler cannot afford any rst-class miles at all if he is to complete his trip, so the amount of coach travel will rise from 666 2/3 to 1000 even though its price has doubled! a. Is coach travel an inferior good here? (What would happen if the travel budget were to rise above $100?) b. Under what circumstances will the traveler choose a corner solution with only coach travel? With only rst-class travel? 13. a. b. If two commodities are perfect substitutes, is it true that the consumers optimum will almost always be a corner solution? Will it ever not be? 14. How would you draw a consumers opportunity set for three goods X, Y, and Z ? What would you call this, instead of a budget line? 15. The discussion in Example 4.4 suggests some possible rationales for noncash gifts. Can you think of any others? 16. If X and Y are normal superior goods, verify that an increase in income tends to shift the Price Expansion Path (PEP) to the right. 17. In Exercise 4.9, what happens at P x = 120? [Hint: This is the individuals choke price.] 18. In Exercise 4.11, the market demand equation X = x A + x B = 20 5 P x is invalid if P x 10/3. Why? [Hint: What is the choke price for each individual?] 19. At a given price ratio, variations in income generate an Income Expansion Path (IEP). If the price ratio were different, we know that a different IEP curve would be generated. For the same individual, could these two IEP curves ever cross? 20. What is the effect of an increased price of one good when the two goods the consumer can buy are perfect substitutes? 21. Suppose a gasoline tax is imposed, taking the form of a xed number of cents per gallon (the same for regular and for premium gas). Consider the following arguments. (1) While we would expect the quantity demanded of both premium and regular gasoline to fall after the tax is imposed, there should be a relatively smaller effect for the premium quality, since a xed number of cents is a smaller proportionate tax for the premium gas. (2) On the contrary, since premium gasoline is more of a luxury good, and regular gasoline more of a necessity good, wed expect a relatively bigger effect for the premium quality. Is one or the other of these arguments totally wrong, or is it a matter of which of two valid arguments is the stronger? Analyze each argument separately and explain. P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 5 5.1 5.2 5.3 5.4 Applications and Extensions of Demand Theory The Engel Curve and the Income Elasticity of Demand 128 The Demand Curve and the Price Elasticity of Demand 132 The Cross-Elasticity of Demand 136 Fitting a Demand Curve 137 Constant Slope versus Constant Elasticity 138 General Demand Functions 139 5.5 5.6 Determinants of Responsiveness of Demand to Price 142 Multiple Constraints Rationing 144 Coupon Rationing 144 Point Rationing 146 SUMMARY 151 QUESTIONS 152 EXAMPLES 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Income Elasticities in New Zealand 130 The Demand for Opium 133 College Students Demand for Cigarettes 134 Demand Elasticities for Pharmaceuticals 136 Demand for Coffee 141 Wartime Point Rationing 149 Gasoline and Waiting Time 150 127 P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 128 5. APPLICATIONS AND EXTENSIONS OF DEMAND THEORY A tax on gasoline will raise its price. By the Law of Demand, gasoline consumption will fall. But how much? And a fall in consumer incomes will likely discourage gasoline usage, but to what extent? This chapter describes the measures that economists use to quantify how consumers respond to changes in price and changes in income. Other questions addressed include: (1) Why are consumers demands sometimes very sensitive to changes in price or in income, sometimes not? (2) What is the effect of nonprice constraints upon choice, for example rationing in wartime? 5.1 THE ENGEL CURVE AND THE INCOME ELASTICITY OF DEMAND For any good X, the change in consumption ( x ) due to a change in income ( I ) could be measured by the ratio x / I . This ratio is the slope of the Engel Curve (see Section 4.3 in the preceding chapter) over the relevant range.1 But there is a difculty with the simple ratio x / I : it is sensitive to the units of measurement. If commodity X is butter, the numerical value of x / I varies depending on whether the amount of butter is stated in ounces or pounds or tons, and whether income is quoted in dollars or cents. The concept of elasticity eliminates this difculty by expressing the variables in proportionate (percentage) terms. DEFINITION: The income elasticity of demand is the proportionate change in the quantity purchased divided by the proportionate change in income. Let x (where is the Greek letter epsilon) symbolize the income elasticity of demand for commodity X; this denition is represented by the rst ratio in equation (5.1). The other expressions are equivalent algebraic forms: x /x I /I x/ I x/I xI Ix (5.1) x EXERCISE 5.1 Sallys income and purchases of apples A over two successive years are shown below. Assuming nothing else has changed, and in particular that the price of apples remains the same, compute her implied income elasticity for apples. Year 1 Income Apples purchased $10,000 100 Year 2 $11,000 116 A N S W E R : The change in income is I = $1,000, and for apples a = 16. The formulas for income elasticity in equation (5.1) also require a numerical value for income itself, and the question arises of whether to use I = $10,000 or $11,000 or 1 Mathematical Footnote: In calculus notation this slope is x/ I. (The partial derivative symbol indicates that other independent variables, such as the price Px , are being held constant.) Note: Henceforth, the text will not provide Mathematical Footnotes that merely indicate how the notation for nite changes could be replaced with differential notation ( or d). P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 5.1 THE ENGEL CURVE AND THE INCOME ELASTICITY OF DEMAND 129 x Figure 5.1. Engel Curve and Unitary Income Elasticity The straight-line Engel Curve ADB has income elasticity of 1, because the slope along the curve is the same as the slope of a ray from the origin to any point on the curve. The nonlinear Engel Curve CDE , tangent at point D to ADB, therefore also has an income elasticity of 1 for small changes in the neighborhood of point D. In the range CD the slope along curve CDE is less than the slope of a ray from the origin to the curve, so x < 1. Correspondingly, x > 1 in the range of CDE between D and E. E Quantityof X x2 C A D B x1 0 I1 Income I2 I something in between. The most convenient approximation is the average of the two: I = $10,500. Similarly for apples, the average is a = 108. Substituting these averages for I and a into equation (5.1) yields the income elasticity: = 16 10,500 = 1.556 1,000 105 a So Sallys income elasticity for apples is 1.556. A 1% increase in her income would increase her purchases of apples by 1.556%. Income elasticity is illustrated geometrically in Figure 5.1. Consider the Engel Curve depicted by the straight line ADB drawn through the origin. Since the curve has positive slope, X is a superior good: more is purchased as income rises. By the geometry of similar triangles, the percentage increase in income I between points A and B is the same as the percentage increase in quantity x .2 In equation (5.1), the rst numerator is the percent change in quantity and the rst denominator is the percent change in price. Since these percentages are equal, the income elasticity is x = 1 everywhere along the line ADB. The same holds along any straight-line Engel Curve through the origin. Now consider the positively sloped but nonlinear Engel Curve CDE drawn tangent to ADB at point D. Along CDE the income elasticity of demand does not remain constant. Nevertheless, at the tangency point D the income elasticity along CDE is the same as along ADB. Why? The second formula for x on the right-hand side of equation (5.1), ( x / I )/(x / I ), involves the slope x / I and the ratio x / I . At the point of tangency, the curves CDE and ADB have the same slopes. And they also have the same x and I. So any nonlinear Engel Curve CDE has income elasticity x = 1 in the neighborhood of its tangency with a straight line drawn through the origin. 2 Mathematical Footnote: By similar triangles, x 2 /x 1 = I 2 / I 1 . So (x 2 x 1 )/x 1 = ( I 2 I 1 )/ I 1 . We could equivalently use x2 and I2 in the denominators, or else the averages (x 1 + x 2 )/2 and ( I 1 + I 2 )/2. P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 130 5. APPLICATIONS AND EXTENSIONS OF DEMAND THEORY In the range CD along the curve CDE, CD is atter than AD. That means that x increases with income, but less than proportionately. Consequently, in this range the income elasticity along CDE is less than 1: x < 1. Reversing the argument, x > 1 in the range DE where x rises more than proportionately than income. For any positively sloped Engel Curve that is a straight line through the origin, the income elasticity is x = 1. But such lines can be drawn from very nearly vertical to very nearly horizontal. So what corresponds geometrically to income elasticity is not the steepness of the Engel Curve, but rather the steepness as compared with a line through the origin. PROPOSITION: An Engel Curve with positive slope has income elasticity greater than, equal to, or less than 1 depending upon whether the slope along the Engel Curve is greater than, equal to, or less than the slope of a ray drawn from the origin to the curve. EXERCISE 5.2 The following equations correspond to four possible Engel Curves: (a) x = I /8; (b) x = 5 + I /10; (c) x = 75 + I /2; (d) x = 30 I /40. Determine the slope and the income elasticity for each curve at the point I = 200, x = 25. (e) In which of these cases is the commodity an inferior good? (f) What if the equation for the Engel Curve were x = 5 + I /8? x / I all along the curve x = I /8 is 1/8. The income elasticity is x = ( x / I )( I /x ) = (1/8)(200/25) = 1. (b) The slope of x = 5 + I /10 is 1/10, and so x = (1/10)(200/25) = 0.8. (c) The slope is 1/2, and x = (1/2)(200/25) = 4. (d) The slope is 1/40, and x = (1/40)(200/25) = 0.2. (e) Commodity X is inferior only in case (d), where the income elasticity is negative. (f) This was a trick question! The equation given is perfectly possible for an Engel Curve, but the specic point I = 200, x = 25 does not lie on the curve. So the question cannot be answered. A N S W E R : (a) The slope EXAMPLE 5.1 INCOME ELASTICITIES IN NEW ZEALAND Using a sample of 3,487 New Zealand households in the period 19811982, David E. A. Giles and Peter Hampton calculated income elasticities for various categories of consumer expenditure.a Effect of income on expenditures (income elasticities) Category Food Housing Household operation Clothing Transportation Tobacco and alcohol Lowest income group 0.63 1.22 0.66 1.29 1.50 2.00 Highest income group 0.84 1.80 0.85 0.98 0.90 0.85 Source: Giles and Hampton, Table 3 (p. 458). P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 5.1 THE ENGEL CURVE AND THE INCOME ELASTICITY OF DEMAND 131 For the low-income group, the income elasticity for Tobacco and Alcohol is surprisingly high. This has possibly disturbing implications for social policy. It suggests that increased income in the hands of the poor might largely be devoted to undesirable commodities such as tobacco and alcohol. (On the other hand, perhaps it is overly paternalistic to disapprove of poor people deriving some solace from smoking or drinking.) COMMENT The comparative income elasticities shown for Food versus Tobacco and Alcohol here are consistent with the reported observation in Example 4.5, Luxuries versus Necessities in a P.O.W. Camp. In the P.O.W. case, a 50% cut in both cigarette and food rations led to a fall in the price of food as compared to cigarettes. In other words, the P.O.W.s, extremely low-income consumers, were attempting to shift consumption away from food and toward cigarettes as their real income fell even further. a David E. A. Giles and Peter Hampton, An Engel Curve Analysis of Household Expenditures in New Zealand, Economic Record, v. 61 (March 1985). It is sometimes useful to distinguish between elasticity at a point and elasticity over some range or arc along a curve. The denition in equation (5.1) covers both cases. Arc elasticity is a kind of average of the point elasticities within the range considered. As the intervals x and I shrink toward zero, the arc elasticity approaches the point elasticity along the curve. A persons income elasticities over all the commodities consumed are connected by an important condition: PROPOSITION: The weighted average of an individuals income elasticities equals 1, where the weights are the proportions of the budget spent on each commodity. If only two commodities X and Y are consumed, their respective weights in the consumers budget are k x Px x / I and k y P y y / I . So for this simplest case the proposition becomes kx x + ky y =1 (5.2)3 3 Mathematical Footnote: It is easy to justify the proposition in the simple two-good case of equation (5.2). Substituting the denitions of k x , k y , and the two income elasticities, the left-hand side of (5.2) is: Px x I Py y xI + Ix I Px x + P y y yI = Iy I The numerator here is the changed expenditure on the two goods taken together, while the denominator is the change in income. Since the two must be equal (assuming that all income is spent), the right-hand side of equation (5.2) must equal 1. P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 132 Px 5. APPLICATIONS AND EXTENSIONS OF DEMAND THEORY I Figure 5.2. Alternative Demand-Curve Slopes Price($ /X ) II The four demand curves represent different responses of quantity purchased to changes in price. Since demand curves are conventionally drawn with price on the vertical axis, a greater response is represented by a atter demand curve. Curve IV has a region that represents the exceptional Giffen case. III IV 0 x Quantityof X EXERCISE 5.3 Suppose there are just two goods, bread and wine. If bread accounts for 95% of the budget and has income elasticity b = 0.9, what can you say about the income elasticity w for wine? A N S W E R : Equation (5.2) here becomes (0.95 0.9) + 0.05 come elasticity for wine must be w = 2.9. w = 1. Solving, the in- It follows that a good that accounts for a very large fraction of a persons budget must have an income elasticity close to 1. Conversely, if a good has extremely high income elasticity, like wine in the exercise above, you can be condent that it constitutes only a small portion of the budget. 5.2 THE DEMAND CURVE AND THE PRICE ELASTICITY OF DEMAND A direct measure of the consumers response to a change in price would be the ratio x / Px . This ratio is the reciprocal of the slope along the demand curve.4 The Law of Demand tells us that the demand curve has negative slope. Figure 5.2 illustrates demand curves with atter and steeper negative slopes; the steeper the curve, the smaller is the absolute magnitude of x / Px . Like the direct measure x / I of sensitivity to changes in income, the direct measure x / Px of a goods sensitivity to changes in price has the disadvantage of being affected by the units of measurement. The responsiveness of quantity to price, x / Px , could numerically be made to appear either great or small depending upon whether quantity 4 Economists conventionally draw demand curves with price Px on the vertical axis. So the slope of the demand curve is Px / x ; the reciprocal of the slope is x / P x . P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 5.2 THE DEMAND CURVE AND THE PRICE ELASTICITY OF DEMAND 133 x were measured in tons or pounds or ounces, or price Px in dollars or cents. To avoid this difculty, economists again use an elasticity measure dened in terms of proportionate changes. Specically, the ratio of the proportionate change in quantity to proportionate change in price is called the price elasticity of demand. (The expression elasticity of demand, standing alone, always refers to the price elasticity of demand.) Only in terms of such proportionate changes, independent of units of measurement, could one meaningfully say, for example, whether the demand for automobiles is more or less sensitive to price than the demand for bananas. DEFINITION: The price elasticity of demand is the proportionate change in quantity purchased divided by the proportionate change in price. In equation (5.3), x (where is the Greek letter eta) symbolizes the price elasticity of demand for commodity X. The rst ratio corresponds to the denition above; the other expressions are algebraically equivalent forms: x x /x Px / Px x / Px x / Px x Px Px x (5.3) Since x / Px is normally negative, so is the price elasticity x . Conventionally, a demand curve is said to be elastic if x < 1, that is, if the elasticity measure exceeds unity in absolute value. In the opposite case, if x has an absolute value less than unity, the demand is said to be inelastic. But since elasticity generally varies along a demand curve, it is rarely advisable to describe an entire demand curve as elastic (or inelastic). Rather, one should say that demand is elastic (or inelastic) in the neighborhood of some given price-quantity point. EXERCISE 5.4 The following equations represent different possible curves for commodity X: (a) x = 240 30 Px ; (b) x = 320 50 Px ; (c) x = 20 + 25 Px . What are the associated price elasticities in the neighborhood of the point x = 120, Px = 4? A N S W E R : From equation (5.2), x = ( x / Px )/( x / Px ). In each case, the value of the denominator is x / Px = 120/4 = 30. Inserting the appropriate numerator ratio, (a) x = 30/30 = 1; (b) x = 50/30 = 5/3; (c) x = 25/30 = +5/6. (Since the price elasticity is positive in the last case, this is a situation where the Law of Demand fails: at a higher price more is purchased rather than less.) EXAMPLE 5.2 THE DEMAND FOR OPIUM An alternative to interdicting the supply of narcotic drugs (see Chapter 2, Section 2.1) is to legalize the drug trafc but subject it to heavy taxation. Or the government might monopolize the business and charge steep prices. How effective might high prices be for discouraging consumption of narcotics? That depends upon the elasticity of demand. A study by Jan C. van Ours examined the demand for opium in the Dutch East Indies in the period 19321938 when its consumption was legal the supply being provided by a government monopoly.a P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 134 5. APPLICATIONS AND EXTENSIONS OF DEMAND THEORY The author estimated the elasticity of demand for opium in this period to be around 0.7 with respect to overall consumption, and around 0.4 with respect to number of users. That is, a 1% increase in price was associated, other things equal, with a 0.7% decrease in the total consumed and a 0.4% decrease in the number of regular users. (It follows, of course, that those continuing to consume did not decrease their usage by the full 0.7%.) COMMENT To the extent that these data might be applicable to narcotics today, they suggest that a 50% increase in price would reduce consumption by around 35%. But as a practical problem, prices much higher than those currently being paid in the street would encourage illegal smuggling with the result that, just as before, costly interdiction would be required. Perhaps the argument for legalization should not be based upon any expectation of actually reducing drug consumption by means of higher prices. A more practical goal might be to make the legal price about the same as the current effective street price. Unfortunately, removing the risks and stigma of illegality would certainly, if the price were to remain about the same, increase consumption of narcotics. So a considerable rise in narcotics usage would have to be anticipated after legalization. As against this, society would gain by saving the resources now dissipated in the effort to interdict illegal supplies. a Jan C. van Ours, The Price Elasticity of Hard Drugs: The Case of Opium in the Dutch East Indies, 19321938, Journal of Political Economy, v. 103 (April 1995). It is often thought that addictive commodities are necessarily characterized by low price elasticity: a consumer who is hooked cannot be very sensitive to price variation. And indeed, in the preceding Example the indicated demand for opium was in the inelastic range, though not extremely so. The next Example considers the elasticity of the demand for tobacco. EXAMPLE 5.3 COLLEGE STUDENTS DEMAND FOR CIGARETTES Frank J. Chaloupka and Henry Wechsler studied how cigarette prices inuenced the smoking choices of students at 140 American four-year colleges and universities.a Owing to differing state and local taxes, and other varying inuences upon supply or demand, at any moment of time cigarette prices differ from region to region. These differences provide the price variation needed for estimating demand elasticity. The authors calculated the overall price elasticity of demand for cigarettes to be in the elastic range, around = 1.4. Higher prices reduced consumption through two approximately equal effects: smaller per capita usage by smokers, and fewer people choosing to smoke. This suggests that a 10% price increase would lead to about a 7% reduction in the proportion of college students smoking, and also to about a 7% reduction in cigarettes consumed per smoker. These elasticities are somewhat higher than the gures for opium in the preceding Example. One explanation is that the cigarette study dealt only with students. Elasticity of demand is likely to be higher for young persons, whose habits are not yet so rmly ingrained. In fact, the authors quote various estimates indicating that, for adults, the elasticity of demand for cigarettes is considerably smaller around P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 5.2 THE DEMAND CURVE AND THE PRICE ELASTICITY OF DEMAND 135 = 0.4. So higher cigarette prices for young people are likely, owing to their effect upon habit formation, to reduce not just current use but lifetime patterns of consumption. a Frank J. Chaloupka and Henry Wechsler, Price, Tobacco Control Policies and Smoking among Young Adults, Journal of Health Economics, v. 16 (1997), pp. 359373. The Law of Demand says that a reduction in the price of good X will increase the quantity consumed. But if price falls and quantity increases, there are offsetting effects upon E x Px x , the consumers total spending on good X. The price elasticity can tell us whether the price effect or the quantity effect dominates. Suppose x is numerically greater than 1 (that is, x < 1), so that demand is elastic. Then from the rst ratio in equation (5.3), the proportionate change in quantity x/x exceeds in magnitude the proportionate change Px / Px in price. So, if demand is elastic, after a price decrease the rising quantity outweighs the falling price in proportionate terms meaning that total spending on X increases. Correspondingly, if x > 1 (if demand is inelastic), total spending E x decreases as Px falls. And it follows that if x = 1 (unitary demand elasticity), spending remains constant for small changes in Px up or down. PROPOSITION: If a consumers demand for X is elastic, a reduction in price Px will lead to increased spending E x Px x on commodity X. If demand is inelastic, a price reduction decreases E x . If the demand elasticity is unitary, E x remains the same. EXERCISE 5.5 Roberts demand curve for good X is given by the equation x = 100 2 Px . (a) What is the elasticity of demand at the point x = 20, Px = 40? (b) If price falls from Px = 40 to Px = 35, what happens to total spending E x and what does this imply about the elasticity of demand? (c) Compute the elasticity to verify the Register to View AnswerN S W E R : (a) Along the demand curve x = 100 2 Px , the ratio x / Px (the reciprocal of the demand-curve slope) is a constant equal to 2. Using the second expression for x from equation (5.2): x x / Px 2 = = 4 x / Px 20/40 (b) At Px = 40 the quantity is x = 100 2(40) = 20 and so total spending on X is E x = 800. At Px = 35, quantity is x = 100 2(35) = 30, so total spending is E x = 1,050. Since spending is higher at the lower price, demand is elastic. (c) Since x / Px = 2, taking the midpoint values for x and Px , implies x / Px = 25/37.5 = 0.667. So the elasticity is 2/(0.667) = 3, conrming that demand is elastic in this interval. The logical relationship among price, elasticity of demand, and total spending on any good X can be expressed in another way that will be useful in later chapters. First, Marginal Expenditure can be dened as usual for a marginal magnitude: ME x Ex/ x (5.4) P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 136 5. APPLICATIONS AND EXTENSIONS OF DEMAND THEORY It then follows that: ME x Px (1 + 1/x ) (5.5) (The proof is provided in a footnote.)5 For elastic demand (x < 1), in equation (5.5) the expression in parentheses is positive, so Marginal Expenditure is also positive. By similar reasoning, Marginal Expenditure is negative when demand is inelastic (x > 1). Marginal Expenditure is zero for unitary demand elasticity (x = 1). And, of course, if x = 1 consumers will spend the same amount of dollars on X no matter what the price; Marginal Expenditure is zero. Notice that what is spending from the consumer point of view is revenue from the viewpoint of the sellers. Using this re-interpretation, equation (5.5) will be important when the supply side of the market is taken up in later chapters. 5.3 THE CROSS-ELASTICITY OF DEMAND The amount of butter that consumers buy depends not only upon the price of butter but also upon prices of related goods like bread and cheese. Once again, it is convenient to use a unit-free measure of demand responsiveness. The cross-elasticity of demand is dened as: xy x /x Py / Py x Py Py x (5.6) In Chapter 4, Section 4.2, complements in demand (such as bread and butter) were dened by the following property: a large change in the price ratio between the two goods brings about only a small change in the ratio of consumption. For substitutes in demand (such as bread and margarine) a small change in relative prices causes a large change in relative consumption. The concept of cross-elasticity can quantify these ideas. Complements such as bread and butter can be expected to have negative crosselasticity (xy < 0): a reduction in the price of bread tends to increase the quantity of butter purchased. Between substitutes such as butter and margarine, the cross-elasticity of demand is typically positive (xy > 0): a reduction in the price of butter will tend to decrease the quantity of margarine purchased. EXAMPLE 5.4 DEMAND ELASTICITIES FOR PHARMACEUTICALS A study by Sara Fisher Ellison and colleagues analyzed demand elasticities for four closely related drugs during the late 1980s.a The compounds Cephalexin, Cefadroxil, Cephradine, and Cefaclor fall generally under the heading of cephalosporins, a type of anti-infective drug. Two of the compounds (Brand 1 and Brand 3) went off patent during the period of study: hence generic competitors were able to enter the eld. So 5 Mathematical Footnote : E, the change in total expenditure associated with small changes x and Px is approximately the sum of two components: E x Px x + x Px . (This approximation is more accurate the smaller are the changes x and Px .) Dividing through by x : Ex ME x Px + x x x Px Px 1 + x Px Px x The nal step is to notice that the last fraction on the right is the reciprocal of the demand elasticity x dened in equation (5.3), which leads directly to the expression in the text above. P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 5.4 FITTING A DEMAND CURVE 137 the researchers were able to compare the price elasticities with regard to generic competition as against therapeutic competition the rst of these being the competition between branded and generic versions of the same compound, and the second the competition between similar yet pharmaceutically distinct compounds. Each cell of the table here shows a price elasticity. The cells along the main diagonal are the own-price elasticities. Thus, the entry at the upper left is the demand elasticity of Brand 1 with regard to the price of Brand 1. The value shown is negative (0.38), as of course is to be expected. Reading down the column, the next entry is the demand elasticity of Brand 1 with regard to the price of its generic competitor the generic version of the same compound. Since Brand 1 and Generic 1 are certainly good substitutes, the positive entry here (0.79) is consistent with expectations. As shown in the next cell down, Brand 1s therapeutic competitor Brand 3 is not so close a substitute the gure shown is positive but smaller (0.52). Finally the entry for Generic 3 is even smaller (0.21). This makes sense, since Generic 3 differs from Brand 1 not only in being generic but also in being a different pharmaceutical compound. Demand elasticities of two pharmaceuticals Drug Brand 1 Generic 1 Brand 3 Generic 3 Brand I 0.38 0.79 0.52 0.21 Generic I 1.01 1.04 0.53 0.23 Brand 3 0.20 0.09 1.93 2.00 Generic 3 0.21 0.10 1.12 2.87 Source: Adapted from Ellison et al. (1997), Table 7, p. 441. Also, the own-price elasticities are greater for the generics than for the branded products. This is understandable, since buyers of generic products are likely to be more price-sensitive than purchasers of branded products. In addition, though the reason is unknown, compound 3 has (in both its branded and generic versions) notably higher own-price elasticity than compound 1. a Sara Fisher Ellison, Iain Cockburn, Zvi Griliches, and Jerry Hausman, Characteristics of Demand for Pharmaceutical Products: An Examination of Four Cephalosporins, RAND Journal of Economics, v. 28 (1997), pp. 426446. 5.4 FITTING A DEMAND CURVE Econometricians use historical data to estimate (to t) demand curves. Any such tted curve is more or less articial; a statistician can at best only approximate the true demand function. Since econometricians normally care more about aggregate behavior in markets than about an individuals choices, the discussion in this section will use the uppercase symbols X,Y, . . . that represent marketwide quantities, rather than the lowercase symbols x,y, . . . which refer to individual purchases or consumption. In terms of these marketwide magnitudes, the elasticity formulas of equation (5.3) become: x X/ X Px / Px X Px Px X Px / X Px / X (5.7) P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 138 5. APPLICATIONS AND EXTENSIONS OF DEMAND THEORY Px Px Price($ /X ) 0 X Quantityof X Panel(a) LinearDemandCurve Price($ /X ) 0 X Quantityof X Panel(b) Constant-ElasticityDemandCurve Figure 5.3. Constant-Slope and Constant-Elasticity Demand Curves Simple functional forms are ordinarily assumed in attempting to estimate (to t) a demand curve to observed data (shown as heavy dots in the diagrams). The functional forms most commonly used are linear (constant-slope) demand as in panel (a) and constant-elasticity demand as in panel (b). Constant Slope versus Constant Elasticity To keep the statistical problems manageable, the econometrician often assumes that the demand curve has either constant slope or constant elasticity. Figure 5.3 compares the two. A demand curve with constant slope is a straight line. The demand curve with constant slope in Panel (a) tted to the observed data (heavy dots) is the straight line best answering the question: How do numerical changes of quantity respond to numerical changes of price? The demand curve with constant elasticity in Panel (b) is convex (bowed toward the origin). It answers the question: For these data, how do proportionate changes in quantity depend upon proportionate changes in price? A constant-slope (straight-line) demand curve such as DD in Figure 5.4 does not have constant elasticity. First, from equation (5.7), the elasticity of demand must be zero at D (the intersection with the horizontal axis) since price Px is zero there. Similarly, at point D (the intersection with the vertical axis), the value of X is zero and so the elasticity is innite there. So, evidently, elasticity rises (increases in absolute value) moving northwest along a straight-line demand curve. There is a neat geometrical method for nding the elasticity of demand at any point along demand curve DD in Figure 5.4. Consider the last ratio on the right of equation (5.7). This corresponds graphically to dividing the slope of a ray from the origin to the curve ( Px / X ) by the slope of the curve itself ( Px / X ). So, for the elasticity at any point like T, divide the (positive) slope of OT by the (negative) slope of DD . In the diagram OT is steeper than DD , so the absolute value of the ratio exceeds 1; that is, demand is elastic at point T (x < 1). This geometric technique also applies to estimating the elasticity along a nonlinear demand curve such as FF in Figure 5.4. The elasticity in the neighborhood of point T along FF is the slope of OT divided by the slope of DD (the tangent line to FF at point T ). A direct corollary is that at the midpoint of a linear demand curve, elasticity is always unitary (x = 1). In Figure 5.4, at the midpoint M along DD the positive P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 5.4 FITTING A DEMAND CURVE 139 Px Price($ /X ) D F T M Px F 0 Quantityof X X D Figure 5.4. Graphical Measure of Elasticity Elasticity at a point T along a linear demand curve DD is the slope of a ray OT from the origin to point T divided by the slope of the demand curve. In the situation pictured, OT is steeper (its slope is larger in absolute value) than DD , so at T the demand is elastic (x < 1). Elasticity always equals 1 at the midpoint M along a linear demand curve like DD (since OMD is an isosceles triangle). For a nonlinear demand curve such as FF , the demand elasticity at point T is identical with the elasticity at T along the tangent straight-line demand curve DD. slope of OM is numerically equal to the negative slope along DD . (That is, OMD is an isosceles triangle.) EXERCISE 5.6 Consider the market demand curve Px = 30 X /4. What is the elasticity of demand when X = 60? (b) When X = 120? (c) When X = 0? A N S W E R : (a) The slope of this linear demand curve is 1/4, so elasticity at any point is equal to ( Px /x )/(1/4) or 4 Px /x . At the point X = 60, the price is Px = 30 60/4 = 15, so elasticity at that point is 4(15/60) = 1. ( X = 60 is the midpoint.) (b) At X = 120, Px = 0 and so elasticity has to be zero. (c) At X = 0, elasticity is negative innite. Whereas the demand curve DD in Figure 5.4 had constant slope, the demand curve EE in Figure 5.5 has constant elasticity. Specically, as drawn this constant elasticity is x = 1. This can be veried using the graphic rule described above to compare the slope of a ray from the origin to the curve with the slope along the curve itself. The geometrical construction shows that points F, G, and H are midpoints of the corresponding tangent lines F F , G G , and H H . General Demand Functions A demand curve of constant slope is a straight line. It can be written as a linear equation: X = A + BPx (5.8) P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 140 5. APPLICATIONS AND EXTENSIONS OF DEMAND THEORY Px 8F E Price($ /X ) 4 G F 2 1 H G H E H x 0 100 F 200 G 400 Quantityof X Figure 5.5. Constant-Unit-Elasticity Demand Curve EE is a demand curve with a constant elasticity of 1. At point F the ray OF and the tangent line segment F form an isosceles triangle, and similarly for points G and H along the curve. Here A and B are constants, and B is normally negative in accordance with the Law of Demand. Taking into account other variables that affect demand, such as income I and the prices of related goods like Y and Z, leads to a generalized demand function in linear form: X = A + BPx + CI + DP y + EPz + (5.9) Here A is a constant term. B is the slope along the demand curve, normally negative. C, the coefcient attaching to income, is the slope of the Income Expansion Curve: it is positive when X is a superior good, and negative when X is inferior. The sign of D is negative if X and Y are complements and positive if the two goods are substitutes. The sign of E will similarly depend upon whether X and Z are complements or substitutes. The dots indicate that an indenite number of other variables might also be used in the estimation. When an econometrician statistically ts a demand function, the equation should be interpreted with caution outside the range of the original data. Taken to extremes, a tted equation may give absurd results. For example, equation (5.9) might seem to imply that X could be positive even when I = 0. But of course, people cannot buy positive amounts of good X when they have zero income I.6 6 Apart from the possibility of borrowing or lending, a topic to be taken up in Chapter 14. P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 5.4 FITTING A DEMAND CURVE 141 For constant-elasticity demand curves, the equation is: X = a Pxb (5.10) Here a is a positive constant and b is a negative constant. In fact, b is the constant elasticity of demand.7 Taking logarithms, equation (5.10) becomes: log X = log a + b log Px (5.10 ) So the statistician, in practice, would nd a constant-elasticity demand curve by tting a straight line to the logarithms of price and quantity. The generalized constant-elasticity demand function can be written: x = a Pxb I c P yd Pze . . . log X = log a + b log Px + c log I + d log P y + e log Pz + (5.11) (As before, the dots indicate possible other variables.) In logarithmic form, this becomes: (5.11 ) Here b is the demand elasticity with respect to the price of X itself (x ), c is the income elasticity ( x ), d is the cross-elasticity with good Y (xy ), and e is the cross-elasticity with good Z (xz ). Lastly, the econometrician may nd that some mixed form best explains the data: a constant-slope response for some of the explanatory variables, and a constant-elasticity response for others. EXERCISE 5.7 William always spends exactly half his income on food F. (a) Express this observation in terms of a demand curve. (b) What can you say about his income elasticity f and price elasticity f for food? A N S W E R : (a) The assertion is that, for William, E f Pf f = I /2. As a demand curve, this can be written as follows: f = 0.5 I / P f = 0.5 I P f 1 , or log f = log 0.5 + log I log Pf Evidently, this is a constant-elasticity demand function like (5.11), though with only price Pf and income I as variables. (b) Comparing Williams demand function with equation (5.11), his income elasticity is c = c f = 1 and his demand elasticity is d = f = 1. EXAMPLE 5.5 DEMAND FOR COFFEE Coffee supply often shifts drastically owing to crop uctuations in the exporting nations, notably Brazil. Since demand for coffee is relatively stable, these supply changes provide the data needed to estimate demand functions. Cliff J. Huang, John 7 b Mathematical Footnote: If X = a Px , then: x d X /d Px ba P b 1 b X /Px x = = =b X /Px X /Px X /Px P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 142 5. APPLICATIONS AND EXTENSIONS OF DEMAND THEORY J. Siegfried, and Farangis Zardoshty examined the U.S. demand for coffee from 1963 to 1977, a period when instant coffee was becoming a major force in the market.a For regular coffee the researchers found that the elasticity of demand was nearly the same at high prices as at low prices. As explained in the text, this justied using a logarithmic (constant-elasticity) equation form. The equation that best t the data was: log C = 0.16 log Pc + 0.51 log I + 0.15 log Pt 0.009T + constant Here C represents the quantity of coffee demanded, I is income, Pc and Pt are the prices of coffee and tea, and T is time. (Certain additional variables used by the authors are omitted here.) So the price elasticity for coffee appears to be 0.16, which means that the demand is quite inelastic. The income elasticity is 0.51, so coffee is a superior good. Since the cross-elasticity 0.15 is positive, tea, as expected, is a substitute for coffee. Finally, the time coefcient is negative, indicating that consumption of regular coffee was subject to a declining trend. For instant coffee, the researchers found rather different results. First of all, the logarithmic form of the equation was inappropriate since the elasticity of demand proved not to be constant. Elasticity was high at high prices and low at low prices, a pattern more consistent with a linear demand curve. The price elasticities for instant coffee ranged from 0.89 at the highest prices down to 0.02 at the lowest prices observed. There was no time trend, suggesting that the overall downward tendency of coffee consumption was offset by increasing appreciation of the convenience of instant coffee owing in part, perhaps, to the growing fraction of married women working away from home. a Cliff J. Huang, John J. Siegfried, and Farangis Zardoshty, The Demand for Coffee in the United States, 19631977, Quarterly Review of Economics and Business, v. 20 (Summer 1980). 5.5 DETERMINANTS OF RESPONSIVENESS OF DEMAND TO PRICE Why is demand for some commodities highly sensitive to price (highly elastic), whereas demand for others is not? Here are some possible explanations. 1. Availability of substitutes: Demand for a commodity will be more elastic the more numerous and the closer the available substitutes. This explanation turns on the substitution effect of a price change, as pictured in Figure 4.18 of the previous chapter. In Figure 5.6, Panel (a) shows two goods that are close substitutes, such as butter and margarine. Here a fall in Px , which tilts the budget line from KL to KL , leads to a large change in an individuals consumption of X. (So x1 is considerably greater than x 0 .) Panel (b) shows two goods that are close complements, such as ink jet cartridges and computer copy paper. At the lower price, here the new quantity x1 is only a little larger than x 0 . 2. Luxuries versus necessities: Demand for a luxury tends to be more elastic than demand for a necessity. Recall that, for a luxury, consumption increases substantially as income rises, whereas, for a necessity, rising income brings about only a small increase in consumption. Thus the argument runs in terms of the income effect of a price change. A reduction in price enriches the consumer in real terms, and such an enrichment will affect purchases of luxuries more than purchases of necessities. P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 5.5 DETERMINANTS OF RESPONSIVENESS OF DEMAND TO PRICE 143 y K K y Quantityof Y Q R Quantityof Y Q R 0 x0 x1 L x L 0 x 0 x1 L x L Quantityof X Panel(a) CloseSubstitutions Quantityof X Panel(b) StrongComplements Figure 5.6. Closeness of Substitutes and Demand Elasticity In Panel (a) the two goods are close substitutes. A decrease in Px shifts the budget line from KL to KL and leads to a relatively large change in consumption of X (from x0 to x1 ). In Panel (b) the two goods are poor substitutes (strong complements): a decrease in Px leads to only a small change in the amount of X purchased. 3. High-priced versus low-priced goods: Along a linear demand curve, elasticity is higher at higher prices. At the choke price where the consumer no longer purchases the good at all the vertical intercept of the demand curve elasticity is innite. So if demand for a good is approximately linear, elasticity will tend to be high near the choke price. (For constant-elasticity demand curves there is no choke price; these demand curves never intersect either axis.) The importance fallacy: Another purported explanation of high and low price elasticities is sometimes encountered in textbooks: it has been termed the importance of being unimportant. The idea is that if commodity X represents only a small (unimportant) fraction k x = Px x / I of peoples budgets, demand for X will be inelastic. (For example, if the price of salt falls, you are unlikely to buy much more salt.) And the same argument would seem to imply, of course, that a commodity that is important in peoples budgets should tend to have highly elastic demand. Once again, the argument here is based on the income effect: if the price of an important commodity falls, the consumer is a lot richer in real terms, and so can buy much more of the commodity. But this argument is wrong. It is true that if X is important in Marys budget and its price falls, we can expect x, the absolute increase in Marys consumption, to be large. But elasticity concerns not the absolute change x but the proportionate change x/x. Since for an important commodity Marys consumption x was very likely large to begin with, the percentage change x/x after a reduction in price need not be large. EXERCISE 5.8 Mary consumes only cheese and wine. Her demand functions for the two products have the constant-elasticity forms c = 0.99 I / Pc and w = 0.01 I / Pw . (a) How P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 144 5. APPLICATIONS AND EXTENSIONS OF DEMAND THEORY important is each commodity for her; that is, what percentages of her budget are accounted for by cheese and wine, respectively? (b) What are the demand elasticities? A N S W E R : (a) The demand equations imply that Pc c = 0.99 I and Pw w = 0.01 I . Mary spends 99% of her income on cheese and only 1% on wine, so the two goods differ in importance by a ratio of 99:1. (b) Still, as follows directly from the fact that her total expenditures on each good remain the same regardless of price (so long as her income is unchanged), her demand elasticities for cheese and for wine are identical: c = w = 1! Yet it is true that the demand for salt is inelastic. If unimportance is not the reason, what is? Actually, all three of the valid explanations listed above apply. Salt has no close substitutes (#1 above), it is a necessity rather than a luxury (#2), and its price is usually very low (#3). These reasons sufce; there is no need to call upon the fallacious unimportance argument. 5.6 MULTIPLE CONSTRAINTS RATIONING The market opportunity set was described in Chapter 4 (see Figure 4.1). If preference directions are up and to the right (that is, if commodities X and Y are both goods), the consumers optimum will be along the budget line the northeast boundary of the opportunity set. But, as noted in Chapter 4, other constraints such as rationing in wartime may prevent the individual from attaining this ideal optimum position. Historically, rationing in wartime or other periods of scarcity has taken one of two forms: coupon rationing or point rationing. Coupon Rationing In World War II most of the nations at war imposed coupon rationing for essential commodities. Since the major purpose of rationing was to prevent rich persons from absorbing a disproportionate fraction of these essential goods, coupons were mainly distributed on a per capita or per family basis.8 Figure 5.7 depicts a consumers choices when gasoline G is rationed. In each panel the vertical dashed line indicates the ration limit Rg . Suppose Panel (a) represents Joans situation. Notice that the ration limit Rg is not binding upon her choices. Though the dashed vertical line does truncate her opportunity set (the shaded area), making unavailable some of the area along and under the budget line KL, her consumption choice C is unaffected since, at the ruling prices, the amount of gasoline she wants to purchase is less than what the ration permits her to buy. In Panel (b) the ration limit Rg is tighter; now the ration constraint binds. Here Joans best achievable point is T. Although forced to consume less of G than desired, she partially compensates by consuming more of the other unrationed good Y. Even so, her best achievable combination at point T leaves her on a lower indifference curve than the original optimum C . 8 Rationing has also been used for purposes other than equalizing consumption. In Nazi Germany, smaller rations were assigned to Jews than to Aryans. During the period 19171921 in revolutionary Russia, formerly upper-class or middle-class citizens were subjected to more stringent food rationing than individuals of proletarian origin. P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 5.6 MULTIPLE CONSTRAINTS RATIONING 145 y K y K Quantityof Y C Quantityof Y T C U U U 0 Rg L g 0 Rg L QuantityofGasoline Panel(b) RationBindin g g QuantityofGasoline Panel(a) RationNotBinding Figure 5.7. Rationing of One Commodity Possible ration limits Rg upon purchases of gasoline are shown as vertical dashed lines. In Panel (a) the ration limit truncates the market opportunity set, but the consumers preferences are such that the limit is not actually binding. In Panel (b) the ration limit is binding. The consumers best attainable combination is at point T, where less gasoline is purchased but more of the other commodity Y. EXERCISE 5.9 Richards Marginal Value for gasoline G in terms of the numeraire good Y that is, the absolute slope of his indifference curve on the g and y axes is MVg = 2 y/g. The prices are Pg = 3 and Py = 1, and his income is I = 180. (a) In the absence of rationing, what is his optimal consumption basket? (b) What if gasoline is subject to a ration limit Rg = 50? (c) What happens if the ration is tightened to Rg = 20? (d) Returning to the original ration limit Rg = 50, what if his income doubles to I = 360? A N S W E R : (a) The data here correspond to Exercise 4.4 of the previous chapter. When the Substitution Balance Equation (in the form MVg = Pg / Py ) and the budget equation ( Pg g + Py y = I ) are solved simultaneously, Richards optimum consumption basket C is g = 40, y = 60. (b) The ration limit Rg = 50 is not binding, so Richards consumption decision remains unchanged. (c) Since the ration limit Rg = 20 now binds, Richard can consume no more gasoline than g = 20. But this permits him to spend the remainder of his income upon good Y, so y = 120. (d) At the higher value of I, Richards C optimum would be g = 80, y = 120. Had Richard been that afuent, the original ration limit Rg = 50 would have been binding. In that case his best consumption basket would have been g = 50 and y = 120. In Figure 5.8, both commodities G and Y are subject to rationing. In Panel (a), although the opportunity set is now truncated at both ends, neither ration is binding: the originally preferred consumption basket C remains attainable. In Panel (b) the Yration is binding but the G-ration is not. Panel (c) shows the opposite situation. Finally, P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 146 5. APPLICATIONS AND EXTENSIONS OF DEMAND THEORY y K K y C Quantityof Y Quantityof Y Ry C Ry T U U U 0 Rg L g 0 g Rg L QuantityofGasoline Panel(b) Y-RationBinding QuantityofGasoline Panel(a) RationsNotBinding y K UU Quantityof Y Quantityof Y Ry K y C Ry T U U T C 0 Rg L g 0 Rg L g QuantityofGasoline Panel(c) G-RationBinding QuantityofGasoline Panel(d) BothRationsBinding Figure 5.8. Rationing of Two Commodities Here the ration limits are Rg and R y (the vertical and horizontal dashed lines). In Panel (a) the ration limit truncates the market opportunity set at both ends, but the consumers preferences are such that the limit is not actually binding for either good. In Panel (b) only R y is binding, whereas in Panel (c) only Rg is binding. In Panel (d) both ration constraints are binding, so at the best attainable position T the consumer is left with unspent income. Panel (d) illustrates a situation where both ration limits are binding. In this last case the consumer is left with unspent income. Point Rationing Coupon rationing as just described is a crude technique. It does not guarantee that poor people will receive the good, but merely limits the consumption of the rich in the hope that more will be left for the poor. Furthermore, goods do not go where they are wanted P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 5.6 MULTIPLE CONSTRAINTS RATIONING 147 most. Suppose tea and coffee are both rationed. Alfred may not care very much for tea, yet, once his coffee ration is used up, he may consume tea for lack of anything better. Similarly Barbara, who only barely tolerates coffee, may nd herself ingesting the stuff once her tea ration is exhausted. The obvious solution would be to let Alfred and Barbara exchange tea and coffee coupons. Historically, such a market solution has rarely been permitted by rationing authorities, seemingly because it comes too close to exchanging coupons for money.9 In the later years of World War II, several countries adopted more sophisticated point rationing schemes. Instead of ration coupons, each individual (or in some cases, each family) was granted a periodic ration-point total N. Like cash, ration points could be spent as desired. The authorities assigned ration-point prices p x and py to commodities, generally differing from the money prices Px and Py . To buy an item, the consumer had to pay both the money price and the point price. Thus, the maximum amount of good X that a consumer could purchase was the smaller of I/Px and N/px . The ordinary incomebudget equation is now supplemented by a point-budget equation, so a consumer faces a two-fold constraint: Px x + P y I px x + p y y N Income constraint Point constraint (5.12) These expressions are both inequalities, which means that part of the available money income, or some of the available point total, may be left unspent. Two possibilities are shown in Figure 5.9. In Panel (a) point income is so large, relative to ordinary cash income, that only the money income constraint binds. This could be the situation of a poor person. Panel (b) represents the opposite case: a rich person for whom cash income is so ample that only the point constraint binds. EXERCISE 5.10 (a) Dennis has cash income I = 180 and faces money prices Px = 3 and Px = 1. He also has N = 400 points; the point prices are px = 4 and p y = 2. Is his effective opportunity set illustrated by either panel of Figure 5.9? (b) What if his point total were N = 200 instead? A N S W E R : (a) His money income budget line has x-intercept 180/3 = 60 and y- intercept 180/1 = 180. His point budget line has x-intercept 400/4 = 100 and yintercept 400/2 = 200. So the picture is like Panel (a) of Figure 5.9: only money income binds for Dennis. (b) Here the point budget line has shifted inward. The x-intercept becomes 200/4 = 50 and the y-intercept 200/2 = 100. Now only points are binding, so the picture is like Panel (b) of Figure 5.9. Last, it may be that money income I limits consumption over part of the opportunity set, whereas elsewhere point income N is binding. In Figure 5.10 the income budget line KL is steeper than the point budget line GH: Px / P y > p x / p y . So commodity X is relatively expensive in terms of ordinary income, whereas commodity Y is expensive in 9 Recall that a major motive for wartime rationing is to equalize consumption despite wealth differences. Allowing exchange of coupons for money partially defeats this purpose even though, since the exchange would be voluntary, both rich and poor benet thereby (at least in their own eyes). The authorities seem to have feared that poorer people, if permitted to sell their coupons, would cut back on the rationed essentials of life and spend more on frills and luxuries. P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 148 5. APPLICATIONS AND EXTENSIONS OF DEMAND THEORY y I/Py N/py I/Py G y K Quantityof Y Quantityof Y K N/p y G L 0 I/Px H N/px x 0 L H N/px I/Px Quantityof X Panel(b) PointConstraintBinding x Quantityof X Panel(a) IncomeConstraintBinding Figure 5.9. Point Rationing Only One Constraint Binding Consumption is subject to an income constraint I as well as a ration-point constraint N. Commodity X is more expensive in terms of income, and commodity y is more expensive in terms of points. The income budget line KL is, therefore, steeper than the point budget line GH. In Panel (a) the point total N is so large that only income is binding; Panel (b) represents the opposite case. terms of points. It follows that consumers who particularly like commodity X tend to nd the income constraint binding; those more interested in consuming Y would tend to nd the point constraint binding.10 Figure 5.10 also illustrates how optimum positions vary with personal preferences. Alberts highest attainable indifference curve UA is at the tangency with the point constraint line GH in its effective (solid) range GM. Bettys highest attainable indifference curve UB is at the intersection point M. And Charless highest indifference curve is at the tangency along the income budget line KL in its effective (solid) range ML. For Albert, only the point constraint is binding; he ends up not spending all his money income. For Charles, only the income constraint is binding and he ends up not spending all his points. Betty spends all her income and all her points. EXERCISE 5.11 (a) Helen has money income I = 200 and faces money prices Px = 3 and Py = 1. She has N = 400 available points, the point prices being px = 2 and p y = 4. Show that her two budget lines intersect, nd the point of intersection, and determine whether it corresponds to Figure 5.10 or to the reverse situation where the point constraint is steeper than the money income constraint. (b) If her preferences are represented by MV x = y/x , to which of the three types of tangencies in Figure 5.10 does her consumption optimum correspond? 10 The opposite case, where the two budget lines intersect but GH is steeper than KL, can be analyzed in a corresponding way. P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 5.6 MULTIPLE CONSTRAINTS RATIONING 149 y I/Py K UA N/Py Quantityof Y G UB C A M C B C C UC L I/Px Quantityof X H N/Px x Figure 5.10. Point Rationing Both Constraints Possibly Binding The point constraint limits consumption in the range GM (the solid portion of the line GH), and the income constraint in the range ML (the solid portion of KL). Alberts highest attainable indifference curve U A is at the tangency point along GM (only the point constraint is binding). For Charles, the highest attainable indifference curve UC is along ML (only the income constraint is binding). Bettys highest attainable indifference curve U B is at the intersection: for her, both constraints are binding. A N S W E R : (a) Simultaneously solving the budget equations for income ( P x x + P y y = I ) and for points ( p x x + p y y = N), the intersection is at x = 40, y = 80. The absolute slope P x / P y = 3 of the income constraint exceeds the absolute slope p x / p y = 0.5 for the point constraint, so this is like the situation pictured in Figure 5.10. (b) If the highest attainable indifference curve is at the intersection point M, it must be that the indifference-curve slope at M is steeper than the slope of the point constraint (line GH ) and atter than the slope of the income constraint (line KL). Helens absolute indifference-curve slope at M is MV x = y/x = 80/40 = 2. Since the slope of the point constraint is 0.5, and that of the income constraint is 3, the condition just stated does indeed hold. So Helens consumption optimum is at the intersection M = (40,80), where both constraints are binding. EXAMPLE 5.6 WARTIME POINT RATIONING Cheese and canned sh were among the commodities rationed by points during World War II in the United States. L. A. Epstein compared the 1942 (prerationing) P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 150 5. APPLICATIONS AND EXTENSIONS OF DEMAND THEORY purchases of different income groups with the quantities that were purchased during 1944 when rationing was effective.a Average weekly purchases by housekeeping families in cities (lb.) $1,000 or less 0.26 0.21 0.24 0.06 Over $4,000 1.03 0.37 0.52 0.28 Income 1942 Cheese Canned sh 1944 Cheese Canned sh $1,0002,000 0.57 0.36 0.33 0.12 $2,0003,000 0.64 0.56 0.44 0.17 $3,0004,000 0.81 0.44 0.49 0.22 Source: Adapted from Epstein, p. 1148. The last three columns show that, in 1944 for the three highest income groups, the consumption patterns in 1944 were almost identical. In that year the richest group consumed 0.52 pounds of cheese and 0.28 pounds of canned sh very little more than the two next-richest groups in the adjoining columns. Consumers in these income brackets were in the situation pictured in Panel (b) of Figure 5.9. Purchases of both cheese and canned sh was almost entirely limited by points, so income being a little higher or lower made little difference. What of price changes? In this period the money price of canned sh relative to cheese approximately doubled between 1942 and 1944. For the lowest income group, the sh/cheese consumption ratio fell from 0.21/0.26 = 0.81 in 1942 to 0.06/0.24 = 0.25 in 1944, showing strong sensitivity to price disparities. (Fish and cheese were evidently close substitutes for these consumers.) But for the highest income group the sh/cheese consumption ratio for 1942 remained almost unchanged in 1944. The reason was, as indicated above, that dollar prices were simply not binding upon the consumption decisions made by families in the upper income ranges. a L. A. Epstein, Wartime Food Purchases, Monthly Labor Review, v. 60 (June 1945), p. 1148. Time as well as income may constrain consumption. Activities such as playing a round of golf, watching a movie, or eating a meal absorb time as well as cash. As society becomes more afuent, the time constraint will grow in importance. People nds themselves wealthier, but increasingly harried for lack of time to do everything they can nancially afford. EXAMPLE 5.7 GASOLINE AND WAITING TIME In the spring of 1980 there was an oil crisis. A quirk of government regulation required certain Chevron gasoline stations in California to charge from 16 to 21 cents per gallon less than competing stations. As would be expected, long lines formed at the low-priced Chevron pumps. Motorists could then choose to wait in line for the cheap gasoline, or else avoid delay by purchasing more expensive gasoline elsewhere. Robert Deacon and Jon Sonstelie surveyed customers at a low-priced Chevron station and at two neighboring stations, a Mobil and a Union, where prices were P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 SUMMARY 151 uncontrolled.a The table shows some of the data collected for 109 Chevron customers and 61 non-Chevron customers. Average values of variables Chevron Gallons purchased % weekend customers % with passengers % employed full-time % housewives 11.6 31.2 7.3 67.9 5.5 Non-Chevron 8.8 26.2 18.0 83.6 3.3 Source: Adapted from Deacon and Sonstelie, p. 636. As can be seen, average purchases were larger at the stations where waiting in line was required. For consumers who will be waiting a long time in line, it makes sense to hold off relling until the fuel gauge reads (say) 10% rather than 25%. The Chevron customers, the ones more willing to wait in line, were also more likely to be purchasing on weekends (where time pressures are normally less severe) and more likely to be housewives. Conversely, the non-Chevron customers (those who preferred not to wait) were more likely to be employed full time or to be carrying passengers. Calculating in terms of the size of purchase and the minutes spent in line, the authors were also able to estimate gasoline purchasers value of time. The average Chevron customer saved $1.94 by waiting in 14.6 minutes, implying an average time value of $7.97 per hour. But this value differed by type of customer, ranging from $3.52 to $5.39 per hour for part-time workers up to $11.26 to $17.26 per hour for those fully employed and reporting income over $40,000. a Robert T. Deacon and Ron Sonstelie, Rationing by Waiting and the Value of Time: Results from a Natural Experiment, Journal of Political Economy, v. 93 (August 1985). SUMMARY Elasticity is a unit-free measure of how a change in one variable is associated with a change in another variable. 1. The response of quantity demand to changes in income is measured by the income elasticity of demand for commodity X, denoted x . It is the percent change in the quantity of X purchased, divided by the percent change in income I. Income elasticity is positive for superior goods, and negative for inferior goods. 2. The response of quantity demand to changes in price is measured by the price elasticity of demand for good X, denoted x . It is the percent change in the quantity of good X purchased, divided by the percent change in the price of good X. The Law of Demand implies that price elasticity is negative. Demand is said to be elastic if x < 1; a fall in the price of the good then leads to increased spending on that good. Demand is inelastic if x < 1; a fall in the price of the good then leads to lower spending on that good. Demand is unitary elasticity when = 1; a fall in the price the good leaves spending unchanged. 3. The cross-elasticity of demand xy is the percent change in the quantity demanded of good X, divided by the percent price change of a different good. If the P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 152 5. APPLICATIONS AND EXTENSIONS OF DEMAND THEORY cross-elasticity is positive, the two goods are substitutes. If the cross-elasticity is negative, the two goods are complements. The additional spending on a good induced by a small increase in the quantity sold is Marginal Revenue to the seller, and equals Px (1 + 1/x ) Demand functions are commonly estimated (tted) from data using either a constantslope (linear) form or a constant-elasticity form. Price elasticity changes along a linear demand curve, increasing in absolute value moving northwest along the curve. Demand elasticity is high: (1) if the good has close substitutes; (2) if the good is a luxury (a strongly superior good); (3) if the price is high, that is, near the consumers choke price. However, it is not in general true that an important good (one accounting for a large proportion of the consumers budget) tends to have high elasticity, or that an unimportant good tends to have low price elasticity. Consumption opportunities may be constrained by factors other than market price, for example by limitations of time or by rationing in wartime. If good X is rationed by coupon, the ration may or may not be binding depending upon the consumers income and preferences. If the ration is binding, the consumer will in part compensate by buying more of other commodities. Under point rationing, either points alone may be binding, or dollars alone may be binding, or both may be binding. QUESTIONS The answers to daggered questions appear at the end of the book. For Review 1. What is the general denition of all elasticity measures? Why is the income elasticity of demand considered a more useful measure than the simple slope along an Engel Curve? Why is the price elasticity of demand considered a more useful measure than the simple slope along a demand curve? Are elasticity measures always better than the simple measures? (See question 2.) 2. Consider this paradox: Income elasticity is supposed to measure the responsiveness of consumption to changes in income. But income elasticity is unity along any Engel Curve that is a straight line through the origin, whether very steep or very at. Since Engel Curves of different steepness surely show different responses of consumption to income, how can they all be characterized as having the same income elasticity? 3. True or false: Income elasticity is unity at any point along an Engel Curve such that the tangent at that point extends through the origin. Explain. 4. True or false: Since income elasticities must average out to unity, any commodity accounting for a very large fraction of income expenditure must have an income elasticity close to 1. Explain. 5. a. b. c. What is meant by elastic demand and inelastic demand? How can elasticity at a point along a linear demand curve be determined by inspection? Along a nonlinear demand curve? 6. Let the demand curve be P = A BG, where A and B are positive constants. a. What is the elasticity at G = 0? b. At G = A/ B ? c. At G = A/(2B)? P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 QUESTIONS 153 7. If the demand curve is PG = 100, what is the price elasticity of demand at G = 10? At G = 50? At G = 100? 8. What is the analytical form of a demand function that is linear in both income and price? What is the analytical form of a demand function that has constant elasticities with respect to both income and price? Explain the economic meaning of each form. 9. If a single all-important commodity absorbs all of the individuals income, what is its price elasticity? What is its income elasticity? 10. Gasoline rationing was proposed in 1973 and again in 1979 as a remedy for the energy crisis. If all persons are given identical rations, compare the opportunity sets of a wealthy and a poor consumer for gasoline consumption versus all other goods. Would permitting sale of coupons be a good idea? For Further Thought and Discussion 1. On average over all goods, income elasticity must be unity. Prove this proposition. 2. a. b. c. d. Consider the demand curve PG = 100. What happens to the elasticity of demand as price falls? What happens to importance (share of the consumer budget spent on G) as price falls? Apply the previous questions for the demand curve P 2 G = 100. For the demand curve P 1/2 G = 100. What can you infer about the relation between elasticity and importance? 3. The American economist Irving Fisher argued in 1891 that a poor community will hardly distinguish quality grades of a commodity like beef, while a rich community would. In the country districts of the West all cuts of beef sell for the same price (about 10 cents per lb.). In the cities of the West two or three qualities are commonly distinguished, while in New York a grocer will enumerate over a dozen prices in the same beef varying from 10 to 25 cents per lb. [Irving Fisher, Mathematical Investigations in the Theory of Value and Prices (New Haven: Yale University Press, 1925), p. 74.] a. Construct the implied indifference curves, at low and high levels of income, between low-quality beef and high-quality beef. b. Why should different beef qualities be better substitutes at low incomes than at high incomes? What would you anticipate about the price elasticity of demand for low-quality beef in poor versus rich communities? For high-quality beef? 4. Name some goods you expect to have elastic demand and some with inelastic demand. Justify your choices. 5. Tickets to a sports match are available only on a black-market basis. Professor G, calling from out of town, gives purchasing instructions to his secretary: If the price is $30 each, buy one ticket for me; at $20 each, buy two; if it is $10, buy three. The secretary says: Prof, there must be something wrong here. Youre saying youd be willing to pay more in total for two tickets than for three! Is the secretary correct? Explain. 6. For a commodity with snob appeal, consumers might be willing to buy more at a higher price than at a lower price (violation of the Law of Demand). Is this possible or likely? Explain. 7. If uninformed consumers judge quality by price, they may also be willing to buy more at a higher than at a lower price. Is this possible or likely? Explain. 8. What could cause a commoditys Engel Curve to become steeper, while remaining linear through the origin? [Hint: What if the purchased quantities were to double at each income level?] P1: JzG 0521818648c05.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:25 154 5. APPLICATIONS AND EXTENSIONS OF DEMAND THEORY 9. From the numbers shown in Figure 5.5, can you gure out what is the xed total spending E x P x X associated with demand curve EE ? 10. Suppose that a good X has a close substitute Y and a distant substitute Z. Do you expect the cross-elasticity of demand for X with respect to the price of Y to be positive or negative? The cross-elasticity of demand for X with respect to the price of Z ? Which elasticity do you expect to be larger? 11. In wartime rationing situations it is generally illegal to buy another persons ration allowances for cash, or to exchange ration coupons. a. Is there any justication for this? b. Are there adverse consequences of forbidding such exchanges? P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 III THE FIRM AND THE INDUSTRY 155 P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 156 P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 6 6.1 The Business Firm Why Firms? Entrepreneur, Owner, Manager 158 Economic Prot versus Accounting Prot 160 The Separation of Ownership and Control 160 6.2 The Optimum of the Firm in Pure Competition 165 The Shutdown Decision 172 An Application: Division of Output among Plants 174 6.3 Cost Functions 176 Short Run versus Long Run 176 Rising Costs and Diminishing Returns 180 6.4 An Application: Peak versus Off-Peak Operation 182 SUMMARY 186 QUESTIONS 187 EXAMPLES 6.1 6.2 6.3 6.4 6.5 6.6 Mergers and Takeovers 161 Takeover Defenses, Corporate Governance, and Stock Prices 162 CEO Compensation 164 Scale Economies in Electric Power Distribution 166 Scale Economies Nuclear versus Fossil Fuels 181 Peak versus Off-Peak Operation: Water Supply 182 157 P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 158 6. THE BUSINESS FIRM Part II of this text analyzed consumer choices the demand side of the market for goods and services. Part III now deals with the supply side. This chapter explains the nature of business rms and the relations among entrepreneurs, owners, and managers. The chapter then describes the rms cost and revenue functions and its prot-maximizing level of production. 6.1 WHY FIRMS? ENTREPRENEUR, OWNER, MANAGER Business rms are articial creations, organized to produce goods and services for the market. But individuals or groups can produce for the market without creating a rm. So if rms are not essential, why are they formed? Firms exist to take advantage of team production while minimizing costs of contracting. All but the simplest production processes call for team effort. Manufacturing typically requires machine operators, inspectors, and clerks together with nonlabor inputs such as electricity, materials, and buildings. The same holds for mining, transportation, retail sales, and so forth. Still, team production could take place without forming a rm. A movie could be produced via a multilateral contract specifying the types and quantities of inputs to be provided, at stated places and times, by the producer, director, actors, camera operators, and so on. The contract would also need to dene each persons nancial obligations and rewards. Such multilateral deals do occur. But the high costs of negotiation and enforcement make them rare. If instead a rm produced the movie, only bilateral contracting would be required. Each resource-owner would need only to contract with the rm itself, on a one-to-one basis. Yet people can really deal only with other human beings. Some person or group, management, is needed to act in the name of the rm. Management must necessarily be granted some discretion for example, to decide how many workers to employ. So forming a rm replaces a set of highly specic contracts among team members with a more general contract that grants management leeway for dealing with suppliers, employees, and customers. Management differs from ownership. The owners of a rm are the residual claimants, those legally entitled to the rms income or assets after all contractual payments are made. Although combining ownership and management has advantages, larger rms usually divide the two functions. Owners, instead of managing the rm themselves, authorize someone else to negotiate and enforce the rms contracts with other resource-suppliers. But who monitors the managers? Ultimately, it is up to the owners to do that monitoring themselves. This inescapable decision-making aspect of rm ownership is called entrepreneurship. Even though rms are set up to reduce costs of contracting, the owners (if there are more than one) must still contract among themselves to set up the rm. If owners do not themselves manage the rm, then the owners must contract with the managers. The corporate form is a specic type of contract among multiple owners of a rm. It has been hugely successful, thanks to two key features: limited liability and transferable shares. Limited liability means that the contractual obligations of the corporation are not personal obligations of the individual owner or owners. A supplier owed money can sue the corporation, but cannot sue any individual stockholder. Shares may become P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 6.1 WHY FIRMS? ENTREPRENEUR, OWNER, MANAGER 159 valueless (at worst), but the rest of the owners assets are safe. And transferability make it possible for any individual stockholder who needs cash, or who is dissatised with corporate practices or policies, to exit by selling his or her stock. These two features are connected. Under unlimited liability, were a stockholder with a good credit rating to sell out to another with shakier nancial standing, the rms creditors would surely object. But if liability is limited anyway, creditors dont care who the owners are. Why would creditors ever deal with a rm whose owners have only limited liability? Banks that lend to the rm, and workers paid only at the end of the month, must worry about the money owed them. The same holds for consumers who make advance payments: you become a creditor of a corporation such as American Airlines when you buy an airline ticket. So, it may appear, nanciers and suppliers and consumers should all prefer to deal with companies whose owners have unlimited liability in the event of default. Other things equal, this is true. But no one is forced to do business with corporations on a limited-liability basis. Indeed, banks, before lending to a small corporation, often insist that the owners back up the corporations credit by accepting personal liability for its debts. People deal with corporations on limited liability terms because despite the risk on balance they expect to gain thereby. It is up to the corporation to offer terms favorable enough so that, despite limited liability, suppliers and customers are willing to do business with it. What types of people are likely to become owner/entrepreneurs, residual claimants? Consider farming. The landowner might possibly be the owner/entrepreneur, hiring labor at a contractually xed wage. Alternatively, the working farmer might be the owner/entrepreneur, leasing the land at a contractually xed rent. Similarly, in a software rm, the entrepreneur might be the programmer, the nancial ofcer, or the person with the innovative idea. All these possibilities occur, but a few general principles apply. One is the need for monitoring. It is easier for a working farmer to know the quality of the land than it is for the landowner to check how hard a farm laborer is working. So agricultural enterprises are more often owned by working farmers than by absentee landlords.1 A small restaurant is more likely to be owned by the cashier or the chef or the food buyer, each of whom might otherwise be in a position to cheat or shirk, than by the landlord of the building or the supplier of the silverware. More generally, inputs whose provision can easily be checked for quantity or quality tend to be bought or rented under contract, whereas owners are more likely to provide those goods or services that are difcult to monitor. A second factor is the distribution of risk. Since residual claimants are more exposed to the hazards of doing business, someone very averse to risk is likely to prefer xed contractual payment instead. Corporate bonds (nonownership investments) are typically owned by trust funds and other risk-averse investors, whereas corporate shares (ownership investments) are generally held by investors willing to accept risk.2 1 2 Hence the proverb: The best fertilizer is the owners footprint in the soil. In farming and some other businesses, under share-cropping arrangements landowner and worker each receive a percentage of the crop. So each side must monitor the other, which might be costly. The advantage of share-cropping is that the risks of crop failure and of price uctuations can be divided between the parties. P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 160 6. THE BUSINESS FIRM Economic Prot versus Accounting Prot Individuals maximize utility, but what do rms maximize? Economists usually assume that the rm maximizes its prot the difference between Total Revenue and Total Cost. A rms revenue is its receipts from sales. Cost is a more complicated concept. The economic cost of any activity, its opportunity cost, is the value of the best foregone alternative. To attract inputs necessary for production, the rm must pay each resourceowner an amount sufcient to warrant sacricing his or her next best opportunity whether that be some other employment of the resource or choosing to retain it for reservation uses (as will be explained in more detail in Chapter 12). The concept of economic prot tells the rm whether it should remain in business, or instead shut down. If economic prot is positive, owners of the rm will want to remain in business. And from the viewpoint of the economy as a whole, positive economic prot means that the value consumers place upon the rms production (Total Revenue) exceeds the value that suppliers attach to the best alternative uses (Total Cost). In contrast, if economic prot is negative the owners of the rm would want to shut it down. And for the economy as a whole, negative economic prot indicates that the resources would be more productive elsewhere. Accounting prot is a measure used for quite different purposes, among them controlling fraud and computing tax liabilities. In contrast to economic prot, accounting prot does not deduct the alternative opportunity value of the owners self-supplied services. A shopkeepers accountant might report annual revenue of $96,000 and expenses of $64,000 so that the accounting prot was $32,000. But if the shopkeeper could have clerked that year at a local supermarket for $42,000, and if there are no other costs that need be considered, the economic prot of the business is $96,000 $64,000 $42,000 = $6,000, a negative number. So whereas the accountant would say the rm is making a prot (and the tax authorities will want to collect a slice), the shopkeeper would do better by shutting down. (We set aside other possible considerations, such as the satisfaction of running ones own business.) Failure to allow for alternative uses of the entrepreneurs self-supplied resource makes accounting prot exceed economic prot. The costs taken into account by the concepts of economic prot and accounting prot also diverge. Suppose the rm owns a building that has risen or fallen in value. In estimating accounting prot the accountant would deduct an annual depreciation gure based upon the historical cost of the building. But for estimating economic prot, the relevant cost is what some other party would pay for the property today. If in the meantime the building has risen in price, the accountants measure of depreciation would understate the true cost of operating the business. Or of course, if the building has declined rather than grown in value, the bias would go the other way. The Separation of Ownership and Control Some critics claim that in modern corporations the economists standard assumption that rms maximize economic prot is false. Instead, they allege, managers can run things pretty much their own way even though theoretically they are merely employees of the owners (the stockholders), are supervised by elected Boards of Directors, and are subject to legal constraints. Supposedly, this especially applies to very large rms, whose ownership may be so highly diffused that any one person or family owns only a small P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 6.1 WHY FIRMS? ENTREPRENEUR, OWNER, MANAGER 161 fraction of the shares. If so, though collectively the stockholders elect the directors and thus indirectly choose the managers, each shareholder may be individually powerless. Still, there are limits to managerial control. If shareholders were literally powerless, management could do whatever it wished, even dissipate the value of the rm by enormous executive salaries and expense accounts. But managers do not quite have a license to steal. Shareholders can and do sue executives for violating the contract setting up the rm (the corporate charter) or the managers contract with the rm. And although it might not pay small stockholders to monitor management, large stockholders may be motivated to do so. The 2002 merger of Hewlett Packard and Compaq was publicly opposed by members of the Hewlett family, although the deal was eventually approved by a close shareholder vote. So at least some owners do indeed monitor corporate managers. An additional check on managerial control arises when outsiders stand ready to supplant a self-serving or inefcient management. If the rms earnings are less than they should be, the companys stock price will be low. An outside group might then try to take over the rm, buying shares at their current low prices or else challenging existing management in a proxy contest for control. EXAMPLE 6.1 MERGERS AND TAKEOVERS When management of a corporation performs poorly for shareholders, the stock price tends to fall. An outside group could attempt to gain control by (i) purchasing shares in the open market, (ii) making a tender offer to stockholders for a controlling block of shares, or (iii) winning shareholder support in a proxy ght. Or possibly, the threat of a takeover contest may lead existing management to negotiate a transfer of power, usually by merging the rm with the outsiders corporation. If the general market opinion is that the new management will run the company more protably, a successful takeover will lead the stock price to increase. Factoring out movements of the stock market as a whole, Michael C. Jensen and Richard S. Ruback calculated the abnormal stock price effect attributable to the takeover itself.a Table 1 summarizes some of their estimates, which integrated several studies based mainly on pre-1980 data. Table 1 Abnormal stock price changes Takeover classication Successful takeovers Tender offer Mergers Proxy contests Unsuccessful takeovers Tender offers Mergers Proxy contests Price change (%) 30 20 8 3 3 8 Source: Adapted from Jensen and Ruback, Tables 1 and 2, pp. 78. Evidently, shareholders proted from successful takeovers; this suggests that previous management had not maximized prots for the shareholders. Shareholders gained little if anything after unsuccessful takeover attempts. The low returns may P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 162 6. THE BUSINESS FIRM reect disappointment by investors that a potentially more effective management had failed to gain control. Or the takeovers may have failed because the stockholders doubted that the challenging group would do any better. A later study by George Andrade, Mark Mitchell, and Erik Stafford examined the frequency of hostile takeovers since 1973.b The rst column of Table 2 shows that in 19731979 hostile bids took place for 8.4% of the stocks listed on the New York Stock Exchange, the American Stock Exchange, or Nasdaq. Of these, 4.1%, around half, were successful. The middle column shows a sharp jump in the frequency of hostile bids during the 1980s, and the last column reveals an even more drastic dropoff in the 1990s. One important reason for the decline is the adoption of antitakeover defenses, among them poison pills and golden parachutes (see Example 6.2). An alternative explanation is that the takeover threat has historically done its job, so that managements on average have now become more responsive to the interests of stockholders. Table 2 Merger bids and abnormal stock returns 19731979 % Hostile bids % Successful hostile bids % Gain to target rms % Gain to acquirer rms 8.4 4.1 16.0 0.3 19801989 14.3 7.1 16.0 0.4 19901998 4.0 2.6 15.9 1.0 Source: Adapted from Andrade et al., Table 1 and Table 3. Table 2 also conrms that shareholders in target rms consistently gained from successful takeovers. (The abnormal return tabulated here is the percent gain on the stock in the 3-day period surrounding the merger announcement.) But acquirer rms seem to come out, on average, a bit behind! It may be that many takeovers are motivated by nonpecuniary considerations such as empire-building or powerseeking. Or, alternatively, the takeover business may be so competitive that (at least on average) large prots cannot be earned. a Michael C. Jensen and Richard S. Ruback, The Market for Corporate Control: The Scientic Evi- dence, Journal of Financial Economics, v. 11 (1983), pp. 550. b George Andrade, Mark Mitchell, and Erik Stafford, New Evidence and Perspectives on Mergers, Journal of Economic Perspectives, v. 15 (2001), pp. 103120. Managements have sometimes been able to secure state legislation to restrict takeover attempts. Also, the Boards of Directors of most large corporations have adopted a variety of antitakeover provisions, usually with stockholder approval. Whether these defenses on balance help or hurt shareholders has been the subject of much debate. EXAMPLE 6.2 TAKEOVER DEFENSES, CORPORATE GOVERNANCE, AND STOCK PRICES Paul A. Gompers, Joy L. Ishii, and Andrew Metrick created an index based on 24 different corporate governance provisions, all associated with defending management against takeovers, and related this index to the level and movements of stock prices.a P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 6.1 WHY FIRMS? ENTREPRENEUR, OWNER, MANAGER 163 The table shows, for a sample of about 1,500 corporations, the percentages that adopted a selection of antitakeover provisions as of 1998. Selected corporate governance provisions (1998) Provision Blank check Classied board Golden parachutes Indemnication Poison pill Percentage 87.9 59.4 56.6 24.4 55.3 Description of provision Preferred stock over which board has wide authority to determine voting, conversion, and other rights Directors serve overlapping terms (so board cannot be overturned all at once) Generous compensation for management if forced out in a takeover Protects ofcers from lawsuits based on their conduct Gives stockholders, other than takeover bidder, rights to purchase stock at steep discount after change of control. Supermajority (beyond that specied in state law) required for takeovers Supermajority 34.1 Source: Selected and adapted from Gompers, Ishii, and Metrick, Table 1. The authors index of corporate governance was essentially the number of such antitakeover measures adopted by a corporation. (So high values of the index represent greater freedom of action for management.) To test how corporate governance affects stock prices, they compared a hypothetical portfolio of stocks in the lowest 10 percent of the index (strongest shareholder rights) with an opposite portfolio of stocks in the highest 10 percent (weakest shareholder rights). The group with strong shareholder rights included well-known companies such as IBM, Wal-Mart, and Du Pont; the group with weak shareholder rights included companies such as NCR, Kmart, and Time Warner. They found that during the 1990s, the rst portfolio earned 23.3 percent per year, but the second only 14 percent. The difference did not seem to reect different levels of riskiness between the two portfolios, or the performance of just a few rms in either portfolio, or different industrial compositions of the two portfolios. These results suggest that antitakeover provisions have on average harmed shareholders. COMMENT Nevertheless, stockholders usually voted to approve these changes in corporate charters. Or at any rate, the shareholders had elected directors who adopted such provisions. This seeming paradox is the subject of continuing discussion and debate among economists and policy-makers. a Paul A. Gompers, Joy L. Ishii, and Andrew Metrick, Corporate Governance and Equity Prices, National Bureau of Economic Research Working Paper 8449 (2001). The critique of the prot-maximizing model need not go so far as to claim that shareholders are powerless. Perhaps management provides a minimum level of profits, enough to head off lawsuits or takeover contests. But beyond this, critics contend, entrenched managers can pursue their own goals rather than those of owners. Managers may seek power (empire-building), publicity in the form of a corporate image, amenities like luxurious ofces, or a stable environment without risk of unpleasant P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 164 6. THE BUSINESS FIRM surprises. Stockholders may sometimes be able to verify that such abuses occurred, at least after the fact. If such an entrenched manager unexpectedly relinquishes control in the extreme case, if he or she dies suddenly, then the stock price should jump.3 The incentives for managers to shirk on their duties to shareholders can arguably be reduced by compensation packages (including salaries, options, and possible other payments) that reward good performance. EXAMPLE 6.3 CEO COMPENSATION Paul L. Joskow and Nancy L. Rose studied the association between compensation received by chief executives and rms success in the period 19701990.a CEO pay packages in that period were typically designed to reect protability in the current and in the two previous years. The averaging tends to minimize the role of random or accidental elements in any single year. CEO compensation contracts, the authors found including salary and bonuses, other company benets, and especially stock options allowed for both the market rate of return accruing to stockholders (reported earnings divided by share price) and the rms accounting rate of return (reported earnings divided by book value of the rms equity). In the 1980s, for example, an increase in the current market return on company shares from 15 to 25% over a three-year period raised CEO compensation on average by around 4.7%. A similar calculation in terms of accounting rates of return (which were typically smaller than stockmarket returns in this bull-market period) was associated with a compensation increase of 11.7%. COMMENT In view of the conceptual superiority of economic prot as opposed to accounting prot, it may seem surprising that Boards of Directors tied CEO compensation to reported corporate earnings, which is closer to accounting prot than to economic prot. But economic prot is calculated in terms of alternative opportunities, which are not directly measurable. In contrast, accounting data are generated under established rules and standards, and hence are more objective even if conceptually less meaningful. Also, managers are commonly compensated in terms of year-toyear earnings changes. Despite the conceptual aws, it is reasonable to assume that year-to-year increases or decreases in accounting earnings typically correlate well with increases or decreases of true economic prot. a Paul L. Joskow and Nancy L. Rose, CEO Pay and Firm Performance: Dynamics, Asymmetries, and Alternative Performance Measures, National Bureau of Economic Research Working Paper No. 4976 (December 1994). 3 Armand Hammer, the long-time chief executive of the Occidental Petroleum Corporation, died in 1990. Since Hammer was 92 years old, this was not totally unexpected, but as the death was due to a home accident there was some surprise. Hammer had often been accused of abusing his executive position for personal advantage. On the day after Hammers death, the New York Stock Exchange was ooded with buy orders for Occidental shares. The stock ended the day up about 9% an increase in market value of over $550,000,000. This might be interpreted as convincing support for the allegations against Hammer. But the increase was completely reversed the next day, and in the week following there were no abnormal changes in the stock price. So it is not clear after all that stock investors regarded Hammers management as exploitive. P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 6.2 THE OPTIMUM OF THE FIRM IN PURE COMPETITION 165 No doubt managers sometimes serve their own interests at the expense of the owners. But does this problem make the hypothesis that rms maximize prot unworkable? Overall, economists have found that viewing rms as maximizing prot has proved to be more useful than alternative assumptions. 6.2 THE OPTIMUM OF THE FIRM IN PURE COMPETITION Economic prot, symbolized here as ,4 is the difference between the rms Total Revenue and Total Cost or, for short, between its Revenue R and Cost C. The cost concept is of course economic cost rather than accounting cost. And Revenue for the rm is price P times output q. In symbols: RC R P q (6.1) (6.2) This chapter deals with a competitive or price-taking rm. By denition, a competitive rm views the market price P as constant, regardless of its own output. (While never literally true, this may approximate reality if the rm produces only a small fraction of the output in its industry.) A hump-shaped Total Revenue curve was pictured in Figure 2.10 of Chapter 2. In the upper panel, R rst increases as output q rises, but then decreases. The reason is that there are two offsetting forces. R is the product q P, but as quantity q rises price P tends to fall. However, the picture in Figure 2.10 does not apply to the price-taking rm of this chapter.5 The assumption here is that price P is constant regardless of the rms own output, so Total Revenue R rises in proportion to output. For a competitive rm the Total Revenue curve R is not hump-shaped, but is instead a ray out of the origin with slope P, as shown in the upper panel of Figure 6.1. The Total Cost function, which was briey described in Chapter 2 (see Figure 2.11), is shown again here as the curve C in the upper panel of Figure 6.1. Note that Cost may be positive even when q = 0. The reason is Fixed Cost, for example rent that has to paid for use of a building even when nothing is produced. So Total Cost is the sum of Fixed Cost (F ) and Variable Cost (F ): C F +V (6.3) Apart from the positive vertical intercept F in the diagram, Total Cost curves have the following typical features: 1. At low output, cost rises with quantity but at a decreasing rate, owing to the advantages of large-scale production. 2. At high output, however, cost rises with quantity at an increasing rate, reecting the Law of Diminishing Returns. 4 5 is the Greek upper-case letter pi. The picture in Figure 2.10 would apply to a monopoly rm, to be studied in Chapter 8. P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 166 6. THE BUSINESS FIRM $ C R Dollars F 1 1 MC P = MR q q OutputQuantity q 0 $/q DollarsperUnitQuantity P AC 0 q q q q OutputQuantity EXAMPLE 6.4 SCALE ECONOMIES IN ELECTRIC POWER DISTRIBUTION John E. Kwoka, Jr. analyzed the cost structure of electric power distribution in a report produced for the American Public Power Association.a Distribution costs fall into two main categories: wire costs (providing the physical network for movement of electricity) were around 60%, and supply costs (marketing and administrative functions such as packaging and selling power, billing, and servicing accounts) were around 40% of the total. The table here shows that, in terms of customer numbers, wire costs and supply costs both displayed economies of scale (falling Average Cost), but only up to a point. Economies of scale were more evident for the physical or wire aspect of the business: unit costs started high, reached a minimum at about 1,470,000 customers, and then turned upward. Unit supply costs were more uniform: they fell less sharply to begin with, reached a minimum at about 530,000 customers, and rose moderately thereafter. The difference is understandable. Wire costs involve big physical investments that must be spread over a large clientele to Figure 6.1. Optimum of the Competitive Firm The prot-maximizing output is q in the upper diagram, where the vertical difference between the Total Revenue curve R and the Total Cost curve C is maximized. The maximized prot is . At q the slopes along curves R and C are equal, so in the lower diagram the Marginal Revenue curve MR and the Marginal Cost curve MC intersect at output q . At output q in the upper diagram, a ray from the origin is tangent to the Total Cost curve, which means that Average Cost equals Marginal Cost. Thus, in the lower diagram q lies at the intersection of the MC and AC curves, where Average Cost is at a minimum. MC AC AR = MR = d q P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 6.2 THE OPTIMUM OF THE FIRM IN PURE COMPETITION 167 become economical, whereas costs of billing are more proportional to customer numbers. Average costs per KWH, by number of customers Number of customers ( 000s) 1 5 10 50 100 500 1000 1500 2000 3000 5000 Unit wire costs (cents/KWH) 1.741 0.9666 0.868 0.782 0.763 0.688 0.635 0.620 0.640 0.788 1.520 Unit supply costs (cents/KWH) 1.035 0.633 0.583 0.542 0.537 0.530 0.531 0.539 0.552 0.596 0.752 Source: Adapted form Kwoka, Table 5. a John E. Kwoka, Jr., Electric Power Distribution Costs: Analysis and Implications for Restructuring, A Report to the American Public Power Association (2001). Looking at the Revenue side in more detail, Average Revenue AR and Marginal Revenue MR were dened in Chapter 2 as: MR R q and AR R q (6.4) (As before, the symbol indicates small changes of the variable.) Geometrically, MR is the slope of the TR curve. For the competitive (price-taking) rm assumed here, the slope is a constant equal to the market price P, as suggested by the small triangle drawn along the curve in the upper panel of Figure 6.1. Since Marginal Revenue is constant and equal to P, in the lower panel MR becomes a horizontal line at height P. Total Revenue and Total Cost are measured in dollars,6 so the vertical axis in the upper panel of Figure 6.1 is scaled in dollar units. But Average Revenue and Marginal Revenue, and Average Cost and Marginal Cost, have the dimension dollars per unit quantity (like price itself), so the vertical axis of the lower panel is scaled in units of $/q. [Caution: As already explained in Chapter 2, it is a mistake to plot average or marginal curves in a total diagram where the vertical axis is scaled in dollars. And do not plot total curves in an average-marginal diagram where the vertical axis is scaled in dollars per unit of output ($/q ).] From the denition of Average Revenue above, since R P q it follows also that AR P R /q . That is, Average Revenue AR is the same as price P.7 Since price is 6 7 As mentioned in Chapter 2, Revenue and Cost can be interpreted as dollars per unit time. Assuming each unit of the product is sold at the same price, as necessarily holds under perfect competition. P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 168 6. THE BUSINESS FIRM constant here, the AR curve in Panel (b) must be a horizontal line at the level of P. Thus, for a price-taking rm the AR curve and the MR curves coincide, as a horizontal line at height P. (This is an example of Proposition 2.2c of Chapter 2: When the average function is constant, the marginal function is equal to it.) Last, note that the horizontal line P = AR = MR can be interpreted as the demand curve d faced by this single rm. EXERCISE 6.1 A rm faces a horizontal demand curve at the market price P = 25, independent of its own output q. What are the equations for Total Revenue, Marginal Revenue, and Average Revenue? A N S W E R : Total Revenue is R = 25q. Since R / q the increase in R per unit increase in q is always 25, we know that Marginal Revenue is a constant with equation MR = 25. And since R /q = 25, Average Revenue is also constant with equation AR = 25. Turning to the cost side, Marginal Cost MC and Average Cost AC are: MC C q and AC C q (6.5) In the upper panel of Figure 6.1, MC is the slope along the Total Cost curve (note the small illustrative triangle drawn along the curve). As plotted in the lower panel, MC rst declines (corresponding to the region where C rises at a decreasing rate) but eventually begins to rise (corresponding to the region where C rises at an increasing rate). The shape of the Average Cost curve AC in the lower panel can be derived similarly. In the upper panel, AC C /q corresponds to the slope of a ray drawn from the origin to the C curve. At q = 0 this ray is vertical, so AC is innite at the vertical axis. As output increases, the slope of the ray falls until output reaches q . This is the point of minimum AC. Thereafter, the slope of the ray rises as q increases. From Propositions 2.2a, b, and c of Chapter 2 we know that when AC is falling, MC lies below it; when AC is rising, MC lies above it; and when AC is constant (at a minimum), MC = AC . Accordingly, the lower panel of Figure 6.1 shows that MC lies below AC for outputs less than q , that MC cuts (equals) AC at q (where AC is at a minimum), and that MC is greater than AC for outputs greater than q . In the upper panel the maximum prot occurs at q , where the Total Revenue curve R and Total Cost curve C are parallel. (The parallelism is suggested by the dashed line drawn tangent to the C curve at q = q .) Since MR is the slope of the R curve, and MC is the slope of the C curve, it follows that in the lower panel MR and MC are equal (the MR and MC curves intersect) at q . So the rm maximizes prot by choosing the output at which Marginal Revenue = Marginal Cost. And since we are dealing with a competitive (price-taking) rm for which MR = Price = AR, this condition takes on the specic form MC = MR = P Maximum-Prot Condition, Competitive Firm (6.6) But there is an important qualication. Setting MC = MR maximizes prot only if the MC curve cuts the MR curve from below. Notice that, in the lower panel of Figure 6.1, the MR and MC curves intersect twice. But at the left-hand intersection (where P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 6.2 THE OPTIMUM OF THE FIRM IN PURE COMPETITION 169 q = q ), MC cuts MR from above. Since to the right of that intersection MR exceeds MC, economic logic tells us that it pays to produce more units until the right-hand intersection is reached where MC cuts MR from below.8 PROPOSITION: The prot-maximizing output for the rm occurs where Marginal Cost equals Marginal Revenue, provided that the Marginal Cost curve cuts the Marginal Revenue curve from below. EXERCISE 6.2 A rm faces price P = 38, independent of its output q. Marginal Cost is MC = 2 + (q 10)2 . (a) At what output or outputs does Marginal Cost (MC) equal Marginal Revenue (MR)? (b) At what output does the MC curve cut the MR curve from below? (c) What is the most protable level of output? A N S W E R : (a) Marginal Revenue here is MR = P = 38. Setting MC = MR implies 2 + (q 10)2 = 38. There are two algebraic solutions: q = 16 and q = 4. The MC and MR curves intersect at both these outputs. (b) By plotting some points it can be veried that MC cuts MR from below only at the larger output q = 16. (c) The most protable output is q = 16. The size of economic prot at the prot-maximizing output q is represented in the upper panel of Figure 6.1 as the bold vertical line-segment between the Total Revenue curve and the Total Cost curve. In the lower graph, prot per unit is the vertical distance between Average Revenue and Average Cost. The denition of total prot directly implies that ( AR AC ) q . That is, prot equals the difference between Average Revenue and Average Cost, multiplied by the level of output. So, in the lower panel the maximized prot is the shaded rectangle with area ( P AC) q . Table 6.1 illustrates hypothetical revenue and cost data for a competitive rm. Price is constant at P = 60, so Average Revenue AR and Marginal Revenue MR also equal 60 throughout. The Total Revenue column (R) is R = 60q . The cost function is assumed to be C = 128 + 69q 14q 2 + q 3 . This formula was used to compute values in the Total Cost column C. These Total Revenue and Total Cost functions reect the general shapes pictured in the upper panel of Figure 6.1, and the average and marginal functions would resemble those in the lower panel. Applying the method of approximating marginal quantities from discrete or tabular data recommended in Chapter 2, consider the approximate Marginal Cost at q = 7 in Table 6.1. The cost increment due to the last unit produced (that is, between q = 6 and q = 7) is 268 254 = 14. [We can think of this as the Marginal Cost at q = 61/2.] The cost increment from the next unit produced (that is, between q = 7 and q = 8) is 296 268 = 28. (We can think of this as the Marginal Cost at q = 71/2.) Our recommended approximation for Marginal Cost at q = 7 is then the average of 8 Mathematical Footnote: Maximizing R C with respect to q by differentiating and setting equal to zero, the rst-order condition for a maximum is d R /dq = dC /dq , or MR = MC. The second-order condition for a maximum is d 2 /dq 2 < 0, or d 2 R /dq 2 < d 2 C /dq 2 . So MR must be falling relative to MC, meaning that MC must cut MR from below. (The left-hand intersection of MC and MR in the lower panel, which violates the second-order condition for an optimum, corresponds to the output that minimizes prot.) P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 170 6. THE BUSINESS FIRM Table 6.1 Hypothetical revenue and cost functions: competitive rm R = 60q, C = 128 + 69q 14q 2 + q 3 P AR MR 60 60 60 60 60 60 60 60 60 60 60 Recommended approximation of marginal cost 45 26 13 6 5 10 21 38 61 q 0 1 2 3 4 5 6 7 8 9 10 R 0 60 120 180 240 300 360 420 480 540 600 C 128 184 218 236 244 248 254 268 296 344 418 MC (exact) 69 44 25 12 5 4 9 20 37 60 89 AC 184.0 109.0 78.7 61.0 49.6 42.3 38.3 37.0 38.2 41.8 VC 0 56 90 108 116 120 126 140 168 216 290 AVC 56 45 36 29 24 21 20 21 24 29 these two, specically Marginal Cost = 21 as shown in the table.9 Last, the true Marginal Cost at integer values of q is shown by the column labeled MC (exact), based on the equation MC = 69 28q + 3q 2 derived by calculus.10 With P = 60, setting the true Marginal Cost equal to price leads to the correct protmaximizing solution q = 9.11 At q = 9, Total Revenue is 540 and Total Cost is 344; hence the maximized prot is = 196. (Using our recommended approximation method and linearly interpolating, a very similar solution would be obtained.) EXERCISE 6.3 Suppose Total Revenue remains R = 60q as in Table 6.1, but the Total Cost function becomes C = 10 + 5q 2 . (a) How does this Total Cost function differ from that pictured in the upper panel of Figure 6.1? (b) How does Marginal Cost differ from that pictured in the lower panel of Figure 6.1? (c) What is the prot-maximizing output, and what is the associated prot? A N S W E R : (a) Plotting several points and sketching, the C curve here always rises at an increasing rate (whereas in Figure 6.1 the C curve initially rises at a decreasing rate). (b) The points t the equation MC = 10q. (This is also the exact Marginal Cost that can be obtained by calculus.) Unlike the MC curve in Figure 6.1, here MC is a straight line through the origin with positive slope. (c) Since MC = 10q and MR = P = 60, setting MC = MR leads to a prot-maximizing solution at q = 6. (Here the MC curve intersects the MR curve only once.) At this output, R = 6 60 = 360 and C = 10 + (5 62 ) = 190, so prot is = 360 190 = 170. 9 10 11 Failure to use our recommended method for example, taking the Marginal Cost as the cost increment associated either with the last unit or with the next unit produced can lead to considerable error, as was illustrated in Chapter 2. Mathematical Footnote: C = 128 + 69q 14q 2 + q 3 . Then MC dC /dq = 69 28q + 3q 2 . Mathematical Footnote: The second-order condition should also be checked. Setting MC = 69 28q + 3q 2 = 60 yields two algebraic solutions: q = 9 and q = 1/3. The incorrect solution, q = 1/3, violates the second-order condition for a maximum. P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 6.2 THE OPTIMUM OF THE FIRM IN PURE COMPETITION 171 $ C R = Pq c Dollars VC R = Pq v F q OutputQuantity Panel(a) TotalMagnitudes $/q DollarsperUnitQuantity 0 MC AC AVC Pc Pv 0 q OutputQuantity Panel(b) Average-MarginalMagnitudes Figure 6.2. The Cost Function In the upper diagram, Total Cost C rises with output, rst at a decreasing rate but ultimately at an increasing rate. The curve VC showing Total Variable Cost lies below the curve C by the amount of the xed cost F. In the lower diagram the Marginal Cost MC curve cuts rst through the low point of Average Variable Cost AVC, and then through the low point of Average Cost AC. The rm will shut down if in the long-run price is less than PC . If price is below PV , the rm produces nothing even in the short run. The last two columns of Table 6.1 show Total Variable Cost VC and Average Variable Cost AVC. From equation (6.3) and the denition of the average concept, it follows that VC C F and AVC VC/q (C F )/q (6.7) In comparing the curves of Total Cost and Total Variable Cost in the upper panel of Figure 6.2, note that VC is everywhere lower than C by a constant vertical distance equal to F. Marginal Cost MC, Average Cost AC, and Average Variable Cost AVC are shown in the lower panel of Figure 6.2. At q = 0, AC C /q is necessarily innite, but P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 172 6. THE BUSINESS FIRM AVC (C F )/q generally is not.12 Notice that as q increases, AC and AVC converge. The difference between them, the term F/q, becomes ever smaller as q rises. Marginal Cost was dened as the slope of the Total Cost curve C. Since at any given output the VC curve has the same slope as the C curve, MC is also the slope along VC. In other words, the level of xed costs does not affect Marginal Cost.13 Following are some other important features of Figure 6.2: 1. At q = 0, Marginal Cost (MC) equals Average Variable Cost (AVC). In Table 6.1, note that as q approaches zero, MC and AVC approach one another.14 2. MC is related to AVC in the same way as to Average Cost (AC). That is, when AVC is falling, MC < AVC ; when AVC is rising, MC > AVC, and when AVC is constant (at its minimum level), MC = AVC. So MC cuts through the minimum points of both AC and AVC. 3. The minimum of AVC is to the left of the minimum of AC. This must hold if the rising MC curve is to cut the minimum points of both AC and AVC. In Table 6.1, both MC and AVC equal 20 when q = 7; hence this is the minimum of AVC. And both MC and AC equal 37 at q = 8, so this output minimizes AC.15 The Shutdown Decision Even when a competitive rm satises the condition MC = MR = Price, and even if the MC curve in the lower panel of Figure 6.2 cuts the horizontal price line MR = P from below, Total Revenue may be less than Total Cost. The best possible positive output might still generate a loss (prot is negative). So should the rm go out of business? (A multiproduct rm should ask whether it should exit from this particular line of business.) For this shutdown decision, the minimum values of Average Cost and of Average Variable Cost are crucial. Whether the rm should shut down depends on whether the decision involves the short run or the long run. As will be explained below, the economic meaning of the short run is not a period of time but rather refers to a decision situation in which certain choices in this case, amounts of some of the inputs are not subject to revision. In meeting a temporary surge in demand, the factory and machinery might be considered xed. Then the desired increase in output has to be achieved by changing only some of the inputs, for example using more overtime labor. In the long run, however, all inputs can be varied. In the short run, then, a rm should continue to produce if Total Revenue exceeds Total Variable Cost: R VC, or equivalently P AVC No-Shutdown Condition, short run (6.8a) 12 13 14 15 Mathematical Footnote: C/q must be innite at q = 0. But at q = 0, (C F )/q is the difference between two innite magnitudes, C/q and F/q, and so it is not in general innite. Mathematical Footnote: Since C VC + F and F is a constant, the derivative MC dC /dq is the same as d (VC )/dq . Mathematical Footnote: At q = 0, AVC = 0/0 is indeterminate. But applying LHopitals Rule, the limit (as q 0) of VC/q equals the limit of d (VC )/dq . So MC and AVC coincide at q = 0. Mathematical Footnote: To nd the exact minimum of AVC, differentiate AVC = q 2 14q + 69 and set the derivative equal to zero. The solution is q = 7. To nd the minimum of AC, differentiate AC = q 2 14q + 69 + (128/q ). A cubic equation is obtained, but the only root in the relevant range is q = 8. P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 6.2 THE OPTIMUM OF THE FIRM IN PURE COMPETITION 173 In Figure 6.2, the rm should continue operating in the short run if price exceeds PV , the minimum of Average Variable Cost (AVC). The idea is that if the rms long-run expectations warrant staying in business (or, for a multiproduct rm, warrant remaining in a particular line of activity), it pays to keep operating (to produce positive output) in the short run. Total Revenue covers the Total Variable Cost, with possibly something over to meet some of the Fixed Cost. But in the long run, a rm should continue to operate only if all its costs are covered. So the long-run No-Shutdown Condition is R C , orequivalently P AC No-Shutdown Condition, long run (6.8b) In Figure 6.2 the lowest price meeting the long-run No-Shutdown Condition is PC . PROPOSITION: A price-taking rm maximizes prot by producing that output where Marginal Cost = Marginal Revenue = Price (provided that Marginal Cost cuts Marginal Revenue from below, that Price Average Variable Cost in the short run, and that Price Average Cost in the long run). EXERCISE 6.4 Using the data of Table 6.1, what are the short-run and long-run shut-down prices PC and PV ? A N S W E R : The minimal Average Variable Cost occurs at about q = 7, where AVC = 20. So the short-run shutdown price is P V = 20. The minimum Average Cost occurs at about q = 8, where AC = 37. So the long-run shutdown price is P C = 37. Fixed costs are sometimes confused with sunk costs. Suppose an aircraft assembly plant had bought a wing-stamping machine for a certain model of airplane. It nanced the machine by a noncancellable bank loan, to be paid off in annual $1,000,000 installments over several years. Sales are slow, and the company is considering abandoning this line of business. Since the annual installment remains payable whether or not any wings are produced, the annual $1,000,000 is surely not a variable cost of production. But is it a xed cost from the point of view of the abandonment decision? The crucial principle to remember is that, for there to be an economic cost, a resource must have alternative uses. For simplicity, suppose there are no other uses whatsoever for this machine.16 Since the rm cannot avoid the $1,000,000 annual commitment even by permanently abandoning this line of business, the outlay is sunk and should not enter into the calculation. To summarize, xed costs, although applicable only for the long-run decision, are actual economic costs. So-called sunk costs, in contrast, are irrevocably lost to the rm. They are irrelevant to any present or future decisions, and so are not economic costs at all.17 16 17 That of course is an extreme assumption. Almost always there is some minimal alternative use, if only to break up the machine for scrap metal. The treatment of sunk costs is one of the differences between economic prot and accounting prot. The annual $1,000,000 installment would be counted as a cost in calculating accounting prot. P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 174 $/q 6. THE BUSINESS FIRM $/q DollarsperUnitQuantity MCb MCa Figure 6.3. Division of Output between Plants A rm with two plants should divide any given output q in such a way that Marginal Costs in the two plants, MC a and MC b , are equal. 0 qa OutputofPlant a qb OutputofPlant b 0 An Application: Division of Output among Plants Suppose a rm can divide output q between factories in Albany (plant a) and Buffalo (plant b): qa + qb q By a straightforward extension of equation (6.6), the optimizing rule is: MCa = MCb = MR P (6.10) (6.9) In words, the rm should divide its production to make the Marginal Costs in the different plants equal. Furthermore, both Marginal Costs should be set equal to Marginal Revenue. (For a price-taking rm, of course, Marginal Revenue is identical with price P.) Figure 6.3 depicts the rst of the above equalities, the optimal division of output between two plants. The rms total output q is taken as given in the diagram; q is indicated by the horizontal distance between the two vertical axes. The Albany output qa is measured in the usual way, as the distance to the right of the left-hand axis. The Buffalo output qb is measured in the opposite direction, as the distance to the left of the right-hand axis. Then the equality MCa = MCb occurs at the intersection of the $/q MCb DollarsperUnitQuantity MCa MC P = MR Figure 6.4. Optimal Outputs with Two Plants The rms Marginal Cost curve MC is the horizontal sum of the plant MCa and MCb curves. In setting rm output q where MC = P , the corresponding plant outputs q a and q b are such that MCa = MCb = P . G 0 qb qa q qa, qb, q PlantandFir mOutputs P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 6.2 THE OPTIMUM OF THE FIRM IN PURE COMPETITION 175 two Marginal Cost curves. Assuming both Marginal Cost curves rise throughout as illustrated here, this is indeed the best division of the given output q between the two plants. What if the MCa and MCb curves, each an increasing function of its own plant output, never intersect? This means that, for the specied total output q, one plants Marginal Cost is always higher than the others. Then the plant with the lower Marginal Cost should produce all the output. EXERCISE 6.4 (a) Suppose the Marginal Cost functions for the two plants are MCa = 5 + 2qa and MCb = 40 + qb. If the total output is q = 25, how should the outputs be divided? (b) What if the total output were q = 15? A N S W E R : (a) Setting the Marginal Costs equal implies 5 + 2qa = 40 + qb. Making use of qa + qb q = 25 and substituting, the solution is qa = 20, qb = 5. (b) For q = 15, setting the Marginal Costs equal would indicate a negative output for plant b. This is impossible. The explanation, which can be veried by sketching, is that the MCa and MCb curves do not intersect when the required total output is q = 15. The best solution is to assign all output to the lower-cost plant in Albany, that is, to set qa = 15 and qb = 0. At qa = 15 the Albany plants MCa is only 35, whereas MCb is never less than 40. Now consider the second part of equation (6.10). Output q cannot be taken as given, but must be chosen so that MCa and MCb both equal MR = Price. In Figure 6.4 the bold curve MC represents the rms Marginal Cost function. It is the horizontal sum of the separate MCa and MCb curves.18 Thus, setting MC = P as illustrated in the diagram also implies setting MCa = MCb = P in accordance with equation (6.10). The overall optimal rm output q and the separate optimal plant outputs q a and q b can be read off along the horizontal axis. EXERCISE 6.5 Using the Marginal Cost data of the previous exercise, suppose the market price is P = 45. (a) Find the optimal outputs for the separate plants and for the rm as a whole. (b) What is the equation for the rms MC curve in Figure 6.4? A N S W E R : (a) The conditions MCa = MCb = P = 45 imply qa = 20 and qb = 5, so q = 25. (b) The trick here is to remember that we are summing quantities. The separate plant Marginal Cost equations can be written qa = (MCa 5)/2 and qb = MCb 40. Summing over quantities, and remembering that the rms MC is dened in terms of the equated values of MCa = MCb, we have q = (MC 5)/2 + MC 40. Solving, MC = 2/3 (q + 42.5). As a check, setting this MC equal to P = 45 does conrm the solution q = 25. 18 Notice that the MCb curve for the higher-cost plant does not enter into the horizontal summation until MCa equals the minimal (initial) level of MCb . (For a somewhat similar geometrical construction see Figure 2.5, Introduction of an Import Supply.) P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 176 6. THE BUSINESS FIRM $ LRTC SRTC 3 SRTC 2 SRTC 1 Dollars Figure 6.5. Short-Run and Long-Run Cost Functions In the upper diagram, LRTC is the Long-Run Total Cost function showing the cost of producing any output q when all inputs are allowed to vary. The Short-Run Total Cost curve, SRTC, applies when the xed input is held constant at a level appropriate for small-scale production (q 1 ); similarily, SRTC2 and SRTC3 are associated with the higher levels of xed cost appropriate for medium-scale production (q 2 ) and large-scale production (q 3 ). The corresponding average and marginal curves are shown in the lower diagram. At output q 1 , SRAC1 = LRAC (the curves are tangent) and SRMC1 = LRMC (the curves intersect); similar conditions hold for output levels q 2 and q 3 . At any point, the Total Cost curves and the Average Cost curves are never higher in the long run than in the short run. (Note that no such statement can be made for the Marginal Cost curves.) F3 F2 F1 q1 q2 OutputQuantity $/q DollarsperUnitQuantity LRMC q3 q SRAC 3 SRAC 1 SRAC 2 LRAC M SRMC 1 SRMC 2 SRMC 3 q1 q2 OutputQuantity q3 q 6.3 COST FUNCTIONS Short Run versus Long Run This section goes more deeply into the distinction between the long run and the short run. The fundamental difference has to do with the range of inputs taken as xed. This is not a yes/no contrast but rather a matter of degree. The longer the planning horizon, the greater the extent of costs that are variable rather than xed. In a manufacturing rm, toward the variable end are expenses for electric power, materials, and labor. Toward the xed end are costs associated with ownership or leasing of real estate and machinery. Suppose a machine breakdown called for an hour-long reduction in output. Some electric power would be saved. But little else could be changed; for this output decision, almost all costs are xed. If output were to be cut back over a period as long as a day, casual labor might also be laid off. Over a period such as a month more workers could be discharged (their wages would become a variable cost), and some leased equipment such as trucks could be returned. Last, if the rm planned to reduce output permanently, it could sell off machinery and reduce its real-estate commitments. For simplicity in the following discussion, unless otherwise indicated long run will mean that all costs are variable; short run will mean that some costs are xed. So there is a single Long-Run Total Cost curve LRTC, as shown in the upper panel of Figure 6.5. P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 6.3 COST FUNCTIONS 177 Furthermore, this curve goes through the origin: at zero output, LRTC = 0. (In the long run all costs are variable, so no costs are incurred if nothing is produced.) The Long-Run Total Cost function shows the lowest cost of producing any given level of output. Why the lowest cost? Because, when all costs are variable, at any output q the rm is free to choose the best (the most economical) mix of all resources employed. Three different Short-Run Total Cost functions are shown in the upper panel of Figure 6.5. SRTC1 is associated with a low xed cost F 1 . This level is assumed optimal for the relatively small rate of output q 1 . If the lowest cost of producing output q 1 is with xed cost F 1 , then the Short-Run Total Cost as given by curve SRTC1 at q 1 must equal the Long-Run Total Cost at q 1 . Any other output will call for a different level of optimal xed cost. The Short-Run Total Cost curve SRTC1 must therefore lie above the Long-Run Total Cost for all outputs other than q 1 . Then the curve SRTC1 is necessarily tangent to LRTC at output q 1 . Operating along SRTC1 is ne for small outputs. But at larger outputs the curve SRTC1 rises steeply. So moderately large levels of production are cheaper along the curve SRTC2 , where SRTC2 represents the short-run costs associated with a somewhat higher xed cost F2 that is best for output q2 . Last, SRTC3 is associated with a xed cost F3 that is optimal for the large output q3 . It represents the best of the three situations for high output, but the worst for low output. Notice that the LRTC curve in the diagram is a lower envelope of all the SRTC curves. [Caution: Here is a common mistake. Consider a retail store. Since short-run adjustments involve increasing only some of the inputs (say, the number of salespeople), whereas long-run adjustments may involve increases in all inputs (including, perhaps, oor space), one might think that short-run costs of increasing output must necessarily be lower than long-run costs. Isnt it cheaper to increase sales by expanding only the workforce than by expanding both the workforce and the oorspace? Expressed this way, the fallacy is evident. The store will expand its oorspace (incur a higher xed cost) only when doing so is less costly (involves lower expense overall) than expanding output by increasing variable costs (the sales force) alone.] Let us now translate from the total units in the upper panel of Figure 6.5 to averagemarginal units in the lower panel. Recall that SRTC1 lies above LRTC everywhere except at the tangency point where q = q 1 . It follows that the corresponding Short-Run Average Cost curve SRAC1 lies above the Long-Run Average Cost curve LRAC everywhere except at q 1 . A similar argument applies for the relation between SRAC2 and LRAC and so forth. The upshot is that LRAC is a lower envelope of the SRAC curves, just as LRTC is a lower envelope of the SRTC curves. Notice that SRAC1 is tangent to LRAC at a point where both curves slope down. The minimum of the SRAC1 curve therefore lies to the right of (at a greater output than) the tangency at q = q 1 . For SRAC3 the reverse holds; the minimum of SRAC3 is to the left of q = q 3 . A famous economist once made the following error. In the belief that the LRAC curve, representing the least-cost way of producing any output q, must go through the minimum points of all the SRAC curves, he asked his Research Assistant to draw the LRAC accordingly. Experimenting with the curves will show that it is geometrically impossible to draw an LRAC curve through the minimum points of the SRAC curves and still have LRAC lie everywhere below these curves. The principle to hold onto is that Long Run Average Cost is the lowest possible unit cost of producing any given level of output. P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 178 6. THE BUSINESS FIRM What about short-run and long-run Marginal Costs? At the tangencies of the SRTC and LRTC curves in the upper panel of Figure 6.5, both the levels and the slopes of the curves in contact are equal. Since the marginal function is always the slope of the corresponding total function, at output q 1 Short-Run Marginal Cost SRMC1 equals Long-Run Marginal Cost LRMC; at q 2 , SRMC2 = LRMC; and at q 3 , SRMC3 = LRMC. This leads to the relation among the various short-run and the long-run marginal curves shown in the lower panel. Notice that the LRMC curve is generally atter than the SRMC curves. This feature will play a role in the distinction between the short-run and long-run supply functions of the rm, to be discussed in the next chapter. PROPOSITION: Given the market price P, a competitive rm makes the best long- run adjustment (selects the correct level of the xed input) and the best short-run adjustment (selects the prot-maximizing output q) by satisfying the conditions LongRun Marginal Cost = Short-Run Marginal Cost = Price. (Assuming that the MC curves cut the price line from below, and that the no-shutdown conditions are met.) EXERCISE 6.5 A rms Long-Run Total Cost curve is LRTC = q2 . The Short-Run Total Cost curve is SRTC = 2 B + q4 /(8 B ), where B represents the level of the input xed in the short run, for example, the number of machines. Suppose B = 4, so that SRTC = 8 + q4 /32. Then it can be shown by calculus (or approximated by tabulating) that the associated Marginal Costs are LRMC = 2q and SRMC = q3 /8. (a) At what output are LRTC and SRTC tangent? (b) What can you say about the Marginal Cost functions LRMC and SRMC at this output? (c) At what price P is B = 4 the best level of xed input for the rm? (d) How does the overall picture here differ from the cost function diagrammed in Figure 6.5? A N S W E R : (a) At a point of tangency the curves must touch and have equal slopes. If LRTC and SRTC touch, it must be that LRTC = SRTC. So q2 = 8 + q4 /32. This condition is met at q = 4. Since the marginal functions correspond to the slopes of the total functions, is it true that, at q = 4, LRMC = SRMC? Direct substitutions in the LRMC and SRMC equations show that indeed 2 4 = 43 /8. So the LRTC and the SRTC curves associated with B = 4 are tangent at q = 4. (b) In (a) above, LRMC = SRMC held true at q = 4. Calculus or plotting veries that SRMC is steeper than LRMC. In other words LRMC and SRMC intersect at q = 4, but are not tangent to one another there. (c) At q = 4, SRMC = LRMC = 8. So when P = 8, choosing B = 4 allows the rm to meet both the short-run and long-run conditions for optimal output: LRMC = SRMC = P . (d) The main difference is that the LRTC curve here rises throughout at an increasing rate. This implies that both LRAC and LRMC have positive slopes throughout, and are not U-shaped as in the diagram. (But the short-run SRAC curves all have the usual U-shape.) The continuous LRAC envelope curve in the lower panel of Figure 6.5 in effect assumes that the xed input can take any value whatsoever in the range of interest. What if the xed inputs come in discrete lumps? Using the notation of the preceding exercise, at the extreme imagine that the xed input can take on only one of the two distinct values B = 1 or B = 2. Then the envelope would have a discontinuous appearance, somewhat as illustrated in Figure 6.6. Below the crossover output q the LRAC runs P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 6.3 COST FUNCTIONS 179 $/q DollarsperUnitQuantity SRAC1 (B =1) SRAC2 (B =2) LRAC q OutputQuantity q Figure 6.6. Short-Run and Long-Run Average Costs with Discrete Fixed Input Here the xed input can only take on one of the two levels B = 1 or B = 2, and the SRAC curves are drawn accordingly. The LRAC curve runs along the lower edges of the two SRAC curves. along the SRAC1 curve, and afterward along the SRAC2 curve. (In Figure 6.6 the very lowest point along LRAC occurs with the larger xed input B = 2, but the reverse is also possible.) Is the concept of xed costs meaningful? Commonsense tells us that a rm, intending to halt production for an hour, will not sell off its buildings and machinery with the intent of buying them back an hour later. But is this consistent with our analytical models? Why should a rm continue to incur any needless xed costs, even for an hour? If machines and buildings are not needed, even for an instant of time, why not sell them off and then buy them back? Transaction costs, a topic that came up earlier in the chapter in exploring the reasons why rms exist at all, are part of the answer. The cost and difculty of negotiating and executing complex contracts make it impractical to sell and rebuy a factory building in an hour. But a somewhat subtler consideration is also involved: specialization of resources to the rm. Machinery may have been made to order and buildings partitioned or remodeled to the rms specications. Since such highly specialized assets are of lesser use to other rms, they may have little or no resale value. So, even if transaction costs were zero, the rm could not advantageously sell off such assets to meet a temporary reduction of output. (And knowing that resale value will be low, rms will be less ready to acquire highly specialized resources for a temporary production increase.) Even if the rm had leased rather than bought such resources, cancelling the lease can be costly. The owner of a building remodeled for a particular tenant, for example, will surely insist upon steep cancellation penalties. Much the same applies for employees. Suppose a worker has received specialized job training of value only within the rm. If the rm bears the cost of the training, it would be reluctant to lay off the worker for fear of having to train a replacement. And the worker would be reluctant to bear the cost of training without some long-term job protection. So there may be an element of xity in employing human as well as nonhuman inputs. If transaction costs were absent, and if only unspecialized resources were used in production, one would not need to distinguish between the long run and the short run. P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 180 6. THE BUSINESS FIRM Transaction costs and specialization force a rm to choose between responding to a decline in demand in a short-run way or in a long-run way. In the short-run response, appropriate for a temporary reduction of output, the rm holds its specialized (or hightransaction-cost) resources xed and continues to count spending on them as a cost of doing business. Thus, a loss may be incurred in the short run (Average Cost may exceed price): the rm should accept a temporary loss rather than dispose of a resource that it would shortly rebuy or rehire. The long-run response, appropriate for a permanent decline in output, is to dispose of the resource. Hence its cost is no longer xed. (Any accounting loss suffered in the disposition of specialized inputs is sunk, the result of a possible past error of judgment, and thus not a cost at all.) Corresponding considerations apply to an increase in demand. A rm that regards the increase as temporary will hesitate to acquire additional specialized or high-transactioncost inputs, in view of the penalties incurred when the time comes to dispose of them. If the demand change is believed to be permanent, however, incurring additional xed costs is justiable, in order to increase production at lower unit cost along the Long-Run Average Cost curve. CONCLUSION Inputs may be held xed in the face of a temporary demand uctuation for two reasons: (1) to avoid round-trip transaction costs associated with selling and rebuying (or ring and rehiring) inputs, and (2) to save the costs of specializing inputs to the rm. Holding some inputs xed makes sense if the rm is dealing with a short-run uctuation in demand. If the rm regards the demand change as permanent, it will make a long-run response, varying the amounts of all inputs. Rising Costs and Diminishing Returns Throughout this chapter, both Marginal Cost and Average Cost were pictured as (eventually) rising functions of output. These characteristics must apply if the rm operates under competitive price-taking conditions. What if instead Marginal Cost (MC) were falling throughout? Recall that the protmaximizing condition Marginal Cost = Marginal Revenue = Price is valid only if the MC curve cuts the MR curve from below. Since competitive conditions dictate a horizontal MR P curve, an ever-falling Marginal Cost curve cannot cut Marginal Revenue from below. So a competitive optimum cannot be found.19 What if Average Cost (AC) falls throughout? Then any rm getting a sufciently large output lead over other rms could produce at lower cost, thus driving its competitors out of business. So falling Average Cost can create a natural monopoly, as will be discussed in Chapter 8. [Question: If Marginal Cost always declines with output, does Average Cost necessarily decline? If Average Cost falls everywhere, must Marginal Cost also fall? Answer : Verify that Average Cost falling throughout does not necessarily imply that Marginal Cost falls throughout. On the other hand, a negatively sloped Marginal Cost curve dictates that the corresponding Average Cost curve declines throughout.] Marginal Cost and Average Cost curves that eventually rise are associated with the famous Law of Diminishing Returns, a topic to be covered in more detail in Chapter 11. That law is a technological principle that explains, for example, why it is impossible 19 If MC cuts the constant MR = P from above, by producing more output the rm could increase its prot forever which is impossible. P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 6.3 COST FUNCTIONS 181 to grow all the worlds food in a owerpot. The principle can be stated as follows: If one or more productive inputs are held xed, then additional production requires that the other (variable) inputs be increased at an increasing rate. Thus, holding constant the amount of soil in the owerpot, the attempt to grow more food if successful at all requires ever-rising additions of labor, fertilizer, and so forth. Of course, rising amounts of inputs imply rising costs. Thus, diminishing returns (marginal and average) translate into rising costs (marginal and average). The Law of Diminishing Returns applies in the short run, dened by the condition that one or more inputs are held xed by the rm. Figure 6.5 shows the Short-Run Marginal Cost and Short-Run Average Cost curves as eventually rising. It also shows the Long-Run Marginal Cost and Long-Run Average Cost curves as rising. Can these shapes be justied? If it were literally true that in the long run all inputs were variable, the Law of Diminishing Returns would not apply. It would be possible to choose the best resource combination, and then expand or contract output by proportionately increasing or decreasing all the inputs together. Then the Long-Run Average Cost curve would be horizontal; the Long-Run Marginal Cost curve would also be horizontal and equal to Long-Run Average Cost (Proposition 2.2c of Chapter 2). But varying all inputs together is not actually possible. Some inputs, and in particular entrepreneurship, may not be readily expandable. Also, a rm is often associated with some more or less unique productive opportunity. A mining company, for example, may be exploiting a particular ore deposit. It could raise output by using more labor and machines, but the rm cannot duplicate the ore body itself. So, in any economically possible long run, the Law of Diminishing Returns ultimately applies: Long-Run Marginal Cost and Average Cost curves must eventually rise. EXAMPLE 6.5 SCALE ECONOMIES NUCLEAR VERSUS FOSSIL FUELS David R. Kamerschen and Herbert G. Thompson, Jr. compared the costs of generating electric power from nuclear versus fossil fuels.a Using 1985 data, they found that normal U-shaped Long-Run Average Cost curves applied for both types of plant. For fossil fuels the minimum occurred at about 10,000 GWH (million kilowatt-hours), at a unit cost of about 3.7 cents per KWH (kilowatt hour). For nuclear plants the minimum occurred at about the same scale of output, but the unit cost was lower about 2.5 cents per KWH. The table summarizes some of their data. Average costs of power generation nuclear versus fossil fuels Unit cost (cents/KWH) Output (GWH) 5,000 10,000 15,000 20,000 25,000 30,000 Fossil fuels 3.90 3.75 3.78 3.80 3.85 3.90 Nuclear fuel 2.60 2.55 2.58 2.60 2.70 2.80 Source: Estimated visually from Kamerschen and Thompson, Figure 3, p. 21. P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 182 6. THE BUSINESS FIRM Despite the lower costs of nuclear generation, no U.S. utility has ordered a nuclear power plant for over 25 years. The reason is that environmental concerns. and public fears of Chernobyl-type incidents, have made it difcult almost impossible, it seems to gain the necessary political and regulatory approvals. The authors comment that growing anxieties about greenhouse effects and other forms of pollution associated with coal and oil may make nuclear power more acceptable in the future. On the other hand, increasing concerns about terrorism cut the other way. COMMENT Around half of the fossil fuel plants, and the great majority of the nuclear points studied, were located in the range of falling Long-Run Average Cost. As indicated in the text, this could not be a prot-maximizing solution for competitive rms. However, electric power utilities generally exercise some regional monopoly power, and are accordingly usually subject to government regulation. The price-quantity optimum for monopolistic rms, and the principles on which such rms are regulated, will be analyzed in Chapter 8. a David R. Kamerschen and Herbert G. Thompson, Jr., Nuclear and Fossil Fuel Steam Generation of Electricity: Differences and Similarities, Southern Economic Journal, v. 60 (July 1993). 6.4 AN APPLICATION: PEAK VERSUS OFF-PEAK OPERATION Many industries must deal with sharp variations between peak demands and off-peak (slack) demands. Telephones are more heavily used during business hours than during evenings or weekends, local transit demands are greatest in the morning and afternoon commuting hours, restaurants are busiest at mealtimes. In arid areas water is more intensely demanded in summer than in winter. A rm facing peak and off-peak demands must decide how to divide its efforts between the two. Assume for simplicity that the peak and slack periods are of equal duration. Under pure competition the rm would be a price-taker in both markets. The peak price Pp would exceed the off-peak price Po . In a city served by competing restaurants, for example, dinner (peak period) prices are generally higher than lunch (slack period) prices. But, by assumption, in each market the price will be independent of the rms own output (as shown by the horizontal price lines in Figure 6.7). It is essential to distinguish between the common costs and the separable costs of serving the two types of demand. Common costs apply to both peak and off-peak service. For a restaurant they can include the cost of renting and maintaining the premises, of dishes and silverware, of management and accounting services, and so on. Separable costs are those incurred to serve only one market or the other. Some waiters could be hired only to serve lunch, others only to serve dinner. (The distinction between common and separable costs is quite apart from our earlier distinction between xed and variable costs. Common costs can be xed or variable, and the same holds for separable costs.) EXAMPLE 6.6 PEAK VERSUS OFF-PEAK OPERATION: WATER SUPPLY In urban water supply, especially in the arid west of the United States, the major peaking problem is seasonal. In the summer months precipitation and stream ow P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 6.4 AN APPLICATION: PEAK VERSUS OFF-PEAK OPERATION 183 are low, and demand for irrigation and other uses is high. Darwin C. Hall estimated the costs of providing water for Los Angeles in the winter and summer seasons.a The table here shows Marginal Costs in terms of billing units (BU) 748 gallons (100 cubic feet). Marginal cost per billing unit of water, city of Los Angeles Winter ($) Supply Capital Operation and maintenance Transmission and treatment Capital Operation and maintenance Distribution and tank storage Capital Operation and maintenance TOTALS 1.38 0.63 0.00 0.01 0.00 0.00 2.02 Summer ($) 1.28 0.90 0.08 0.01 0.30 0.00 2.67 Source: Hall, selected from Tables 1 and 2 (pp. 8687). Since the greater summer demand determines the need for capacity, the marginal capital requirements for Transmission and treatment and for Distribution and tank storage are considered separable costs and assigned entirely to summer production. (It is puzzling however that the capital costs for the supply category are higher for winter than for summer.) Also, since Los Angeles purchases water from outside sources in the winter (when it is cheap) and stores it for use during the summer, certain increased storage expenses are incurred that are listed under the category of operation and maintenance. a Darwin C. Hall, Calculating Marginal Cost for Water Rates, Advances in the Economics of Envi- ronmental Resources, v. 1 (1996), pp. 7794. The analysis that follows deals only with short run solutions and makes simplifying assumptions about costs. (1) For common variable costs, Marginal Common Cost (MCC) is assumed constant at the level M, which means that Average Common Cost (ACC) also always equals M. In the diagram, therefore, the MCC and ACC curves coincide as a horizontal line of height M. (2) Separable variable costs, illustrated by the curves for Marginal Separable Cost (MSC) and Average Separable Cost (ASC) in the diagram, are assumed identical for both periods. (However, although the cost function is the same, the rm will typically choose different on-peak and off-peak levels of output q along the cost function. Even if it costs the same to serve any given number of meals, a restaurant may employ more waiters at peak dinner hours.) It turns out there are two differing types of possible situations, called the stablepeak and shifting-peak cases. Stable-Peak Solution : In Figure 6.7 for the off-peak market, the Marginal Common Cost (MCC) may be regarded as already having been incurred to meet the larger peak demand. (The restaurant has scaled its dining capacity to serve the larger dinner market.) P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 184 6. THE BUSINESS FIRM $/q MCC + MSC Pp MSC DollarsperUnitQuantity ASC Po M MCC = ACC q o OutputQuantity q p q Figure 6.7. Peak versus Off-Peak Operation, I In the peak-demand period, the price-taking rm will set the sum of the Marginal Common Cost and the Marginal Separable Cost (MCC + MSC) equal to the peak-period price P p . In the off-peak period only the separable costs are incurred, so the rm should set MSC equal to the off-peak price Po . Peak-period output is q and off-peak output is q o < q . p p So the off-peak period is a by-product. If so, only its separable costs are relevant for the off-period output decision. The off-peak period marginal cost is then MCo = Marginal Separable Cost (MSC), and the optimal off-peak output q o is determined by the condition MCo = MSC = Po . In the diagram, the restaurant produces q o lunch meals at the point where the rising MSC curve cuts the horizontal Po price line. However, both the common and the separable variable costs are incurred in meeting the larger peak demand. So the peak-period Marginal Cost is higher: it is the vertical sum MCp = MCC + MSC (the dashed curve). The optimal on-peak output q is determined by the p condition MCp = P p , where the dashed curve intersects the horizontal Pp price line. It follows that q > q o more meals are served at peak than at slack hours. p Shifting-Peak Solution: The other possibility is pictured in Figure 6.8. Here the procedure outlined above setting the peak output by the condition Marginal Common Cost + Marginal Separable Cost = Pp and the slack output by the condition Marginal Separable Cost = Po leads to a paradoxical shifting peak result. That is, the indi cated peak output q would be less than the slack output q o . The restaurant would p serve more meals at lunch than at dinner! Something is wrong. The mistake was to assume that the Marginal Common Cost MCC is always incurred for the peak demand only. That assumption was valid in Figure 6.7. There the price difference P p Po was sufciently great to warrant incurring some additional common cost MCC of serving only the on-peak market. But when the price difference is small, and in particular if P p Po < MCC, incurring the Marginal Common Cost cannot be warranted by service to the peak trade alone. In this situation, as pictured in Figure 6.8, the last units of common cost can protably be incurred only for serving both markets together. It follows that, if P p Po < MCC, the peak and off-peak outputs q p and q o must be equal. But equal at what level? The answer is that the relevant or joint Marginal Cost P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 6.4 AN APPLICATION: PEAK VERSUS OFF-PEAK OPERATION 185 $/q MCC +2 MSC MCj Po + Pp MCC + MSC MSC Pp Po G H K M MCC MRj qp q qo p qo q Figure 6.8. Peak versus Off-Peak Operation, II Here, if the common costs are charged solely to the peak-period demand (by setting MCC + MSC = P p for the peak period and MSC = Po for the off-peak period, as in Figure 6.7), a paradoxical result is obtained. The off-peak quantity supplied (q o ) would be larger than the peak-period quantity (q p ), which cannot be correct. This paradox occurs when p p Po < MCC when the price difference between periods is less than the Marginal Common Cost. In this case the prot-maximizing solution is to produce the same in each period, setting q = q o at the level of output where MCC + 2MSC = p P p + Po . At this output the combined prices just sufce to cover the Marginal Separable Costs and the Marginal Common Cost. MCj for serving the two markets together is the vertical summation MCj = MCC + 2MSC (the dotted curve). As for the demand side, the joint Marginal Revenue MRj is the sum MR j = P p + Po (the dotted horizontal line). The correct q and q o , now equal p to one another, are determined by the intersection of the dotted MCj and MRj . PROPOSITION: For a price-taking rm facing peak and slack markets of equal dura- tion, and assuming Marginal Common Cost (MCC) is constant, there are two classes of short run solutions: (a) Stable-Peak: If MCC is less than the price difference P p Po , peak output is determined by setting the peak-period Marginal Cost MC p equal to the peak-period price Pp where MCp is the sum of the Marginal Common Cost MCC plus the peak periods Marginal Separable Costp . Off-peak output is de termined by the condition MCo = MSCo = Po . Thus q > qo more is produced p on-peak than off-peak. (b) Shifting-Peak: If the Marginal Common Cost exceeds the price difference P p Po , the prot-maximizing peak and off-peak outputs are equal, determined by setting the joint Marginal Cost MCj equal to the price difference: MCj = MCC + 2MSC = P p + Po . As an interpretation of the shifting-peak case, notice that at the correct joint output q = q o in Figure 6.8, each periods price yields some excess over the Marginal p Separable Cost. In the diagram the distance GK, the vertical difference P p MSC, can be regarded as the contribution of the marginal on-peak sale toward covering the P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 186 6. THE BUSINESS FIRM common cost MCC. Similarly, the smaller distance HK, the vertical difference Po MSC, is the contribution of the marginal off-peak sale toward this common cost. By construction in the diagram, the sum of the distances GK and HK exactly equals Marginal Common Cost so that, at the optimal joint output, the aggregate of the two contributions exactly covers the Marginal Common Cost. Since the off-peak market is less protable, the rm may consider abandoning it entirely. Whether it should do so can be determined by extending the short-run No Shutdown Condition discussed earlier. The rm should abandon the off-peak market if, in Figure 6.7, the horizontal off-peak price line Po were to lie below the minimum of the Average Separable Cost (ASC) curve. Then, even at the prot-maximizing output, the rms total off-peak separable costs exceed the total revenue received from its off-peak customers. SUMMARY Business rms are articial economic units organized for team production. When many separate resource-suppliers are involved, creating a rm reduces transaction costs. Members of the team need only contract with the rm itself (bilateral contracting) rather than with one another. The owners of a rm are entitled to the residual rewards that remain after contractually agreed payments to other resourcesuppliers. Costs of monitoring performance, and differing preferences for risk, help explain why some suppliers are employed on a contractual basis while others become the owners of the rm (residual claimants). A rms goal is to maximize economic prot the difference between revenue and economic cost. Its Total Revenue equals price times quantity: R PQ. For a competitive (price-taking) rm, price P is assumed constant, so that P Average Revenue Marginal Revenue. Accounting costs count only contractual payments as expenses, but economic costs also include opportunity costs. In addition, accountants value assets (before depreciation) at their historical acquisition cost, whereas economic prot measures asset depreciation by loss of current market value. Marginal Cost is the added cost of producing a unit of output. Marginal Cost may initially be falling, but at sufciently high levels of cost will rise with output. Average Cost is Total Cost divided by output. Variable Cost is Total Cost minus Fixed Cost. Average Cost and Marginal Cost must ultimately rise with output because of the Law of Diminishing Returns. With some inputs held xed, eventually at least, additional output requires increasing increments of the variable inputs. Some inputs that are xed in the short run become variable in the long run. At any output, Short-Run Total Cost is at least as great as Long-Run Total Cost; similarly, ShortRun Average Cost is at least as great as Long-Run Average Cost. Short-Run responses, which hold some inputs xed, are appropriate for demand changes that the rm expects to be temporary. A rm in a competitive industry maximizes prots by setting that level of output at which Marginal Cost equals price. The rm will shut down in the short run if the going price is less than the minimum of Average Cost. Firms often deal in markets with distinct peak-period and slack-period demands. If there is a sufcient gap between the peak-period and the slack-period prices, the protmaximizing peak output is determined by the condition that the sum of Marginal Common Cost + Marginal Separable Cost equals the (higher) peak-period price. Output P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 QUESTIONS 187 in the off-peak period satises the condition that the Marginal Separable Cost alone equals the (lower) off-period price. Output in the off period is smaller. In that stable peak case the peak period alone bears the common cost. But if the price gap is not so great, the peak period alone cannot bear the full Marginal Common Cost, since off-peak output would exceed on-peak output. The solution is to have the same quantity sold in both periods, at prices reecting the marginal willingness to pay of the on-peak and off-peak demanders. But the sum of the prices charged must cover the full Marginal Cost of supplying both periods: the Marginal Common Cost + the sum of the two Marginal Separable Costs. QUESTIONS The answers to daggered questions appear at the end of the book. 1. Why is most productive activity carried out by rms rather than simply by individuals who contract mutually with one another? 2. Partnership rms are generally small and managed directly by their owners. Why? How does the corporate form facilitate the organization of larger enterprises? 3. a. What is meant by economic prot? b. Is prot maximization an appropriate goal for owners? For managers? c. What tends to happen if owners are not also managers? 4. What would be the effect upon the rms decisions of a 50% tax upon economic prot? Upon accounting prot? 5. How will an increase in a rms xed costs affect its Marginal Cost curve? What will be the effect of such an increase in xed costs on the rms supply curve? 6. Consider a rm with Marginal Cost MC = 10 + 5q , Average Variable CostAVC = 10 + 2.5q , and xed costs of $250. a. What is the rms Total Cost function? b. If the market price for the rms output is $50 per unit, what is the rms protmaximizing output? c. Is it making an economic prot? For Review 7. a. b. If Marginal Cost falls throughout, does Average Cost necessarily fall? If Average Cost falls throughout, does Marginal Cost necessarily fall? 8. If Marginal Cost MC is rising throughout, will the Average Cost curve AC necessarily be rising? If AC is rising throughout, is MC necessarily rising? 9. When will a rm respond to changes in economic conditions by a short-run adjustment? When by a long-run adjustment? 10. Evaluate the following reasoning: In the short run a retail store can increase some of its inputs, such as salespeople, but not others, such as oor space. Since increasing some inputs costs less than increasing all inputs, short-run marginal cost is less than long-run marginal cost. 11. Show why no Long-Run Average Cost curve can satisfy both of the following conditions: a. It shows the lowest cost at which any given output can be produced (i.e., it is a lower envelope of the Short-Run Average Cost curves). b. It shows the lowest-cost output at any given level of the xed input (i.e., it goes through the minimum points of all the Short-Run Average Cost curves). Which of the two conditions is the correct one? P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 188 6. THE BUSINESS FIRM 12. Is the rms Total Cost curve necessarily rising, or can it have a falling range? Is the rms Average Cost curve necessarily U-shaped, or can it be rising throughout (or falling throughout)? What about the Average Variable Cost curve? For each allowable shape of the Average Cost and Average Variable Cost curves, show the implied shape of the Marginal Cost curve. 13. In Figure 6.3, how should output be allocated if both Marginal Cost curves fall throughout? What if one is rising and the other falling? 14. How should the LRMC curve be drawn in Figure 6.6? 15. Microprocessors for computers are produced in fabs, large high-tech factories which can require billions of dollars of xed investment. Do you expect there will be a range of declining average cost in the microchip industry? How does your answer relate to Example 6.4 on scale economies in electric power distribution? For Further Thought and Discussion 1. What types of production that take place in the household are not delegated to rms? 2. A Maa leader was on trial for directing his enforcers to break the legs of anyone defaulting on a debt owed him. The leader readily admitted the fact, but explained, We provide a valuable service to borrowers who do not have good enough credit standing to obtain loans from banks. In the interests of full disclosure, we always inform our borrowers that we will break their legs if they default. We have found that borrowers would very likely fail to exercise due diligence in their use of the borrowed funds if we allowed them to walk away from their loans whenever unable to pay. Indeed, it would be impossible to carry on our business if we allowed something like a declaration of bankruptcy to cancel the debts owed us. Answer the following, and explain briey in each case. a. Is this type of business a valuable service to borrowers? b. Would it be efcient to permit contracts in which borrowers agreed in advance that their legs would be broken if they failed to repay? c. Does it follow that this form of contract enforcement should be legalized? 3. In railroading, about two-thirds of costs are said to be xed and only one-third variable. If so, AVC is approximately one-third of AC. It would therefore always be nancially advantageous for railroads, it has been argued, to take on additional trafc even at a price lower than Average Cost. Is this argument valid? Explain. 4. a. Why will a rm ever keep any inputs xed in the face of changing economic conditions? b. What determines which inputs are held xed, and which varied? 5. Compare the effect upon a competitive rms output of a tax of $1 per unit upon output versus a license fee of $200 payable each year regardless of output. 6. Consider the most efcient way of dividing output between two plants (as in electricity load dispatching). If the Marginal Cost curves are rising, when will one of the plants not be operating? What can be said if one or both of the Marginal Cost curves are falling? 7. What is wrong with the following reasoning on the part of a factory manager: My plant is working steadily at its most efcient output. Nevertheless, I could always meet a short-run surge in demand simply by running the machines a little faster and deferring maintenance. So in the short run my Marginal Cost is practically zero. 8. Electric utilities commonly keep their most modern and efcient generating equipment, characterized by a low ratio of fuel input to power output, working around the clock. P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 QUESTIONS 189 Older equipment still on hand is used only to meet periods of higher load. What does this imply about the shape of the Short-Run Marginal Cost curve for generation of electricity? 9. An urban rapid-transit line runs crowded trains (200 passengers per car) at rush hours, but nearly empty trains (10 passengers per car) at off hours. A management consultant makes the following argument: The cost of running a car for one trip on this line is about $50 regardless of the number of passengers. So the per-passenger cost is about 25 cents at rush hour but rises to $5 per passenger in off hours. Consequently, we had better discourage off-hour business. a. b. Is there a fallacy in the consultants argument? Commutation tickets (reduced-price, multiple-ride tickets) sold by some transit systems are predominantly used by rush-hour riders. Are such tickets a good idea? P1: OBM/JzG 0521818648p03.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:27 190 P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 7 Equilibrium in the Product Market Competitive Industry 7.1 The Supply Function 192 From Firm Supply to Market Supply: The Short Run 192 Long-Run and Short-Run Supply 195 External Economies and Diseconomies 199 7.2 7.3 Firm Survival and the Zero-Prot Theorem 201 The Benets of Exchange: Consumer Surplus and Producer Surplus 203 An Application: The Water-Diamond Paradox 205 An Application: Benets of an Innovation 206 7.4 Transaction Taxes and Other Hindrances to Trade 207 Transaction Taxes 208 Supply Quotas 209 An Application: Import Quotas 210 Price Ceilings and Shortages 213 SUMMARY 217 QUESTIONS 218 EXAMPLES 7.1 7.2 7.3 7.4 7.5 7.6 7.7 Cotton Spindles 197 Economies of Scale and the Survivor Principle 202 Lotto and Consumer Surplus 205 Import Quotas 212 Two San Francisco Housing Crises 213 Inefcient Housing Allocation in New York City 215 Repressed Ination in Postwar Germany 216 191 P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 192 7. EQUILIBRIUM IN THE PRODUCT MARKET COMPETITIVE INDUSTRY The preceding chapter was devoted to an optimization problem: in a competitive industry, what level of output maximizes the rms prots? For example, how many shoes will a footwear manufacturer want to produce? This chapter moves on to the equilibrium problem. Looking now at the industry as a whole, we ask when shoe prices will be high and when they will be low. What about the quantities produced and consumed? The answers of course depend upon supply and demand. Chapter 4 analyzed how the market demand curve for a good was derived from the consumption choices of individuals. Similarly, this chapter will show how the separate decisions of the different rms lead to an industrys market supply curve. Together, the market demand curve and the market supply curve determine the equilibrium price and the overall quantities produced and consumed. Later in the chapter Consumer Surplus will be introduced as a measure of the gains to buyers from market exchange, and Producer Surplus as a measure of the gain to suppliers. The analysis will be extended to demonstrate how hindrances to trade such as transaction taxes affect market equilibrium and prevent full achievement of the benets of exchange. 7.1 THE SUPPLY FUNCTION From Firm Supply to Market Supply: The Short Run For a competitive (price-taking) rm, the preceding chapter showed that the price P of its product is necessarily identical to its Marginal Revenue (the additional revenue per additional unit sold). The key proposition derived was that a competitive rm, under appropriate conditions, maximizes prot by setting output so that Marginal Cost equals price: MC = P MR. The rms supply curve s f , pictured in Figure 7.1, showing how a rms output q responds to different levels of price P, basically runs along its MC curve. However, the No-shutdown conditions discussed in the preceding chapter must also be taken into account. The diagram depicts the rms short-run supply curve, applicable when some inputs are held xed. The No-Shutdown condition then dictates zero output whenever the market price ( P ) is less than the minimum (PV ) of Average Variable Cost AVC. So s f in the diagram is a broken curve. For prices below PV the supply curve lies along the vertical axis. Then, at P = PV , the supply curve skips to the right (dotted line) to point K. Last, for all higher prices the supply curve is identical to the rising branch of the MC curve. EXERCISE 7.1 Let a rms cost function be as shown in Table 6.1: C = 128 + 69q 14q2 + q3 . Find the supply function for this rm, using the exact formula for Marginal Cost: MC = 69 28q + 3q2 . A N S W E R : The rms supply curve is based on the rule Marginal Cost = Price, which implies P = 69 28q + 3q2 . The equation is valid, however, only for P greater than or equal to PV , the minimum of Average Variable Cost. (For P less than PV , the best output is q = 0.) The next step is to nd PV . From the equation for Cost it follows that Average Variable Cost (C F )/q = 69 14q + q2 . Marginal Cost (MC) and Average Variable Cost (AVC) always intersect at the minimum of the Average Variable Cost curve. P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 7.1 THE SUPPLY FUNCTION 193 P P sf MC B Figure 7.1. Supply Function of a Competitive Firm: Short Run Price P Pv K AVC A At product prices less than PV , the minimum of Average Variable Cost AVC, the rms best output is q = 0 (the rms supply curve s f runs along the vertical axis). Above this price, s f coincides with the Marginal Cost curve MC. q 0 qv q OutputQuantity q Setting MC = AVC , 69 28q + 3q2 = 69 14q + q2 . Solving algebraically, MC and AVC intersect at q = 7 where MC = AVC = 20 (as was also indicated in Table 6.1). So the supply function is: P = 69 28q + 3q2 , q=0 for P 20 otherwise Any specic good is typically produced only by a limited group of rms, the industry associated with that commodity. The industrys supply curve, the market supply curve for that good, is the horizontal sum of the individual rms supply functions. (Just as the overall market demand curve is the horizontal sum of the individual demand functions, as was shown in Chapter 4.) EXERCISE 7.2 An industry consists of 100 identical rms. Each rm has the cost function of the preceding exercise: C = 128 + 69q 14q2 + q3 . What is the industry supply curve? A N S W E R : Let industry output be Q 100q, where q is the output of each rm. Going directly to the supply function of Exercise 7.1 and substituting Q/100 for q : P = 69 28( Q/100) + 3( Q/100)2 , Q= 0 for P 20 otherwise There is one further consideration. By denition, in perfect competition each rm views the product price as given independently of its own output decision, but nothing has yet been said about input prices. Implicitly, the assumption has been that the competitive rm views these also as given. A single coal mine, in expanding output after a rise in coal price, may be able to hire more workers without causing the wages of coal miners to increase. But to analyze the industry supply that function, one must ask what would happen if all coal mines simultaneously expanded output. The wages of coal miners would surely rise, increasing costs of production for each and every rm. Similarly, a P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 194 P 7. EQUILIBRIUM IN THE PRODUCT MARKET COMPETITIVE INDUSTRY S Figure 7.2. Industry Supply Function: Input-Price Effect sf sf Price P K H G P 0 QQ Q Q At price P the industry will provide quantity Q , determining G as one point on the industry supply curve. If the product price rises to P but input prices remain unchanged, the new equilibrium would be at point H along curve s f , which is the horizontal sum of the rms separate supply curves at the initial input prices. However, normally the rise in industry output will force input prices upward. As rms costs rise, their supply curves shift upward. The new equilibrium will be at point K along the curve s f that aggregates the rm supply curves at these higher input prices. The industry supply curve through points such as G and K is therefore steeper (less elastic) than the aggregate of the rms supply curves. IndustryQuantity single PC manufacturer could buy more memory chips without noticeably affecting their prices but if the entire computer industry increased its output, the prices of memory chips would tend to rise. In Figure 7.2, suppose that the price of coal was initially P and that aggregate industry output was Q . So P and Q dene a point G on the industry supply curve S. For simplicity, suppose also that all rms have Marginal Cost curves like MC in Figure 7.1, and that P > PV (so that the region where rm supply curves run along the vertical axis can be ignored). The curve labelled s f is the horizontal summation of the individual rm s f curves under the input-price conditions associated with industry output level Q . To nd another point on the industry supply curve, we ask what happens if product price rises from P to P . It might be thought that the new higher output is found by moving along the curve s f to the output level Q at point H. If, however, the expansion of aggregate output raises miners wage rates, each rm will discover that its entire Marginal Cost curve has shifted upward. So the industry as a whole cannot expand output along the s f curve. Instead, at the higher wage for miners, the industry supply curve is s f . The new quantity supplied is indicated by point K, where s f intersects the horizontal price line P = P . The industry supply curve, the dashed curve S in the diagram, therefore runs through points G and K rather than through G and H. Curve S is steeper than the s f or s f curves because of the adverse effect on cost of an increase in the prices of inputs. An observer who failed to take this input-price effect into account would therefore predict too big a supply response of the industry to variations in output price P. CONCLUSION The short-run supply curve of a competitive rm, above the minimum of its Average Variable Cost curve, is identical to its Marginal Cost curve. The short-run supply curve of a competitive industry is the horizontal sum of the rms supply curves, but only after allowing for the input-price effect that raises Marginal Cost curves as industry output rises (or lowers Marginal Cost curves as industry output falls). The P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 7.1 THE SUPPLY FUNCTION 195 input-price effect reduces the magnitude of the supply response to changes in output price, making the industry supply curve steeper than it would otherwise be. Just as elasticity of demand measures how quantity demanded responds to changes in price, elasticity of supply measures the response of quantity supplied to price changes. DEFINITION: Elasticity of supply is the proportional change in quantity supplied divided by the proportional change in price: Q/ Q P/P QP PQ (7.1) Recall that elasticity of demand is, apart from the exceptional Giffen case, always negative. In contrast, elasticity of supply is normally positive.1 Since elasticity is dened in terms of proportionate changes, it is independent of the units of measurement. As explained in Chapter 5, this allows us to meaningfully say, for example, that steel is more (or less) elastically supplied than cotton. So the conclusion about the responsiveness of an individual rm versus the industry as a whole to price changes, can be expressed: PROPOSITION: The input-price effect normally makes the industrys short-run supply curve less elastic than the separate rms short-run supply curves. Long-Run and Short-Run Supply In the rms short-run supply function pictured in Figure 7.1, some input or inputs were held xed. For a coal mine, the number of shafts might be such a xed input. Facing a temporary product price increase, the rm might nd it inadvisable to open new shafts or to close existing shafts if the price of coal momentarily falls. But if the rm believes the price of coal has permanently changed, it will want to adjust all of its inputs in choosing its long-run optimal output q.2 In Figure 7.3 the rms long-run supply function Ls f is discontinuous, like the shortrun supply function s f in Figure 7.1. The long-run supply curve must take into account the long-run No-Shutdown condition. So for the rm to remain in business, price P must be greater than PC , the minimum of its Long-Run Average Cost curve. The supply curve Ls f therefore runs along the vertical axis up to PC , then skips to the right (dotted line), and thereafter overlies the curve of Long-Run Marginal Cost LRMC. Suppose the product price is initially P o , so that the rm produces the amount qo the level of output at which LRMC = P o . Now let the market price jump to P . A rm that regards the price change as temporary will choose output q S , where SRMC = P . But a rm that expects the price change to be permanent will set output at q L , where LRMC = P . 1 2 For supply as for demand, cross-elasticities may be important. The cross-elasticity of supply would reect, for example, how output of mutton would respond to changes in the price of wool. Only the direct price elasticity of supply will be taken up here. How rapidly it pays to move to the optimal long-run level of the xed factor depends upon the durability and the resale value of the xed equipment specialized to the rm. Suppose the rm reduces output. If resale value is relatively high, the rm may sell off the excess equipment and move to the correct scale almost immediately. But if resale value is very low, it may pay the rm to retain the equipment until it wears out. (Note that it may or may not take a long period of calendar time to make a long-run scale adjustment.) P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 196 7. EQUILIBRIUM IN THE PRODUCT MARKET COMPETITIVE INDUSTRY P SRMC LRMC P LRAC SRAC P Price Lsf PC M 0 q qS qL OutputQuantity q Figure 7.3. Firms Long-Run Supply Function The rms long-run supply function L s f runs along the vertical axis (zero quantity supplied) up to PC , the minimum level of the Long-Run Average Cost curve LRAC. Above this price, the supply function coincides with the Long-Run Marginal Cost LRMC. EXERCISE 7.3 Using the data of Exercise 6.5 of the preceding chapter, suppose Long-Run Total Cost is LRTC = q2 and Short-Run Total Cost is SRTC = 2 B + q4 /(8 B ), where B is the amount of the xed input. For Marginal Costs use the exact calculus formulas LRMC = 2q and SRMC = q3 /(2 B ). (a) If B = 4, nd the rms short-run supply curve. (b) Find its long-run supply curve. (c) At what price and output do these supply curves intersect, and what is the signicance of this intersection? (d) What happens if price rises to P = 27, temporarily or permanently? A N S W E R : (a) The short-run supply curve is given by the condition SRMC = P , or P = q3 /8. (b) The long-run supply curve is similarly given by LRMC = P , or P = 2q. (c) The curves intersect at q = 4, P = 8. The intersection signies that if the xed input can be varied, B = 4 is its optimal level. The short-run supply curve for B = 4 and the long-run supply curve both dictate the same output, q = 4. (d) If price rises to P = 27 and the rm regards the change as temporary, it would respond along the Short-Run Marginal Cost curve, setting q3 /8 = 27. The new short-run optimal output would be q = 6. But if the rm regards the price change as permanent, it would make a long-run response and choose output where LRMC = 2q = 27, so that q = 131/2. The long-run output response is greater. For convenience, long-run versus short-run has been interpreted as a simple dichotomy. But its really a matter of degree. Some inputs lie toward the xed end of the spectrum, others toward the variable end, and still others are in between. Similarly, some price changes are regarded as highly permanent, others as relatively transitory. How permanent the price change is considered to be, and how xed the various inputs P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 7.1 THE SUPPLY FUNCTION 197 are, determine the extent to which the rm adjusts production in response to a price change. Within the industry as a whole, different rms will in their mix of xed versus variable costs, and also in their estimates about the permanence of a price change. Consequently, any historical price change is likely to elicit, over time, a mixture of short-run and long-run rm responses. EXAMPLE 7.1 COTTON SPINDLES Cotton spinning in the United States has historically been a highly competitive industry. Originally located mainly in New England, in the 20th century the industry gradually shifted toward the southern states to take advantage of cheaper labor and a warmer climate. Comparing the South and New England, the table here shows the average variation of spindle hours by calendar quarters during the midcentury period (1945 1959). Spindles are essential for spinning, so spindle hours are a measure of output. Changes in spindle hours (variations in output) may be due either to changes in hours per spindle or to changes in the number of spindles. The rst of these, Variation in Hours per Spindle, reects rms short-run adjustments to the price changes taking place quarter by quarter. Variation in Active Spindles represents rms long-run adjustments as they alter amounts of xed equipment. Changes in cotton spindle hours, per quarter 19451959 Average variation in hours per spindle (%) 90.5 76.5 Average variation in active spindles (%) 9.2 21.8 Area Southern states New England Source: U.S. Census data cited in G. J. Stigler, The Theory of Price, 3rd ed. (New York: Macmillan, 1966), p. 144. Cotton prices were generally falling in this period. In addition, irregular quarter-byquarter changes in demand were taking place. The table suggests that rms usually interpreted these demand changes as temporary. That is why hours per spindle (short-run response) varied so much more than the number of spindles (long-run response). In particular, Southern rms responded to demand changes almost exclusively by adjusting variable inputs (hours per spindle). These rms felt little need to adjust their long-run position. But in the declining region, New England, rms more frequently made long-run adjustments by disposing of xed spindle equipment. The industry long-run supply curve, like the industry short-run supply curve, is the horizontal sum of the corresponding rm supply curves. An additional element operating in the long run is the entry-exit effect. In long-run equilibrium every rm in the industry must earn non-negative economic prot, which means that price must cover Long-Run Average Cost: P LRAC . Any rm that cannot meet this condition will eventually go out of business. And conversely, if there are prot opportunities within an industry, outside rms whether newly organized, or now operating in some other industry will eventually enter. P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 198 7. EQUILIBRIUM IN THE PRODUCT MARKET COMPETITIVE INDUSTRY P D IS SS LS D PI Price PS PL P F D D 0 Q Q S QL Q IndustryQuantity Figure 7.4. Market Response to Change in Demand The initial demand curve is DD and equilibrium is at point F (price P o and output Q o ). In the immediate run an upward shift in the demand curve from DD to D D has no effect on output because, by assumption, the quantity Q o cannot be immediately changed (the supply curve is the vertical line IS). The entire effect is therefore upon price, which rises to P I . In the short run (i.e., if rms can vary output but believe the demand change is temporary), the upward sloping supply curve SS is relevant; aggregate quantity increases to Q S and price declines from P I to PS . In the long run (if rms believe the demand change is permanent), the relevant supply curve is LS; quantity sold increases to Q L , and the price falls from PS to P L . Exit and entry affect the industrys long-run supply curve. If an indenitely large number of essentially identical rms always stand ready to enter or leave, the long-run industry supply curve will be highly elastic. At the extreme, the supply curve is horizontal (innitely elastic). Even a tiny price increase attracts an indenitely large number of rms, and the reverse holds for a price decrease. Such extreme conditions are unrealistic. The most important reason is that rms are not identical. If (as seems reasonable) new entrants typically have higher costs than rms already in the industry, the long-run supply curve will have positive slope. [Note: Although potential entrants may be higher-cost rms, that does not mean they are necessarily less efcient. Their economic costs may be higher in this industry only because they have more favorable alternative opportunities for operating in some other industry.] Supply tends to be more elastic in the long run. First, the response of each individual rm to changes in price is likely to be larger, since Long-Run Marginal Cost curves rise less steeply than Short-Run Marginal Cost curves. Second, changes in the number of rms (entry and exit) work in the same direction. So a high coal price leads in the long run to each rm mining more coal, and also leads to an increase in the number of coal-mining rms. The converse holds for a low coal price. Figure 7.4 illustrates the effect of length of run on the supply-demand equilibrium. The initial equilibrium is represented by price P o and quantity Q o along demand curve P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 7.1 THE SUPPLY FUNCTION 199 DD. Suppose the demand for coal shifts upward to D D . The vertical curve labeled IS is the immediate-run supply function. Think of it as representing a time interval so short that production has no chance at all to respond. Since the quantity produced is xed, price is determined by the intersection of supply curve IS with demand curve D D at the level PI . If the demand change lasts long enough for coal mines to adjust their variable inputs, for example the number of miners, quantity will respond as indicated by the positive slope of the short-run supply curve SS. In the new short-run equilibrium, price PS exceeds the initial price P o , but is lower than the immediate-run price PI . Last, the long-run supply curve LS (which allows coal-mining rms to unx the xed inputs by opening new shafts, acquiring new machinery, and so on) is still more elastic. Consequently, the long-run equilibrium price PL is lower still, though remaining higher than the original P o . CONCLUSION If an industry has an upward-sloping supply curve, after an increase in demand both price and quantity will rise. But in moving from the immediate run to the short run to the long run, the price increase is progressively moderated whereas the quantity increase is accentuated. And similarly for a decrease in demand, the longer the run the smaller the change in price and the greater the change in quantity. External Economies and Diseconomies In examining an industrys response to changes in demand, it is useful to distinguish between (1) inuences that are internal to the separate rms and (2) those that are internal to the industry as a whole but external to the separate rms. The internal inuences that limit individual rms responses to a price change are summarized by their short-run and long-run cost functions, whose rising shapes reect internal diseconomies of scale. (There may be an initial range of falling average and marginal costs, or internal economies of scale, but in the neighborhood of equilibrium, rms Marginal Cost functions must be rising.) The input-price effect pictured in Figure 7.2 above is an external diseconomy of scale. The upward shift of the individual rms cost function is due not to the rm itself, but to the overall level of industry output. External economies and diseconomies can be either pecuniary (monetary) or technological. The input-price effect is a pecuniary diseconomy: industry output impacts upon individual rm costs through nancial considerations, the prices that must be paid to resource suppliers. Pecuniary externalities are almost always diseconomies. A technological externality, which can go either way, occurs when changes in industry output directly affect a rms physical possibilities of production. Think of farming on marshy land. To increase production, farmer A must drain his land. But his pumping drains the lands of neighboring farmers B, C, D, . . . , reducing their costs of production and vice versa. So these farming operations involve a technological external economy of scale. On the other hand, suppose the farm lands are too dry rather than too wet. To irrigate, each farmer pumps water from underground wells. Doing so drains water from neighbors wells, thus raising their irrigation costs. This would represent a technological external diseconomy. Figure 7.5 illustrates an external economy. The original industry price-quantity equilibrium is at point G. When product price rises from P to P , the s f curve (the P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 200 P 7. EQUILIBRIUM IN THE PRODUCT MARKET COMPETITIVE INDUSTRY sf sf H G P K S P Price Figure 7.5. Industry Supply Function: External Economy An external economy makes each rms cost of production fall as industry output expands, and therefore attens the industry supply curve. (Note that the picture here is the reverse of Figure 7.2.) 0 Q Q Q Q IndustryQuantity horizontal sum of the rms MC curves above the shutdown price) indicates an equilibrium at point H with industry output Q. But the assumed technological external economy lowers each rms MC curve, and so the horizontal sum of the rms MC curves shifts down to s f . The new equilibrium is at point K, where output is Q . Thus the supply curve runs through points G and K: the external economy makes the industry supply curve S more elastic than the separate supply curves of the component rms. (Whereas Figure 7.2 pictured an external diseconomy, Figure 7.5 illustrates an external economy of scale.) Favorable externalities can be so powerful as to make the industry supply curve slope downward. This can occur even though individual competitive rms still operate in the range of rising Marginal Cost, so that all the individual rm supply curves necessarily slope upward. In Figure 7.6, starting from the initial equilibrium at point F, suppose demand increases from D to D . Momentarily at least, product price P rises. Then rms expand output, so industry output must also increase. But thanks to the assumed strong external economy, the horizontal sum of the rms MC curves shifts downward from P Figure 7.6. Negatively Sloped Supply Function Due to External Economies sf sf G P D S D P F 0 Q Q Q The initial demand curve is D and the industry supply curve is s f ; the equilibrium is at point F. An upward shift in the demand curve to D temporarily raises price; rms begin to respond along their individual supply curves. However, the external economy means that increased industry output reduces rms costs of production, shifting the sum of the rms supply curves downward from s f to s f . If the external economy is sufciently strong, as shown here, the new equilibrium at G represents larger quantity at lower price. Thus, the industrys supply curve S is negatively sloped. Price IndustryQuantity P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 7.2 FIRM SURVIVAL AND THE ZERO-PROFIT THEOREM 201 s f to s f . The new equilibrium at point G has higher quantity but lower price! So the industry supply curve through points F and G has negative slope. External economies of scale partly explain why computers, CD players, and other electronic devices have all fallen in price despite huge increases in demand. Rapidly growing output in these industries has generated huge numbers of ideas that spread from rm to rm. The more production, the more ideas, and the lower the costs all around. EXERCISE 7.4 A small island contains a plum-producing industry consisting of 100 identical farms, each with Marginal Cost MC = 10 + 8q Q/10, where q is a single farms own output and Q is the industry output. (a) Does this cost function reect an external economy or diseconomy? (b) Is the external effect here pecuniary or technological? (c) What is the equation for the industry supply curve? (d) Which diagram in the text pictures this situation? A N S W E R : (a) As can be seen from the equation, larger industry output Q reduces each rms Marginal Cost. So this situation represents an external economy. (b) The question has not provided the information necessary to answer this. Each rms Marginal Cost fell as industry output Q grows, but there are different possible reasons. Larger aggregate plum shipments could induce the local ferries to invest in more efcient vessels, lowering transport rates. For the plum industry, that would be a pecuniary external economy. But if Marginal Cost fell with Q because of improved soil drainage, as described in the text, that would be a technological external economy. (c) Since each farm sets Marginal Cost = Price, its supply function is P = 10 + 8q Q/10. Substituting Q 100q, the industry supply curve is P = 10 + 8 Q/100 Q/10 = 10 0.02 Q. (d) The situation is like the picture in Figure 7.6: the industry supply curve has negative slope. CONCLUSION In a competitive industry, the internal effects (how changes in a rms output affect its own costs) must be diseconomies in the neighborhood of equilibrium, since the rms optimum requires that Marginal Cost slope upward. The external effects (how changes in industry output inuence rms cost functions) are of two types pecuniary and technological. Pecuniary effects are normally diseconomies, since rising industry output tends to raise the input prices faced by individual rms. But technological externalities can be economies or diseconomies; increases in industry output can have either favorable or unfavorable effects upon the production functions of the individual rms. 7.2 FIRM SURVIVAL AND THE ZERO-PROFIT THEOREM Competition tends to reduce economic prot to zero.3 A prot opportunity in an industry induces new rms to enter, so industry output grows and product prices fall. This squeezes prot from above. And increased output also raises resource prices (the 3 Accounting prot (see Chapter 6) must be positive if the rm is to survive, since accounting prot does not deduct the opportunity costs of inputs supplied by the rms owners. P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 202 7. EQUILIBRIUM IN THE PRODUCT MARKET COMPETITIVE INDUSTRY input-price effect), pressing upon prot from below. Prot in a competitive industry is thus continually squeezed by pressure from above and from below. Entry stops (long-run equilibrium is attained) when no rm still outside the industry can earn a prot within it. It follows that the marginal rm, just on the borderline of entering or leaving the industry, can earn only negligibly more within the industry than outside. For such a marginal rm, economic prot (excess of revenues over the best alternative foregone) is zero. But it doesnt follow that, in long-run equilibrium, rms with lower costs than the marginal rm earn positive economic prots. All rms in the industry earn zero economic prot in the long run! To have lower cost of production than the marginal rm, an inframarginal rm must have access to some superior productive resource. But then every rm in the industry will want to bid for that special resource, raising its price. Consider copper mining. If a marginal rm working a thin copper ore just breaks even, it might be thought that rms exploiting richer ores will be earning large prots. But all rms in the industry can bid against one another for the right to work the richer ore. So, in the long run, the price of such a special input will rise to the point where economic prot is eliminated even for inframarginal rms. Similarly, if a software rm employs a brilliant programmer who can code faster than anyone else, other rms will want to hire that programmer, increasing his wage and reducing the prots of the rm that employs him. If the mining rm itself owns the richer ore deposit, its accounting prot may indeed be high. But that rm could lease or sell the right to exploit that ore deposit to another rm. It should therefore charge itself, as an economic cost of its mining operations, the highest bid an outsider would make for the right to work its ore. So, as a mining rm, its economic prot will be zero in long-run equilibrium. (Similarly, if the brilliant programmer owns the rm himself, the forgone opportunity to work for a high wage at another rm is part of the economic cost of being in his own business.) PROPOSITION: In the long run, economic prot for any rm in a competitive in- dustry is zero. Of course, in an ever-changing world long-run equilibrium may never come about. But the tendency toward zero economic prot, stemming from downward pressure on product prices and upward pressure on input prices, is always operating. EXAMPLE 7.2 ECONOMIES OF SCALE AND THE SURVIVOR PRINCIPLE Firms choosing wrong levels of xed inputs will have higher production costs. In the long run, if they are to survive in the industry, such rms must shift to a more appropriate scale. The survivor principle draws inferences about rms cost functions from changes in the proportions of large and small producers in an industry. The survivor principle was applied to medical practice by H. E. Frech III and P. Ginsberg,a who compared the market shares of physicians engaged in solo versus joint practice for the years 1965 and 1969. A later study by William D. Marder and Stephan Zuckermanb extended the results through 1980. The table shows that between 1965 and 1980 the market share accounted for by solo or two-physician practices declined, whereas larger-sized groups gained steadily. But it seems that by 1980 the decline in one- or two-physician practices had tapered off. P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 7.3 THE BENEFITS OF EXCHANGE 203 Market share by group size, medical practice Group size 12 37 825 2699 100+ Total 1965 84.69% 8.37% 4.30% 1.33% 1.31% 100% 1969 78.25% 11.53% 5.09% 3.00% 2.12% 100% 1975 68.67% 13.31% 8.53% 5.08% 4.42% 100% 1980 67.45% 13.14% 7.78% 4.66% 6.97% 100% Sources: Frech and Ginsberg, p. 30; Marder and Zuckerman, p. 167. The data in the table can be interpreted quite differently, depending on whether a static or dynamic viewpoint is adopted. From the static point of view, even in 1980 most of the market consisted of single-physician or two-physician groups. This suggests that small size must indeed be the most efcient in medical practice. On the other hand, these sizes declined relative to all others. So it appears that, on the margin, larger rms have been more protable. New entrants have found it protable to form larger groups, whereas exiting rms have come disproportionately from the one-to-two-physician category. A possible explanation is that in any period there is an efcient mixture of rm sizes. Even though one-physician and two-physician rms may on the whole be most efcient, in recent years there may have been relatively too many rms of these sizes. So market shares have shifted in favor of the larger groups. a H. E. Frech III and P. Ginsberg, Optimal Scale in Medical Practice: A Survivor Analysis, Journal of Business, v. 47 (January 1974), p. 30. b William D. Marder and Stephan Zuckerman, Competition and Medical Groups: A Survivor Anal- ysis, Journal of Health Economics, v. 4 (June 1985), p. 167. 7.3 THE BENEFITS OF EXCHANGE: CONSUMER SURPLUS AND PRODUCER SURPLUS One of the most important principles of economics is The Fundamental Theorem of Exchange : PROPOSITION: Trade is mutually benecial. Voluntary exchange benets all parties involved. An alternative, mistaken view might be called the exploitation theory the idea that what one side gains in exchange is a loss to the other side. The proof of the Fundamental Theorem of Exchange, and disproof of the exploitation theory, is elementary. In voluntary exchange between rational persons, both sides must expect to gain. True, owing to mistakes or trickery, one or both participants might lose out. However, if beliefs are not systematically mistaken, the proposition remains true. But how much does each side gain from trade? As explained in Chapter 3, economists do not generally believe it possible to compare one persons utility with another persons. So it would be helpful to have a way of measuring the benets of trade in objective units, independent of subjective utilities. Consumer Surplus and Producer Surplus are such measures. In Figure 7.7 the market supply-demand equilibrium is at price P P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 204 P 7. EQUILIBRIUM IN THE PRODUCT MARKET COMPETITIVE INDUSTRY A Consumer Surplus S Figure 7.7. Consumer Surplus and Producer Surplus At the transaction quantity Q , Consumer Surplus is the area that lies below the demand curve D and above the equilibrium price P . It is the difference between the aggregate willingness to pay for the quantity Q (the roughly trapezoidal region OABQ ) and the amount actually paid (the rectangle OP BQ ). The Producer Surplus is similarly the area above the supply curve S and below the price P . Q Price P B F Producer Surplus D 0 Q TransactionQuantity and quantity Q . Consumer Surplus CS is represented by the upper shaded area lying beneath the demand curve D and above the horizontal line P B . Producer Surplus PS is the corresponding lower shaded area lying above the supply curve S and below the horizontal line P B .4 Consumer Surplus measures the advantage to buyers of being able to buy Q units at price P , when they would have been willing to pay higher prices (as shown by the height of the demand curve) until the transaction quantity Q is reached. Producer Surplus similarly measures the gain to producer-sellers from receiving a price as high as P when they would have been willing to supply up to Q units at lower prices. The concepts of demand price (height of the demand curve at any quantity) and supply price (height of the supply curve at any quantity) are useful here. For any individual the demand price for good X is equivalent to Marginal Value MVx as dened in Chapter 4 a persons willingness to pay, in units of the numeraire good, for an additional unit of commodity X. Similarly, for the market as a whole the demand price at any specied quantity is the height of the market demand curve at that quantity. In Figure 7.7, for the rst unit purchased the demand price is OA, meaning that at least one consumer in the market has a Marginal Value that high. But the equilibrium price is only P , so that the consumer gains Consumer Surplus of OA OP = AP on the rst unit bought. Now extend this argument to all successive units. At the transaction quantity Q = Q the sum of the successive demand prices, representing consumers aggregate willingness to pay for quantity Q , is the roughly trapezoidal area OABQ . But the amount that consumers actually pay is only the rectangle OP BQ . So the upper shaded (roughly triangular) area AP B is the Consumer Surplus the difference between aggregate willingness to pay and actual aggregate payments. A corresponding argument applies for Producer Surplus, which can be regarded as the difference between sellers aggregate receipts OP BQ and the minimum aggregate payment OFBQ they would have been willing to accept the area FBP . 4 The names of these measures are somewhat misleading. The benets stem from trading, not from consuming or producing. Instead of Consumer Surplus and Producer Surplus one should, properly speaking, refer to Buyer Surplus and Seller Surplus. P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 7.3 THE BENEFITS OF EXCHANGE 205 EXAMPLE 7.3 LOTTO AND CONSUMER SURPLUS In November 1984 the United Kingdom initiated a weekly National Lottery. Over half the adult population have participated. Each ticket costs 1. There are a variety of prizes, but on average 45% of the revenue is paid out to winners. So, in a sense. the price of participation is 0.55 the difference between the cost of the ticket and the average reward. Under certain conditions a rollover or double rollover occurs, which increases the size of the prizes and thus, in effect, reduces the price of participation. As would be expected, for drawings where such a lower price obtains, more lottery tickets are typically purchased. A study by Lisa Farrell and Ian Walker used these data on price and quantity to estimate the Consumer Surplus attributable to the lottery.a The table here shows some of their results. UK Lotto consumer surplus Revenue ( million) Regular draw Rollover Double rollover 65 78 98 Consumer surplus (/draw) 0.49 0.53 0.68 Consumer surplus ( million) 32 41 67 Source: Adapted from Farrell and Walker, Table 4 and text. The top number in the middle column, 0.49, means that on average buyers would have been willing to pay 1.49 for a lottery ticket priced at 1. (The consumer on the margin would have been willing to pay only a trie above the price of 1, but other buyers would have been willing to pay even more.) COMMENT It may seem curious that, over and above paying 1 for a ticket returning on average only 0.45, Lotto customers would have been willing to spend even more. Evidently, Lotto tickets are not a very good investment, a topic to be taken up in Chapter 15. A plausible explanation of why they are purchased is that Lotto-type games generally involve only small stakes and yield an entertainment value, over and above the rather inadequate monetary return. Or, players might not realize that these bets lose many on average. a Lisa Farrell and Ian Walker The Welfare Effects of Lotto: Evidence from the UK, Journal of Public Economics, v. 72 (1999). An Application: The Water-Diamond Paradox A vital commodity such as water may be very cheap. Diamonds, which meet only a frivolous human desire, are expensive. To understand how this can come about, both supply and demand need to be taken into account. Diamonds are valuable because they are so rare. Thinking in terms of Consumer Surplus and Producer Surplus helps clarify the issue. Figure 7.8 illustrates what the supply and demand curves for water (Sw and Dw ) might look like, in comparison with the corresponding curves for diamonds (Sd and Dd ), when scaled in terms of a common physical unit say, gallons. It is only because of the tremendously disparate P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 206 7. EQUILIBRIUM IN THE PRODUCT MARKET COMPETITIVE INDUSTRY Sd Price($/Gallon) Dw Pd Pw 0 Qd Sw Dd Qw Quantity (Gallons) Figure 7.8. The Water-Diamond Paradox Water is more valuable than diamonds in the sense that consumers aggregate willingness to pay (total area under the demand curve) is greater. However, the supply of water is so enormous, in comparison to demand, that the market value of water (rectangle of width Q w and height Pw ) is small. Purchasers of water therefore derive a huge Consumer Surplus (shaded region). For diamonds demand is smaller, but quantity on the market is smaller still. Compared to the area under the demand curve, the market value of diamonds (rectangle of width Q d and height Pd ) is large and Consumer Surplus is therefore small. quantities available that the price of water is so low. Municipal water services typically provide consumers with about 150 gallons (ve-eighths of a ton) per capita per day, at a price of around 3 cents per hundred gallons. Diamonds, if they were ever accessible in such quantities, would be cheap as dirt. But for the scanty supply actually available, consumers are willing to pay steep prices. Gem-quality diamond prices run upward from $1,000 per carat, which comes to around $20,000,000 per gallon! In the diagram the market value of water, PwQ w , is the at unshaded rectangle lying just above the horizontal axis. In the terminology of Adam Smith, this is waters value in exchange for the quantity Qw . What Adam Smith called the value in use (the total worth to consumers, their total willingness to pay for the same quantity) includes also the huge lightly shaded area lying above the market price Pw and below the demand curve Dw . The additional area, the difference between value in use and value in exchange, is the Consumer Surplus for that quantity of water. For diamonds, in contrast, Consumer Surplus is only the small dark area under the Dd curve and above Pd . So the value in use of water is enormous in comparison with its value in exchange (market value); hence Consumer Surplus is huge. But the value in exchange of diamonds almost equals its value in use; Consumer Surplus is small. An Application: Benets of an Innovation An innovation may be useful in either of two ways: it can reduce costs of production, or it can improve the product in the eyes of consumers. A cost-reducing innovation shifts the supply curve downward, whereas a product-improving innovation shifts the demand curve upward. (Some inventions work both ways: transistors are cheaper to produce than the vacuum tubes they replaced and are also far more reliable and versatile.) Figure 7.9 illustrates a product-improving innovation. The initial equilibrium at point E o is associated with price P o and quantity Q o . The innovation shifts the demand P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 7.4 TRANSACTION TAXES AND OTHER HINDRANCES TO TRADE 207 P B B S Price($/ Q) P P H F K E E D A D Q Quantity Q Q Figure 7.9. Benets of an Innovation A quality-improving innovation shifts the demand curve upward from D to D . The market equilibrium correspondingly moves from E to E . The combined PS and CS, initially the triangle ABE , now becomes the larger triangle AB E , where the stippled area shows the combined gain. PS alone increases from AE K to AE H . The higher price is reected in a reduction in CS corresponding to the trapezoidal area HFE K , but this is smaller than the gain in CS represented by the larger trapezoidal area BFE B . curve up from D o to D , leading to the new equilibrium point E at P , Q . The shaded area shows the combined Consumer Surplus (CS) and Producer Surplus (PS) in the initial situation. Consumer Surplus is the portion of the shaded triangle lying above price P o ; Producer Surplus is the portion lying below P o . The innovation that shifts demand upward to D increases the combined Consumer Surplus and Producer Surplus by the stippled area, where Consumer Surplus and Producer Surplus are now measured in comparison with the new price P . Producer Surplus necessarily increases. But the change in Consumer Surplus is more complex. Although Consumer Surplus is greater overall, some of the former Consumer Surplus has now been transferred to Producer Surplus. 7.4 TRANSACTION TAXES AND OTHER HINDRANCES TO TRADE The preceding section analyzed the benets of trade. Taxes levied upon exchange transactions reduce these benets; as do other market interventions such as price ceilings and price oors. The adverse effect of such hindrances to trade can be quantied in terms of Consumer Surplus and Producer Surplus. P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 208 7. EQUILIBRIUM IN THE PRODUCT MARKET COMPETITIVE INDUSTRY P A S Price P+ P P M G D H B S E 0 Q Q Q TransactionQuantity Figure 7.10. Effects of a Transaction Tax on Consumer Surplus and Producer Surplus An add-on transaction tax shifts the supply curve upward from S to S . At the new equilibrium, the quantity exchanged falls from Q to Q o . The gross price paid by consumers rises from P to P + ; the net price received by sellers falls from P to P . The upper shaded area is a transfer from Consumer Surplus, and the lower shaded area is a transfer from Producer Surplus; the two transfers together constitute the tax collections. The small dotted areas represent losses of Consumer Surplus and Producer Surplus that are not balanced by tax collections. Transaction Taxes Figure 7.10 illustrates an add-on tax as described in Chapter 2 (see especially Figure 2.6) a tax quoted as an addition to the sellers stated price. Recall that imposition of the tax requires distinguishing between the gross price P + paid by buyers and the net price P received by sellers. Before imposition of the tax, the equilibrium price is P and the quantity is Q . The tax leaves the industry supply curve dened in terms of the net price P unchanged. But dened in terms of gross price P + the supply curve shifts upward from S to S . The equilibrium quantity exchanged falls from Q to Q o . At this new equilibrium quantity, the gross price P + is higher but the net price P is lower. Both buyers and sellers are now worse off than before. The higher gross price paid by buyers reduces Consumer Surplus by the at trapezoidal area P + HBP . Since the price received by sellers falls to P , Producer Surplus shrinks by the area P BGP . The combined loss of Consumer Surplus and Producer Surplus is therefore the rectangular shaded area P + HGP plus the stippled triangular area HBG . These two areas have quite different economic signicance. The rectangle corresponds to the governments tax receipts. So that area represents a transfer from buyers and sellers of the taxed commodity to the government. As an approximation, the gains and losses from this transfer might be regarded as cancelling out. (Whether it is better to leave the resources in the hands of individual buyers and sellers, as opposed to transferring control to the government, involves an arguable value judgment.5 ) That leaves the 5 Such issues will be considered under the heading of welfare economics in Chapter 16. P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 7.4 TRANSACTION TAXES AND OTHER HINDRANCES TO TRADE 209 dotted triangle HBG as the net economic loss to society, sometimes called deadweight loss or efciency loss. The loss stems from the reduced volume of mutually benecial exchange. PROPOSITION: Taxes on transactions reduce both Consumer Surplus and Producer Surplus. Some of the loss is a transfer from consumers and producers to the beneciaries of government spending. But the reduced volume of trade also creates a deadweight or efciency loss. EXERCISE 7.5 The market demand curve for caviar is P = 300 Q: the market supply curve is P = 60 + 2 Q. As was shown in Exercise 2.5, using these data the initial equilibrium (simultaneous solution of the two equations) is Q = 80, P = 220. (a) If a tax of T = 15 is imposed on each jar of caviar, what is the new equilibrium? (b) What is the loss of Consumer Surplus? What is the loss of Producer Surplus? (c) What is the amount of the transfer (the tax collections)? (d) How great is the efciency loss? A N S W E R : (a) This problem was solved in Exercise 2.5. The new equilibrium quantity is Qo = 75, the gross price (paid by purchasers) rises to P + = 225, and the net price (received by sellers) falls to P = 210. (b) The original Consumer Surplus corresponds to the area ABP in Figure 7.10. Since the supply and demand curves here are linear, the area is a triangle with size (300 220)(80)(1/2) = 3,200. The new Consumer Surplus is the smaller area AHP+ , or (300 225)(75)(1/2) = 2,812.5. So the loss of Consumer Surplus is 387.5. Similarly, the old Producer Surplus (area EBP ) was (220 60)(80)(1/2) = 6,400. The new Producer Surplus (area EGP ) is (210 60)(75)(1/2) = 5,625, so the loss of Producer Surplus is 6,400 5,625 = 775. (c) The transfer (tax revenue) represented by the rectangular area P + HGP is (225 210)(75) = 1,125. (d) The remainder of the summed losses of Consumer Surplus and Producer Surplus is the efciency loss, corresponding to the small dotted triangle HGB. Numerically it is 387.5 + 775 1,125 = 37.5. Supply Quotas Taxes reduce trade through their effect on prices, by driving a wedge between the gross price P + paid by buyers and the net price P received by sellers. Other restrictions on trade, for example, consumption quotas (rationing of demand) or production quotas (rationing of supply), can also be analyzed in terms of lost Consumer Surplus and Producer Surplus. Figure 7.11 illustrates a situation where government regulations dictate that only a xed quota Q (less than the equilibrium quantity Q ) of a good can be supplied to the market. Quotas have been imposed, for example, to control the supply of milk to urban consumers. Under the usual quota arrangements, the reduced quantity Q is sold at whatever price the market will bear, in this case P which is the consumers demand price at the quantity Q . (There is no need here to distinguish between gross and net prices.) In comparison with the unregulated equilibrium P , Q , the quota both raises price and reduces the quantity exchanged. P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 210 7. EQUILIBRIUM IN THE PRODUCT MARKET COMPETITIVE INDUSTRY P P Price P E G B S C D D 0 Q Q Q TransactionQuantity Figure 7.11. Effects of a Supply Quota Upon Consumer and Producer Surplus Market supply is limited to the quota Q , so price rises from P to P . Consumer Surplus is reduced by area PBCP . Producer surplus increases by the area PBGP minus the area GCD. If this difference is positive, sellers benet from imposition of the quota. However, buyers and sellers, considered together, lose by the amount of area BCD, which represents the combined efciency losses. [Note : There may be an additional loss of PS to the extent that individual rm production quotas are not assigned to the lowest-cost producers.] Rectangle PBGP is part of the loss of Consumer Surplus. Like the tax receipts analyzed earlier, it is a kind of transfer except that the benet now goes to the suppliers of the good rather than to the government. (The suppliers retain the lower shaded area P GDE .) It follows that suppliers may benet from the quota. They will benet if their transfer gain (upper shaded area PBGP ) is larger than their deadweight loss from the reduced sales (lower dotted area GCD). Consumers, in contrast, suffer a transfer loss (PBGP ) plus a deadweight loss (BCG ). Thus, buyers are surely worse off. However, Figure 7.11 shows only a part perhaps only a small part of the efciency loss from quotas. An additional loss of Producer Surplus, which cannot be shown in the diagram, occurs if rm-by-rm production quotas are not assigned to the lowestcost producers. In practice, production quotas have usually been assigned on the basis of past sales (grandfathering). When a high-cost producer is granted a quota and a low-cost producer is not, the loss of Producer Surplus will be greater than shown in the diagram. An Application: Import Quotas Import quotas are partial production quotas, since only foreign supply sources are subject to restriction. Like tariffs, quotas are usually aimed to protect domestic producers of the product. Unlike tariffs, import quotas generate no revenue for the government. Suppose for simplicity that the importing countrys demand is not big enough for the quota to affect world prices of the product. Figure 7.12 then indicates the effect upon Consumer Surplus and Producer Surplus in the nation imposing the import quota. P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 7.4 TRANSACTION TAXES AND OTHER HINDRANCES TO TRADE 211 P Sh Price($ /Q ) P 1 P 2 3 4 M M D Qh Qh Quantity Q Q Q Figure 7.12. Import Quotas and Losses of Consumer and Producer Surplus D is the countrys demand curve for the product, and S h is the home supply curve. At the xed world price P the countrys total consumption is Q , of which Q h is the amount domestically supplied; the horizontal difference M Q Q h is the imported amount. The upper lightly shaded area is the Consumer Surplus in the home country, and the lower heavily shaded area is the Producer Surplus received by domestic suppliers. If the import quota M < M is imposed, the domestic price rises to P . Domestic suppliers now provide a larger quantity Q h , but domestic consumption Q is less than before. The four numbered areas all represent losses of Consumer Surplus. Area 1 is an increase in the Producer Surplus of domestic suppliers. Area 3 is a transfer gain to foreign suppliers. Area 2 is a deadweight loss to the domestic economy on the supply side, due to domestic production that is costlier than the import alternative. Area 4 is an efciency loss on the demand side, because some previous consumers are frozen out of the market by the higher price P . As in Figure 2.5 of Chapter 2, D is the countrys demand curve for the product and Sh is the home supply curve. Figure 2.5 shows the amount that would be imported at each price as a horizontal gap between D and S h . In the absence of an import quota, at the xed world price P the countrys total consumption is Q , of which Q h is the amount domestically supplied. The imported amount is the horizontal gap M Q Q h in the diagram. The upper lightly shaded triangle is the Consumer Surplus in the home country; the lower heavily shaded triangle is the Producer Surplus received by domestic suppliers. Now suppose an import quota M > M is imposed. The domestic price must move up, as shown by P in the diagram, to shrink the horizontal gap between D and S h P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 212 7. EQUILIBRIUM IN THE PRODUCT MARKET COMPETITIVE INDUSTRY to the quota amount M . Domestic suppliers now sell a larger quantity than before ( Q h > Q h ), but domestic consumption declines ( Q < Q ). The effects upon Consumer Surplus or Producer Surplus and Producer Surplus are indicated by the four numbered areas. All four represent losses of Consumer Surplus or Producer Surplus. Area 1 represents a transfer from Consumer Surplus to the Producer Surplus of the domestic suppliers. Area 3 is a transfer gain to those foreign suppliers who receive import quota assignments and can therefore benet from the higher price P . Area 2 represents a deadweight loss to the domestic economy on the supply side: extra costs are incurred in domestic production that could have been avoided by accepting imports instead. Last, area 4 is a deadweight loss on the demand side: consumers who were willing to pay more than P but less than P for the product are now frozen out of the market. EXAMPLE 7.4 IMPORT QUOTAS Using data for the years around 1985, Robert C. Feenstraa analyzed the impact upon American consumers and foreign and domestic suppliers of several U.S. import quota programs. His analysis was more complex than the discussion in the text. Among other things, he allowed for the effects of the program upon world prices. Nevertheless, it is still possible to interpret his results in terms of Producer Surplus and Consumer Surplus. For each group of products considered, the table provides estimates of two categories of annual losses: the U.S. deadweight loss (areas 1 and 4 in Figure 7.12) and the transfer gain to foreign suppliers (area 3). Some costs of U.S. import quota programs ($billion/year) U.S. deadweight loss (areas 2 and 4) Automobiles Dairy Steel Sugar Textiles & apparel 0.7 1.4 0.2 0.1 5.4 Transfer to foreign suppliers (area 3) 5.0 0.25 1.3 0.8 5.0 Source: Adapted from Feenstra, Table 1, p. 163. COMMENT A U.S. import quota on any commodity would tend to reduce its world price. That generates an additional deadweight loss, not listed in the table here: the loss to foreign suppliers who reduce production in response to reduced U.S. sales. Allowing for such changes in world prices, Feenstra estimated that foreign suppliers deadweight losses were comparable in scale to the deadweight losses incurred by U.S. producers and consumers. a Robert C. Feenstra, How Costly Is Protectionism? Journal of Economic Perspectives, v. 6 (Summer 1992). P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 7.4 TRANSACTION TAXES AND OTHER HINDRANCES TO TRADE 213 Price Ceilings and Shortages Prices are continually changing. A ood in Brazil will raise the price of coffee; good farming weather in the Midwest will reduce the price of wheat; advances in technology steadily reduce the price of computers. Those hurt by price changes often press the government to do something about it. Rising apartment rents lead to calls for rent control, falling wheat prices generate political pressures for agricultural price supports, and so forth. Legislation that sets the price of a good below its market-clearing level creates a shortage. A shortage differs from scarcity. Scarcity, meaning that some desires are unsatised, is always present. Diamonds are scarce, but there is no shortage; anyone willing to pay the price of a diamond can buy one. A shortage exists when goods are unavailable even to people willing to pay the price. In a city with rent controls, newcomers may be unable to nd an apartment at all, regardless of willingness to pay. If changing conditions of demand and supply make the product more scarce, consumers are bound to be worse off, one way or the other. If the market is unimpeded, they suffer from a higher price. If the price is controlled they lose from the shortages created. EXAMPLE 7.5 TWO SAN FRANCISCO HOUSING CRISES a In the 1906 earthquake and re, the city of San Francisco lost more than half its housing facilities in three days. Nevertheless, the rst postdisaster issue of the San Francisco Chronicle did not report a housing shortage! Indeed, the newspapers classied advertisements carried 64 offers of houses or apartments for rent, and only 5 advertisements for apartments or houses wanted. Of course, prices of accommodations had risen sharply in the meantime. In contrast, in 1946 San Francisco was gripped by the national postwar housing shortage. In the rst 5 days of 1946 newspapers carried only 4 advertisements offering houses or apartments for rent, but around 150 advertisements by persons seeking rentals. The explanation: after the 1906 catastrophe, no attempt was made to control rents. But in 1946, rents were frozen below the market-clearing price, leading to an excess of quantity demanded over quantity supplied. COMMENT San Francisco housing was much scarcer, in relation to the population seeking accommodation, after the 1906 earthquake and re than in 1946. During the wartime period preceding 1946, housing supply had not decreased at all. But rising money incomes, the return of war veterans, and a growing number of families led to an upward shift in demand for housing. With rents frozen, a shortage ensued. a Discussion based on M. Friedman and G. J. Stigler, Roofs or Ceilings? (Irvington-on-Hudson, NY: The Foundation for Economic Education, September 1946). Figure 7.13 adapts the earlier Figure 7.4, omitting the short run supply curve SS. The initial equilibrium is at the price-quantity combination P o , Q o . An upward shift of demand in an unregulated market brings about a new long-run equilibrium PL , QL . But suppose a ceiling prevents price from rising above P o . At this ceiling price there is a perceived shortage equal to the horizontal distance Q Q o = H . Price, if it were P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 214 7. EQUILIBRIUM IN THE PRODUCT MARKET COMPETITIVE INDUSTRY P IS PI Price LS PL P D D S Q H D Q Q IndustryQuantity Figure 7.13. Effect of a Price Ceiling An upward shift of demand in an uncontrolled market, from D to D , causes price in the immediate run to increase from P o to P I . Producers benet from a temporary windfall gain. Ultimately, the higher price will induce a larger supply; the long-run equilibrium price is P L . However, if a ceiling is enforced at the initial price P o , the supply and demand adjustments are both blocked. The perceived shortage at the ceiling price is H. If price were permitted to rise to P L , D of the larger quantity demanded would be choked off by the higher price, and S would be the supply increment provided. allowed to rise, would jump to PI in the immediate run before quantity had time to adjust but would eventually come back down as new supplies arrived. (The longer the period considered, the smaller the price increase and the larger the increase in quantity supplied.) At the new long-run equilibrium price PL , the pictured interval D is the long-run reduction in demand quantity and S is the long-run increase in supply. EXERCISE 7.6 Suppose demand is described by the equation P = 300 Q. The long-run supply curve is Q = P /2 30 and the short-run supply curve is Q = 36 + P /5. It can be veried that the market is in long-run and short-run equilibrium at quantity Q o = 80 and price P o = 220. Now suppose the demand curve shifts to the right, becoming P = 360 Q. (a) What happens in the immediate run? (b) What is the new shortrun price-quantity equilibrium? (c) What is the new long-run equilibrium? (d) What would be the perceived shortage if a price ceiling prevented price from rising above its initial level P o = 220? A N S W E R : (a) In the immediate run, quantity would be unchanged at QI = 80. The new equilibrium price is found by using the new demand condition: P I = 360 Q I = 280. (b) Solving the new demand equation and the short-run supply equation simultaneously, the new short-run equilibrium is PS = 270, QS = 90. Quantity rises only slightly above QI = 80, and correspondingly price falls by only a small amount from P I = 280. (c) Solving the new demand equation and the long-run supply equation simultaneously leads to larger adjustments: PL = 260, Q L = 100. P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 7.4 TRANSACTION TAXES AND OTHER HINDRANCES TO TRADE 215 (d) If price could not rise above P = 220 the quantity supplied would remain Q = 80, but the quantity demanded would be Q = 360 P = 140. The perceived shortage would be 140 80 = 60 units of output. Returning to Producer Surplus and Consumer Surplus, it might be thought that a price ceiling causes only a transfer from sellers to buyers. That would be correct only in the immediate run, and even then with one important qualication. The qualication is that, under rent controls, families who get apartments are not necessarily those who value the apartments the most. In terms of Figure 7.13, apartments might be rented to families who are willing only to pay P o , while others willing to pay PI or more do not obtain apartments. So even in the immediate run, a price ceiling can reduce Consumer Surplus.6 And, as has been seen, the longer the run considered, the greater the loss of production that would have been forthcoming in the absence of a price ceiling. Consumers who cannot buy desired commodities owing to price ceilings may compete for desired goods in other ways: by waiting in line (see Example 5.7), by ghting, by using political inuence, and so forth. These forms of competition are wasteful because what consumers give up (for example, time spent waiting in line) does not provide any benet to sellers. EXAMPLE 7.6 INEFFICIENT HOUSING ALLOCATION IN NEW YORK CITY Rent controls have been operative in New York City, with relaxations from time to time, since World War II. The city has accordingly been subject over the years to very serious shortages. Large numbers of people have been unable to obtain apartments though willing to pay the legal controlled price. A study by Edward L. Glaeser and Erzo F. P. Luttmer looked at a somewhat different consequence of rent controls, to wit, the effect on the sizes of apartments occupied.a An elderly widow in New York might be living in a seven-room rentcontrolled apartment all by herself, while a struggling working-class family might have to pay as much or more for very cramped accommodations. Using a model of housing demand based upon demographic and income characteristics, the authors calculated what percentage of renters would under normal conditions have occupied apartments of different sizes (number of rooms). Comparing this calculation with the observed occupancy of apartments, they found that in New York City some 20.9% of the apartments are misallocated. As would be expected, the fraction is greatest in Manhattan (26.1%), where the rent controls are the most severely binding. In contrast, the misallocation was considerably less for comparable accommodations in two cities without rent controls, the gures being 7.0% for Chicago and 4.5% for Hartford, CT. a Edward L. Glaeser and Erzo F. P. Luttmer, The Misallocation of Housing under Rent Control, American Economic Review, v. 93 (2003). Suppliers may try to evade price ceilings in more or less subtle ways. Unable to raise prices openly, rms can eliminate customary discounts and suspend off-price seasonal 6 This loss in Consumer Surplus, when available supplies are not assigned to consumers whose demand prices are the highest, parallels the loss in Producer Surplus when supply quotas are not assigned to the lowest-cost producers. P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 216 7. EQUILIBRIUM IN THE PRODUCT MARKET COMPETITIVE INDUSTRY sales, might offer less quality or variety, or might shift toward producing goods that happen to receive a better break from the price-control authorities. Supplies may be legally or illegally exported to more protable foreign markets, leaving even less available for domestic consumers. Black markets may develop. In extreme cases, legitimate trade may disappear. A dramatic case was the great inationary episode in post-World War II Germany. EXAMPLE 7.7 REPRESSED INFLATION IN POSTWAR GERMANYa Germany, like the other major belligerent countries in World War II, nanced her war effort by inationary expansion of money and credit in effect, by printing money while freezing prices. By the end of the war in 1945 the German money supply had risen about tenfold, while prices were still largely xed at their 1936 levels. Meanwhile, available supplies had fallen sharply, owing to wartime bombing, territorial losses, punitive war reparations, and division of the nation into several zones of occupation. In the early postwar years, the Allied occupation authorities in Germany continued the wartime price freeze. Prices were so drastically out of line with supply-demand reality that, over most of the economy, production for legal sale could take place only at nancial loss. Industrial production in the rst half of 1948 was only 45% of the 1938 amount, despite a larger population. According to ofcial statistics of the period, black markets accounted for only 10% of transactions. This gure was so low because in Germany the term black market was narrowly dened as the outright trading of goods for cash at illegal prices. Professional black-marketeers were regarded as disreputable individuals. In contrast, everybody engaged in a form of transaction known as bilateral exchange or compensation trade. Such trade took place at entirely legal prices in money, with one catch: no one could acquire goods or services for money alone. In addition to the money price, every buyer had to provide compensation in real goods and services. Estimates are that one-third to one-half of all transactions took this form. Even the military occupation authorities engaged in it; the noon meal provided to German workers at the occupation administration was often a more important attraction than the monetary salary. Eventually money was effectively eliminated as a medium of exchange, and the economy suffered the inefciencies of barter (as will be discussed in Chapter 14). In June 1948 most price controls were removed. Contemporaneously, a drastic currency reform exchanged new marks for old, at a ratio of about one to ten. The effect was dramatic. Goods suddenly appeared on store shelves, and workers avidly sought jobs in order to buy the now available commodities. According to one observer: It was as if money and markets had been invented afresh as reliable media of the division of labor.b The German postwar economic miracle was under way. a Discussion based on J. Hirshleifer, Disaster and Recovery: A Historical Survey, The RAND Corpora- tion, Memorandum RM-3079-PR (April 1963), pp. 83112. b Horst Mendershausen, Prices, Money and the Distribution of Goods in Postwar Germany, American Economic Review, v. 39 (June 1949), p. 646. So price ceilings cause at least three types of loss even in the immediate run: (1) the wrong (less highly valued) demands may be the ones satised; (2) irregular methods of acquiring goods, such as waiting in line, waste resources; (3) rms may evade the P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 SUMMARY 217 ceilings in ways that either are costly or reduce the value of the good to consumers. Even more important is the longer-run effect. Price ceilings discourage the development of additional supplies by producers. SUMMARY The supply curve of a competitive rm is its Marginal Cost curve, with two qualications: (1) only the rising branch of the Marginal Cost curve is relevant, and (2) price must cover Average Variable Cost AVC in the short run ( P > AVC ) and cover Average Total Cost AC in the long run ( P > AC ). The industry supply curve is the sum of the quantities offered at each price by all the separate rms. It is also necessary to allow for the external effects on rms costs that stem from changes in industry-wide output, and to allow for entry into or exit from the industry. External economies reduce a rms costs as industry output rises; external diseconomies increase costs as industry output rises. If the industry-wide level of output affects only the prices that rms pay for required inputs, the external effects are pecuniary. These externalities make the industry supply curve less elastic than it would otherwise be. If industry wide output directly affects rms production functions, the external effects are technological. Technological external effects can go either way, and might even be so strong as to make the industry supply curve slope downward. In the immediate run, the quantity produced by an industry is constant (the supply curve is vertical), so a shift in demand affects only price. In the long run the supply curve is more elastic because (1) rms Long-Run Marginal Cost curves are less steep than their Short-Run Marginal Cost curves, and (2) new rms enter in response to price increases (or old rms exit in response to price decreases). In long-run equilibrium the marginal rm, just on the border of entry or exit, earns zero economic prot. But even inframarginal rms earn only zero prot in the long run. Whatever the especially desirable input that is responsible for a rms low costs and positive prot, all rms in the industry can compete for that input. Eventually, it will command a price so high that its owner captures the entire benet. The Fundamental Theorem of Exchange states that voluntary trade is mutually benecial. Consumer Surplus, the difference between buyers aggregate willingness to pay and what they pay in the market, measures the benet of trade to buyers. Producer Surplus, the difference between sellers aggregate revenue and the minimum revenue at which they would be willing to offer the good, measures the benet of trade to sellers. Hindrances to trade such as transaction taxes, supply quotas, or price ceilings affect Consumer Surplus and Producer Surplus in two ways: (1) transfers of surplus from one group to another, and (2) deadweight losses caused by the reduced amount of exchange. Following an increase in demand or a decrease in supply, a price freeze creates a shortage an excess of quantity demanded over quantity supplied. By paying a lower price, consumers reap a transfer gain at the expense of suppliers. But the supply response that would have occurred in the long run is blocked; this is an efciency loss to both producers and consumers. Consumer Surplus and Producer Surplus are also reduced when the limited supplies available are distributed inefciently. Wasteful activities (such as standing in line to acquire the good) and deceptive moves by rms (such as subtly reducing quality) are additional sources of deadweight loss from price ceilings. P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 218 7. EQUILIBRIUM IN THE PRODUCT MARKET COMPETITIVE INDUSTRY QUESTIONS The answer to daggered questions appear at the end of the book. For Review 1. At any rate of output, the industry long-run supply curve tends to be less steep than the short-run supply curve. Is it also necessarily more elastic? Explain. 2. In the long run, a rm could always produce twice as much simply by doubling the amount of every input employed. So in the long run there must be constant returns to scale. Evaluate. 3. Does elasticity of supply for an industry tend to be large or small if the rms Marginal Cost curves are sharply upward-sloping? What is the effect on elasticity of supply if higher industry output greatly increases the hire-prices of inputs employed in the industry? 4. If there are N identical rms and no external effects on input hire-prices, is the industry supply curve more or less steep than the rm supply curve? More or less elastic? 5. Explain the distinction between internal and external economies or diseconomies. 6. a. b. In long-run equilibrium, why does the marginal rm (the highest-cost rm in the industry) earn zero economic prot? Why do the other inframarginal rms earn zero economic prot? 7. Consider the exceptional case of an industry with a downward-sloping supply curve. Starting from an initial equilibrium, will a decline in demand lead to a rise or a fall in price? To a rise or a fall in output? Explain. 8. If a tax is imposed upon some commodity, indicate the areas of the following: loss of Consumer Surplus, loss of Producer Surplus, tax collections (transfers of Consumer Surplus and Producer Surplus to government), and efciency losses. 9. Under rent control, why would some individuals rent apartments of size or quality different from what they would have selected without rent control? Why would some individuals have trouble nding a place to rent? 10. Normally, can external pecuniary effects override internal diseconomies of scale? Can external technological effects? What is the slope of the industry supply curve when external economies override internal diseconomies? For Further Thought and Discussion 1. Apartments in New York City are subject to rent control. Apartment owners there often require tenants to purchase their furniture from them. Why? 2. In a competitive industry, for any rm there may be internal economies of scale over a certain range. But each rm must operate in the region where internal diseconomies of scale dominate. True or false? Explain. 3. Under what circumstances would you expect a rise in demand for an industrys product to be met primarily by a short-run output response by existing rms? By a long-run response by existing rms? By entry of new rms? 4. Which of the following is a pecuniary effect, which a technological effect? Which is internal to the rm, which external to the rm (but internal to the industry)? a. As the number of lms produced rises, actors salaries go up. b. As shing activity intensies, each sherman nds sh scarcer. c. As new retail shops open, existing shops nd customers scarcer. d. Steel mills along a river use the water for cooling. But the greater the use, the warmer the water gets, so that the river becomes less effective for cooling. P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 QUESTIONS 219 5. If at a certain equilibrium price every rm in the industry earns zero economic prot, doesnt that imply that a fall in market price would cause all rms to fail? Explain. 6. A number of techniques are available to cope with increased scarcity and higher world prices of petroleum. Analyze the following in terms of supply-demand responses in the short run and long run. a. Price freeze and rationing by queue (waiting in line for gasoline). b. Price freeze and rationing by coupon (nonsalable). c. Rationing by coupon (nonsalable) without a price freeze. d. A tax on all petroleum used. e. A tariff on imports of petroleum. 7. In policy (c) above (rationing by coupon without a price freeze), suppose consumers were permitted instead to sell ration coupons to one another. a. Would this change elicit more supply? b. Would the limited supplies be reallocated to those with greater willingness to pay? c. Explain the consequences in terms of Consumer Surplus. 8. Suppose a price ceiling is imposed on some good X, and that nonsalable ration tickets are all assigned to consumers who are unwilling to pay even the ceiling price. Would that mean that no one purchases good X ? What if the tickets were made salable? 9. Suppose that, after a decline in demand for a product, a oor is placed under its market price. Then the problem arises of managing a surplus instead of a shortage. What are the disadvantages of a price oor? Do the disadvantages tend to increase over time, as in the case of managing a shortage? Would black markets tend to develop? 10. Petroleum regulations in the United States froze prices of old oil coming from existing wells. The justication was that while producers had to be offered more to induce them to drill new wells, the output from existing wells would be forthcoming even at low prices. Is this argument correct? 11. The presence or even the threat of price freezes may induce rms to integrate vertically (to merge with upstream supplier rms or with downstream customer rms). Explain why. 12. a. b. Analyze the effects of a subsidy upon Consumer Surplus and Producer Surplus. Taxes hinder trade, causing an efciency loss. Does it follow that subsidies, which encourage trade, cause an efciency gain? 13. If the Average Variable Cost curve rises throughout, does the short-run supply curve s f have a discontinuity? [Hint : If Average Variable Cost rises throughout, its minimum lies along the vertical axis.] 14. In Exercise 7.3, no discontinuity appears in either the long-run or short-run supply curve. Why? [Hint : What are the long-run and short-run shutdown prices?] P1: JPJ/... P2: JZP/... 0521818648c07.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:29 220 P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8 Monopolies, Cartels, and Networks 8.1 The Monopolists Prot-Maximizing Optimum 222 Price-Quantity Solution 222 Monopoly versus Competitive Solutions 226 An Application: Author versus Publisher 228 An Application: Monopolist with Competitive Fringe 231 8.2 8.3 8.4 Monopoly and Economic Efciency 231 Regulation of Monopoly 234 Monopolistic Price Discrimination 238 Market Segmentation 238 Block Pricing 241 Perfect Discrimination 243 8.5 8.6 Cartels 244 Network Externalities 248 Demand for a Network Good 248 Monopoly or Competition? 250 The Lock-in Issue 250 SUMMARY 253 QUESTIONS 254 EXAMPLES 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 Potential Entry in Monopoly Airline Markets 227 Racetrack Betting 230 Long-Distance Telephone Service 237 Paperbacks versus Hardbacks 241 Peanuts 245 Antitrust and Prices 246 The OPEC 247 QWERTY as Inefcient Lock-in? 251 221 P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 222 8. MONOPOLIES, CARTELS, AND NETWORKS A monopoly exists when an industry contains only a single rm. If a rm can drive out competitors because its costs of production are lower, it enjoys a natural monopoly. Not all monopolies, however, are natural. Governments often award monopoly privileges. Cities grant exclusive franchises to rms providing cable television. The Federal government confers patents that give inventors a monopoly for a period of years. And even without government aid, a rm may possess monopoly power owing to entry barriers for example, if banks believe that nancing a new competitor in the industry would be too risky. In perfect competition, as studied in Chapter 7, the number of rms is large enough to make product price substantially independent of any single rms level of output. Each competitive rm is a price-taker. But a monopolist, facing the entire industry demand curve, must take account of its own inuence upon price: it is a price-maker. Geometrically, a competitive rm faces a horizontal demand curve, whereas a monopolist faces a downward-sloping demand curve. Actually, the number of rms is economically signicant only as a clue to behavior. By forming a cartel, as will be seen later in the chapter, a number of rms can sometimes get together and behave like a collective monopolist. On the other hand, even if only a single rm is active in the industry, such a rm may be unable to exploit its market as a monopolist if outside potential competitors stand ready to enter. Sometimes rms produce unique products that nevertheless compete closely with one another for instance, different brands of digital cameras. This market structure, called monopolistic competition, will be covered in Chapter 9. When there are more than one but only a few rms in an industry, the market structure is called oligopoly competition among the few. Such rms may engage in strategic behavior, to be explored in Chapter 10. 8.1 THE MONOPOLISTS PROFIT-MAXIMIZING OPTIMUM Price-Quantity Solution The upper panel of Figure 8.1 shows the monopolists prot-maximizing optimum in terms of Total Cost C and Total Revenue R. The lower panel displays the corresponding average and marginal functions. Compare this diagram with Figure 6.1 for the competitive rm in Chapter 6. The upper panel of Figure 6.1 showed the Revenue curve R as a ray out of the origin, reecting the xed product price P. But here, in the upper panel of Figure 8.1, R is hump-shaped. Price now falls as the quantity sold increases, and beyond a certain point the revenue loss due to falling price outweighs the revenue gain from rising quantity. And whereas Average Revenue AR and Marginal Revenue MR coincided at the xed price P in the lower panel of Figure 6.1, here in Figure 8.1 AR and MR both decline as the rms output rises. A monopolist rm can choose either product price P or industry output Q.1 It cannot x both. Once price P is set, the market demand function determines the quantity Q that can be sold at that price. Conversely, given any output Q, the market demand curve determines the price at which that quantity can be sold. (In this chapter, it is usually convenient to think of the monopolist as choosing output Q.) 1 In Chapters 6 and 7 the lower-case symbol q represented rm output and the upper-case letter Q industry output. Since the monopolist is a single-rm industry, Q here denotes the output of both the rm and the industry. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8.1 THE MONOPOLISTS PROFIT-MAXIMIZING OPTIMUM 223 $ Profit Dollars R C Figure 8.1. Monopolists Prot-Maximizing Optimum Maximum prot occurs at output Q , where the vertical difference between the Total Revenue curve R and the Total Cost curve C in the upper diagram is greatest. At this output the slopes of the R and C curves are equal (note the dashed tangent lines.) In the lower diagram, the curves of Marginal Revenue MR and Marginal Cost MC intersect at output Q . Prot in the lower diagram is represented by the shaded area, equal to Q times the difference between price P and Average Cost AC at that output. R C 0 Q MonopolyOutput Q $/Q Profit MC P AC DollarsperUnitQuantity AC AR D Q MR MonopolyOutput Q In the upper panel of Figure 8.1, the bold line-segment is the maximized prot the excess of Total Revenue over Total Cost at the prot-maximizing output Q and price P . At this output the R and C curves are farthest apart, which means that the curves have equal slopes (as suggested by the dashed parallel tangent lines). So in the lower panel Marginal Revenue MR (representing the slope of the R curve) and Marginal Cost MC (representing the slope of the C curve) intersect at quantity Q . In the lower panel the Marginal Revenue curve always lies below the Average Revenue (demand) curve. This is an instance of Proposition 2.2a of Chapter 2: when an average magnitude is falling, the marginal magnitude must lie below it. (Notice that although the monopolists optimal quantity is set at the output where MC and MR intersect, the optimal price is not at the height of the point where MC and MR intersect. Instead, the price P associated with the optimal output Q is found higher up, along the industry demand curve AR D ). The maximized prot is shown in the lower panel by the shaded rectangle. The base of this rectangle is the optimum quantity Q ; its height is the difference between P and Average Cost AC. CAUTION Do not confuse Marginal Revenue with the price charged for the last unit sold. In Figure 8.2, as sales increase from Q to Q + 1 units, along the demand curve price falls slightly from P to P . The price received for the last unit is represented by the thin tall rectangle of height P and width Q = 1. But when output increases P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 224 $/Q 8. MONOPOLIES, CARTELS, AND NETWORKS Lostrevenue DollarsperUnitQuantity P P Figure 8.2. Marginal Revenue versus Price of the Last Unit Sold The price of the last unit sold corresponds in revenue terms to the area of the tall shaded rectangle of width Q = 1 and height P . To calculate Marginal Revenue we must subtract the area of the thin at rectangle of height P P P and width Q. This at rectangle corresponds to the loss of receipts due to the reduced price on units that could have been sold at the higher price P . D AR Gained revenue 0 Q Q+1 MonopolyOutput Q by one unit, price falls from P to P on all the units sold. The revenue loss from this price reduction is represented by the at thin rectangle of width Q and height P P P . Marginal Revenue is the difference between the areas of the tall rectangle and the at rectangle. Symbolically, Marginal Revenue is:2 MR P + Q P Q (8.1) Since Q = 1, the rst term on the right-hand side is equivalent to the area of the tall rectangle P ( Q ) and the second term to the area of the at rectangle Q ( P ). Because the demand curve normally slopes downward, P / Q is negative. Thus we see again from equation (8.1) that Marginal Revenue MR must be less than price P. In Figure 8.1 the cost functions (Total Cost C, Average Cost AC, and Marginal Cost MC ) though not the Revenue and demand functions generally resemble the corresponding curves for the competitive rm in Figure 6.1.3 As before, prot is dened as: R C PQ C As shown in Figure 8.1, prot is at a maximum where MC equals MR: MC = MR P + Q P Q Monopolists Maximum-Prot Condition (8.3) (8.2) As in Chapter 6, there are two qualications: (1) the Marginal Cost curve must cut the Marginal Revenue curve from below. (2) The No-Shutdown conditions must hold: the rm will produce a positive output only if P > Average Variable Cost in the short run 2 Mathematical Footnote: Since Total Revenue is R P Q , Marginal Revenue is the derivative: dR/dQ P + QdP/dQ 3 There is one conceptual difference. Chapter 7 covered the topic of external economies and diseconomies effects upon the rms cost function due to changes in aggregate industry output. Since a monopolist rm is the entire industry, what would have been external effects in a competitive industry are all internalized into its cost function. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8.1 THE MONOPOLISTS PROFIT-MAXIMIZING OPTIMUM 225 and if P > Average Cost in the long run. (Henceforth in the chapter, unless indicated otherwise these conditions are assumed to be met.) Converting the denition of the price elasticity of demand in Section 5.2 of Chapter 5 into the notation of this chapter: Q/ Q P /P QP PQ (8.4) Equations (8.1) and (8.4) lead to an expression connecting Marginal Revenue MR and the price elasticity :4 MR P (1 + 1/) (8.5) Since elasticity is ordinarily negative, we see again that Marginal Revenue is less than Price. Recall from Chapter 5 that elasticity generally varies along the demand curve. In fact, elasticity is innite ( = ) where any demand curve intercepts the vertical axis, and elasticity equals zero ( = 0) at its intercept with the horizontal axis. Chapter 5 noted that, when demand is elastic ( < 1), lower price is associated with higher Revenue R P Q . The reverse holds when demand is inelastic. So for levels of output at which demand is elastic, increased output leads to lower price but nevertheless to increased revenue for the rm: Marginal Revenue is positive.5 And similarly, when demand is inelastic, Marginal Revenue is negative. But since Marginal Cost is never negative, and since Marginal Cost must equal Marginal Revenue at the monopolists price-quantity optimum, the monopolist will never produce in the region of inelastic demand. PROPOSITION 8.1: A prot-maximizing monopoly rm always chooses a price- quantity solution in the range of elastic demand along the market demand curve. Another useful theorem is: PROPOSITION 8.2: Given any linear demand curve P = A BQ, Marginal Revenue is MR = A 2BQ. (So the MR curve starts at the vertical intercept of the demand curve on the P-axis and then falls twice as fast as the demand curve.)6 COROLLARY: If the demand curve is a straight line, the Marginal Revenue curve bisects the horizontal distance between the vertical axis and the demand curve. 4 Mathematical Footnote: To derive equation (8.5), start with (8.1) and divide both sides by P: MR Q 1+ P P P Q 5 6 Notice that the last term on the right is the reciprocal of the elasticity in equation (8.4). Substituting and rearranging leads to equation (8.5). In equation (8.5), elastic demand means that the absolute value of exceeds 1, so the negative 1/ term within parentheses will be between 0 and 1, leaving Marginal Revenue positive. In the linear demand equation P = A BQ, the slope of the curve equals B. Substituting on the right hand side of equation (8.3): MR P + Q P / Q = ( A BQ) + Q ( B ) = A 2BQ P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 226 8. MONOPOLIES, CARTELS, AND NETWORKS EXERCISE 8.1 A monopolist faces the demand curve P = 10 Q. (a) What is the equation for Marginal Revenue? (b) If Marginal Cost is MC = 1 + Q, what are the protmaximizing price and quantity? (c) What is the elasticity of demand at this solution? A N S W E R : (a) The demand curve is a straight line. So, from Proposition 8.2, MR = 10 2 Q. (b) Setting MC = 1 + Q equal to MR = 10 2 Q, the solution is Q = 3, P = 7. (c) The slope of the demand curve is P / Q = 1, so from (8.4) the elasticity of demand at the monopolists optimal output is: P Q Q7 7 = (1) = P 3 3 Since < 1, demand is in the elastic range at the monopolists optimum output. Monopoly versus Competitive Solutions Table 8.1, in comparison with Table 6.1 of Chapter 6, illustrates the differences between the monopolistic and competitive solutions. Suppose there are 100 competitive rms, so that Q 100q . If so, the cost data of the two tables correspond. (The Marginal Cost used here is the exact Marginal Cost of Table 6.1.)7 On the revenue side, instead of the assumed P = 60 facing the competitive rm of Table 6.1, in Table 8.1 price declines with output: P = 132 8( Q /100) = 132 0.08 Q . In accordance with Proposition 8.2 the monopolists Marginal Revenue is MR = 132 0.16 Q . Table 6.1 indicated that each competitive rm, setting MC = P , would produce q = 9 when P = 60. So the industry output would be Q = 900.8 (Notice that Q = 900 in Table 8.1 implies that P = 60, so the data in the two tables are consistent.) The monopolist could, of course, also set MC = P and produce Q = 900. But to maximize prot it would set MC = MR instead. In Table 8.1, this equality occurs at Q = 700, where MC = MR = 20. The result is a higher price, P = 76. The monopolists Total Revenue is 53,200 and Total Cost is 26,800, so the maximized prot is = 26,400. The last column of Table 8.1 shows the demand elasticity at various levels of output, computed using equation (8.5). At the monopoly optimum Q = 700, demand is elastic: = 1.36 (as is consistent with Proposition 8.1 above). But for the competitive industry, at the equilibrium Q = 900 the elasticity is = 0.83. So the competitive industry output would be in the inelastic range of demand. In other words, a competitive industry produces too much for its own good! (But, of course, the consumers benet thereby.) PROPOSITION 8.3: The monopoly output solution occurs where Marginal Cost = Marginal Revenue. Since competitive rms produce where Marginal Cost = Price, and since Marginal Revenue < Price, a monopolized industry charges a higher price and produces a smaller output than a competitive industry with the same cost and demand functions. 7 Mathematical Footnote : In this verication the lower-case symbols refer to a single small rm and the upper-case symbols to the monopolist. Since the single large rm corresponds to 100 small rms, from the chain rule of calculus: MC dC dc dq dC 100 mc 1/100 mc dQ dc dq dQ 8 Setting aside possible external economies or diseconomies that might impact upon the rms cost functions and thereby affect the industry supply curve. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8.1 THE MONOPOLISTS PROFIT-MAXIMIZING OPTIMUM 227 Table 8.1 Hypothetical revenue and cost functions: monopolist ( P = 132 8 Q/100; C = 100 [128 + 69 Q/100 14( Q/100)2 + ( Q/100)3 ]) Q 0 100 200 300 400 500 600 700 800 900 1,000 P 132 124 116 108 100 92 84 76 68 60 52 R 0 12,400 23,200 32,400 40,000 46,000 50,400 53,200 54,400 54,000 52,000 MR 132 116 100 84 68 52 36 20 4 12 28 C 12,800 18,400 21,800 23,600 24,400 24,800 25,400 26,800 29,600 34,400 41,800 MC (exact ) 69 44 25 12 5 4 9 20 37 60 89 15.5 7.25 4.5 3.125 2.3 1.75 1.36 1.06 0.83 0.65 Last, one important qualication. Earlier on, this chapter distinguished between monopolies created by government license or franchise and natural monopolies arising from ability to produce at low cost. The governmentally protected monopolist need not fear entry of competitors, but may be subject to regulation (as will be discussed later in the chapter). On the other hand, a monopolist lacking government protection is limited by the threat posed by potential competitors. In particular, a monopolist that wants to deter entry cannot set a price higher than the minimum Average Cost of the lowestcost potential entrant. So the threat of entry may prevent a monopolist from achieving the solution Marginal Cost = Marginal Revenue that would otherwise maximize its prot. EXAMPLE 8.1 POTENTIAL ENTRY IN MONOPOLY AIRLINE MARKETS Margaret A. Peteraf and Randal Reed studied air fares in monopoly markets, that is, in city-pairs served by only one airline.a There were 345 such city-pairs in 1984. For these routes the average fare, excluding rst class, was $0.213 per mile. In studying the effects of potential entry in each market, the authors allowed for several additional inuences upon fares, such as length of trip, city populations at each end, and per capita incomes. They found that prices were indeed inuenced by potential competitors, dened as airlines already serving at least one endpoint of the route. Their results indicated that, in any given market, a 10% reduction in the average cost per seat-mile of the lowest-cost potential entrant would reduce the monopoly fare by about 2%. The authors suggested that the effect was even stronger than these data indicate, since very large airlines serving many locations tended to be disproportionately represented as the lowest-cost alternative. For example, although overall United Airlines does not have particularly low costs, it was the lowest-cost alternative carrier in 53% of the observations. Monopolists facing competition from low-cost carriers such as People Express and Southwest Airlines charged lower fares than did airlines whose primary competition was United Airlines. a Margaret A. Peteraf and Randal Reed, Pricing and Performance in Monopoly Airline Markets, The Journal of Law and Economics, v. 37 (April 1994). P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 228 8. MONOPOLIES, CARTELS, AND NETWORKS $ C Publisher's optimum R P Dollars RP =0.9 R Author's optimum RA =0.1 R A 0 Q P Q A Q Output Figure 8.3. Author versus Publisher Total Revenue from customers is shown by the R curve. Of this revenue, 10% goes to the author ( R A curve) and 90% to the publisher ( R P curve). Output Q maximizes the authors royalty income. The A publishers maximum prot occurs at output Q , where the distance between the R P curve and P P the Total Cost curve C is at a maximum. The publisher prefers a smaller output (wants to set a higher price) than the author. An Application: Author versus Publisher Book prices are usually set by the publisher. But authors can negotiate with publishers over the retail price. As between author and publisher, which would prefer a lower price for the book? Suppose authors royalties are a straight percentage of the publishers revenues from sales of the book, say 10%. Since normally only one rm publishes any title, this is a monopoly situation. R P Q represents the consumer spending on the book, so (as illustrated in Figure 8.3) the authors revenue is R A 0.1 R and the publishers revenue after payment of royalties is R P 0.9 R . The publishers prot-maximizing output Q P occurs where the slope along RP equals the slope along the Total Cost curve C; the maximized prot at that output is indicated by the height of the upper bold line-segment in the diagram. The publishers preferred output, however, is not ideal for the author. Since the author incurs no cost of production, her preferred output is Q A , where RA is greatest. That is, the author prefers the price that maximizes Revenue without regard to production cost. The largest possible royalty income for the author is shown by the lower bold line-segment . So A the publisher prefers a higher price (implying fewer books sold) than the author does. EXERCISE 8.2 The demand function for a certain text is given by P = 20 0.0002 Q and the publishers Marginal Cost is MC = 6 + 0.00168 Q. The authors royalty is 20% of Total Revenue. What is the publishers preferred price-quantity solution? The authors? P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8.1 THE MONOPOLISTS PROFIT-MAXIMIZING OPTIMUM 229 A N S W E R : The publisher wants to set MRP = 0.8 MR equal to Marginal Cost. Since MR = 20 0.0004 Q, eight-tenths of this is MRP = 16 0.00032Q. Setting MC = MRP , the publishers optimum is Q = 5000, P = $19. The author wants to maximize royalty income, which requires that MR = 20 0.0004 Q = 0. The authors optimum is Q = 50,000, P = $10. Note the huge difference between the two solutions. Now consider a more difcult problem: Given that the publisher sets the price of the book, what royalty rate would the author want? Let signify the authors percentage royalty, rate. Then the author would want to maximize R A R P Q . The publisher wants to maximize R P (1 ) R (1 ) P Q . To nd her ideal royalty rate , the author must recognize that the publisher will take this into account in choosing the output (number of copies of the book). This two-level optimization is rather tricky.9 Rather than develop the equations involved, a specic illustration will be instructive. EXERCISE 8.3 Using the data of the preceding Exercise, instead of the xed 20% royalty, suppose the author can set the royalty rate . (a) What is her best , and what are the implications for quantity produced Q, for price P, and for the receipts accruing to author and publisher? (b) Same question, if the publisher can choose . A N S W E R : (a) Using calculus, the best royalty rate for the author is around 36.9%.10 The publisher will take that royalty rate into account in setting MC = MR P (1 )MR. At its prot-maximizing optimum the publisher would produce Q = 3,428 copies of the book, priced at $19.31. Total consumer spending P Q on the book will therefore be around $66,195 of which $24,426 goes to the author and $41,769 to the publisher. From this the publishers production costs must be deducted. Total Variable Costs, obtained by aggregating the Marginal Cost function from q = 0 to q = 3, 428, come to $30,439.11 So, even before allowing for any xed cost, the prot to the publisher is only $11,330. (b) The publisher would enjoy the highest prots if the royalty rate were zero, or if = 0. He then simply sets Marginal Cost equal to Marginal Revenue. This leads to the solution P = $18.65, Q = 6,731, R = $125,555, C = $78,439, and = $47,115. In the preceding exercise, the publishers maximized prot was $47,115 in the absence of royalties but fell to only $11,330 when the author set her preferred royalty 9 10 11 It represents an instance of the Stackelberg solution, discussed in Chapter 10. Mathematical Footnote : The author wants to choose the that maximizes R A PQ, knowing that the publisher will set MC = MR P in choosing output Q . We can solve MC = MR P (1 ) MR to express Q in terms of . In the demand function, P is a function of Q and so can also be expressed in terms of . So PQ reduces to a function of . Taking the derivative and setting equal to zero gives the optimal = 36.9%. Mathematical Footnote : This result can be obtained by integrating the Marginal Cost function: 3,428 0 (6 + 0.00168 Q ) dQ Or, since the Marginal Cost function is a straight line, it could be found geometrically as the area of the trapezoid under the MC curve between Q = 0 and Q = 3,428. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 230 8. MONOPOLIES, CARTELS, AND NETWORKS rate a difference of $35,785. At this ideal royalty rate her receipts were $24,426. Now suppose the publisher proposes a lump-sum payment as an alternative to a royalty. Shifting to zero royalty would mean a loss of $24,426 for the author while the publisher gains $35,785. So the publisher could offer a lump-sum payment somewhere between these two gures, and both parties would be better off. In the negotiations between author and publisher the royalty rate would generally end up somewhere between zero and the percent the author would ideally prefer. But the same principle applies: whatever royalty rate is set, both parties could do better if the publisher made an appropriate lump-sum payment instead. Nineteenth-century authors such as Charles Dickens and Anthony Trollope usually sold their manuscripts to publishers for xed sums. Nowadays, however, the most common arrangement is a straight percentage royalty, or a combination of a lump-sum payment and a percentage royalty. Why? The probable explanation relates to differences in the information available to the parties. An author who is optimistic about prospective sales will tend to prefer a percentage, whereas an author who is pessimistic would take the lump-sum instead. If the author proposes a lump-sum payment, therefore, the publisher might suspect that the author has reason to believe the book will not be a big seller. Conversely, a publisher who is optimistic will favor a lump sum, leading the author to the suspect that a percentage royalty might be a better deal for her! Another factor involved is risk. Under the lump-sum payment, the publisher bears all the risk. In contrast, a royalty is like a share-cropping arrangement for dividing the risk, as will be discussed when risk is taken up in later chapters. Government agencies drawing tax revenues from racetrack betting are in some respects like authors seeking royalty income. Just as an author disregards the publishers costs of production, a taxing agency bears none of the costs of running horse races. There is, however, one big difference: an author is not usually in a position to dictate the royalty rate, whereas the state generally can dictate the tax rate. EXAMPLE 8.2 RACETRACK BETTING Racetrack betting is an important source of tax income for several states in the United States. Of the total amount wagered by bettors (the handle), a fraction (the takeout) is withdrawn from the pari-mutuel pool and not paid out in winnings. The takeout percentage can be regarded as the price paid for the privilege of wagering. This takeout is divided between taxes paid to the government and revenues for the racing industry (payments to the track management, horse owners, etc.) Another source of receipts, breakage, is usually computed by rounding down winnings to the next lower 10 cents. If the pari-mutuel odds would have paid off $5.18 on a winning $2.00 bet, it is presumed that the bettor does not want to bother with the extra 8 cents. So the state kindly retains the odd amounts. For simplicity, breakage can be considered part of the takeout. In accordance with the analysis in the text, since the state incurs no costs of production it would prefer that the track charge prices that maximize revenue (that set MR = 0). And since it can dictate that the track do so, a state that seeks to maximize its revenues should x the takeout percentage where the demand for wagering has an elasticity = 1. The track management, in contrast, would prefer somewhat higher prices so that demand is in the elastic range. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8.2 MONOPOLY AND ECONOMIC EFFICIENCY 231 A 1982 study by W. Douglas Morgan and Jon David Vasche found the demand elasticity at California tracks to be in the elastic range, = 1.3, suggesting that the takeout percentage was too high for the taxing authority though possibly just right for the racetrack rms.a In recent years parimutuel wagering has been declining, probably owing to growing competition from other forms of entertainment. Increasing competition would be expected to lower total demand while raising demand elasticity. A 1992 study by Richard Thalheimer and Mukhtar M. Ali indicated that elasticity of demand has indeed been rising.b For the Louisville Downs racetrack specically, they found a demand elasticity of = 1.88 for the year 1987. COMMENT One ought not simply assume that the governments sole goal is to maximize revenues. Political decision-makers must balance between having more tax revenue, keeping the tracks protable, and pleasing bettors. In the recent period of declining demand, it appears that the racetrack rms have exerted increasing inuence on government decisions. a W. Douglas Morgan and Jon David Vasche, A Note on the Elasticity of Demand for Wagering, Applied Economics, v. 14 (1982). b Richard Thalheimer and Mukhtar M. Ali Demand for Parimutuel Horse Race Wagering with Special Reference to Telephone Betting, Applied Economics, v. 24 (1992). An Application: Monopolist with Competitive Fringe Sometimes a single large rm in an industry coexists with many small rms (the fringe). Currently, Intel is the dominant producer of computer chips, though it shares the market with other relatively small chip manufacturers at home and abroad. Although such a large rm is not a sole seller in its industry and thus is not technically a monopolist, it cannot disregard the effect of its own output upon product price P. Therefore, it acts as a price maker, setting output where MC = MR. Each of the small fringe rms is in contrast a price taker, setting its output where MC = P. The question is, how do these decisions interact to determine the equilibrium of the industry? The solution is easier to see geometrically than to spell out in words. In Figure 8.4, before choosing its output the large rm must consider how much output its fringe competitors will produce at each price. Its effective demand curve D is therefore found by horizontally subtracting the supply curve S F of the fringe rms from the overall market demand D. Associated with the D curve is the large rms effective Marginal Revenue curve MR . The prot-maximizing solution sets MC = MR to determine the large rms optimal output Q . The prot-maximizing price P is determined along D for output Q . At that price, Q F is the quantity supplied by the fringe rms. The overall amount provided to the market is Q , the horizontal sum of Q and Q F . As a check, the summed quantity Q is the overall amount demanded by consumers at price P along the original demand curve D. 8.2 MONOPOLY AND ECONOMIC EFFICIENCY Monopoly, as compared to perfect competition, leads to higher prices and lower output. This makes consumers worse off, but owners of the monopoly rm better off. The P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 232 8. MONOPOLIES, CARTELS, AND NETWORKS $/Q SF DollarsperUnitQuantity P MC D D MR 0 QF Q Q Q Output Figure 8.4. Monopolist with Competitive Fringe D is the overall market demand curve. After horizontally subtracting the supply curve S F of the pricetaking fringe rms, the large rm has an effective demand curve D and Marginal Revenue curve MR . Setting Marginal Cost MC equal to MR leads to the large rms optimal output Q . The corresponding fringe output is Q F . Industry output is Q = Q + Q F . Price P can be found along the D curve at output Q or along the D curve at output Q . concept of efciency loss that is, the net change in Consumer Surplus and Producer Surplus introduced in the previous chapter provides a way of balancing the gains to some against the losses to others. In Figure 8.5, a competitive industry with supply curve S would produce at Qc , Pc where the supply and demand curves cross. Now suppose the industry is monopolized (without any changes in costs of production). The competitive supply curve S then becomes the Marginal Cost curve of the single large rm.12 The monopolist chooses the level of output where Marginal Cost = Marginal Revenue, selling the amount Qm at price Pm . The shaded area in Figure 8.5 is the difference Pm Pc multiplied by the monopoly output Qm . This area was part of Consumer Surplus under competition and is now captured by the monopolist as Producer Surplus; it is a transfer between Consumer Surplus and Producer Surplus, not an efciency loss. The monopoly solution, however, also involves reduced levels of production and exchange, which do entail an efciency loss. The lost Consumer Surplus is the upper dotted triangle in the diagram; the lost Producer Surplus is the lower dotted triangle. Overall, consumers lose both the shaded rectangle (transfer) and the upper dotted triangle (efciency loss). The monopolist 12 As explained in an earlier footnote, any external economies or diseconomies are already incorporated within the monopolists Marginal Cost curve. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8.2 MONOPOLY AND ECONOMIC EFFICIENCY 233 $/Q Figure 8.5. Monopoly and Efciency Loss If there are no productive losses or gains from organizing the industry into a single large rm, the supply curve S of the competitive industry is identical with the Marginal Cost curve MC of the monopolist. The competitive equilibrium is at price Pc and quantity Q c ; the monopoly optimum is at the higher price Pm and smaller quantity Q m . In comparison with the competitive outcome, the shaded area is a transfer from consumers to the monopolist (equal to the price difference times the quantity still produced). The upper dotted area is the loss of Consumer Surplus due to the reduction in quantity produced. The lower dotted area is the corresponding loss of Producer Surplus. A Transfer DollarsperUnitQuantity F G H MR B 0 Qm Qc MC or S Pm Pc E Lost Consumer Surplus D Lost Producer Surplus Q Output gains the shaded rectangle (transfer) but loses the lower dotted triangle (efciency loss). Canceling out the transfer, the net efciency loss is the dotted area. CONCLUSION In comparison with the competitive outcome, monopoly involves a transfer from consumers to suppliers. There is also an efciency loss, the sum of the reductions in Consumer Surplus and Producer Surplus due to reduced trade.13 EXERCISE 8.4 Use the data of Exercise 8.1, and assume that the supply curve S under perfect competition would be the same as the monopolists given Marginal Cost curve. Find (a) the competitive price-quantity solution and the associated Consumer Surplus and Producer Surplus; (b) the monopoly price-quantity solution and the Consumer Surplus and Producer Surplus under monopoly; (c) the efciency loss. A N S W E R : (a) Using the demand equation P = 10 Q and supply equation P = 1 + Q, the competitive solution is Q = 4.5, P = 5.5. Referring back to Figure 8.5,14 Consumer Surplus is the area of the right triangle APc E, which is numerically (10 5.5) 4.5/2 = 10.125. Producer Surplus is the area of the right triangle (5.5 1) 4.5/2, also equal to 10.125. (b) The monopoly solution was given in Exercise 8.1 as Q = 3, P = 7. In Figure 8.5, Consumer Surplus is the triangular area APm F, or numerically the monopoly output times half the distance APm , or 3 1/2(10 7) = 4.5. Producer Surplus is the area BHFPm (a trapezoid in terms of the equations, though only approximately so as drawn in the diagram). The area of the trapezoid is the monopoly output times the average of the vertical distances BPm and FH, or numerically 3 1/2[(7 1) + (7 4)] = 13.5. (c) Since the sum of Consumer Surplus and Producer Surplus has fallen from 20.25 to 18, the overall efciency loss is 2.25. 13 14 One cannot, however, therefore conclude that monopoly should be abolished. (Any more than one could conclude from the analysis in Chapter 7 that taxes, which also reduce Consumer Surplus and Producer Surplus, should be abolished.) Other considerations need to be balanced against the efciency loss. The pictured supply and demand curves are not linear, however, and so do not exactly match the specic equations used here. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 234 8. MONOPOLIES, CARTELS, AND NETWORKS An additional inefciency may arise because of the costs incurred in getting or keeping the monopoly privilege. (A process called rent-seeking, to be discussed further in Chapter 16.) If monopoly prots are $5,000 per day, the monopolist would be willing to spend up to $5,000 per day to acquire and retain the monopoly position. Geometrically in Figure 8.5, to maintain a monopoly the rm would, if necessary, spend any amount up to the value of the Producer Surplus, area BHFPm . The extent to which rent-seeking costs of contending for the monopoly are an efciency loss depends upon the nature of the contest. Suppose the monopoly privilege is simply auctioned off by the government. Then, since running an auction consumes little in the way of resources, the additional efciency loss can be negligible. (The amount the winning bidder pays is a transfer to the government, not a net loss to society.) Cable TV franchises are usually awarded in this way: local governments offer an exclusive franchise to whichever cable company makes the most attractive bid. Sometimes, however, the struggle for a monopoly is very costly. Chicago-style gang wars were attempts to gain monopolies over bootlegging and other criminal activities a destructive activity for all concerned. Less picturesque, entirely lawful, but still often quite expensive, are contests in which a government agency awards prizes at its discretion. The Federal Communications Commission awards broadcasting channels, the Patent Ofce grants patents, and so on. The proceedings typically involve elaborate documentary submissions, hearings at which expensive lawyers and consultants plead their cases, and perhaps large costs secretly incurred to bring political pressures to bear. What if a government ofcial simply awards the monopoly to whoever offers the highest bribe? This is like an auction, so there would or no efciency loss! Only a transfer is involved, in this case going to the private purse of the corrupt ofcial. Note that illegal or immoral methods may involve an efciency loss (gang war) or may not (bribery), just as legal and moral methods may or may not. 8.3 REGULATION OF MONOPOLY Monopoly, as has been seen, can lead to economic inefciency. In addition, excessive monopoly prots are commonly regarded as unfair to consumers. Policies for dealing with monopoly range from laissez faire at one extreme to trust-busting at the other. Monopolies are sometimes owned by government agencies. Railroads and telephone service, for example, are often government monopolies in Europe. This section discusses a different policy: government regulation of the monopolys price, quantity, or quality of service. In the United States privately owned public utilities such as electric power and water, usually thought to be natural monopolies, are commonly regulated. Regulation usually aims to limit the monopolist to a normal accounting prot, just adequate to attract the needed capital and other resources into the business. Normal prot in the accounting sense corresponds to zero economic prot, as explained in Chapter 6. And, as we saw in the preceding chapter, zero economic prot characterizes long-run equilibrium. So, in a sense, regulation aims at achieving the same result that would have occurred had competition been possible. Figure 8.6 shows a monopoly rm with rising Average Cost and Marginal Cost curves. The diagram repeats the monopoly solution Pm , Q m and the competitive solution Pc , Q c seen earlier. It also shows also a zero-prot regulatory solution Pz , Q z . Zero economic prot is equivalent to setting a price and associated output (determined along the consumers demand curve) such that Average Cost = Average Revenue. In the P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8.3 REGULATION OF MONOPOLY 235 $/Q Figure 8.6. Regulation of Monopoly: Increasing Cost The regulatory solution, xing price so that the monopolist receives zero economic prot, is the priceoutput combination Pz , Q z where the Average Cost AC and Average Revenue AR curves intersect. If this occurs in the range where AC rises, regulated output Q z will be even greater than the competitive equilibrium output Q c . In comparison with the competitive solution, the lightly shaded rectangle is a transfer from suppliers to consumers. The dotted area GHK is an efciency loss due to excessive output. This negative Producer Surplus is larger than the heavily shaded area showing the gain of Consumer Surplus. Thus, overall the output increment Q z Q c is inefcient. MC H Dollars Pm Pc Pz G K AC D AR MR E 0 L Qz Qm Output Qc Q situation pictured the unregulated monopoly solution has as compared to the efcient competitive outcome too small an output and too high a price. But the regulatory correction overshoots the competitive ideal. The requirement that output be set where Average Cost = Average Revenue means that output in the industry is too great and price too low! Output can be excessive because resources have alternative uses. As described earlier, an efcient outcome maximizes the sum of Consumer Surplus and Producer Surplus. At the competitive output Qc in Figure 8.6, Consumer Surplus is the triangular area below the demand curve and above price Pc ; Producer Surplus is the corresponding area above the MC curve and below price Pc . But for units between Qc and the assumed regulatory output Qz , MC lies above the demand curve. So this range of output involves an efciency loss: the cost of providing the additional units is greater than their value to buyers. Geometrically, when output rises from Qc to Qz the cost incurred on the additional output is EGHL the area under MC between Qc and Qz . The benet to consumers is only EGKL the area under the demand curve. So the dotted area represents a net efciency loss in comparison with the competitive ideal. Usually, however, one wants to compare regulated monopoly with unregulated monopoly, which also falls short of the ideal. This comparison is indeterminate. The unregulated monopoly produces too little, the regulated monopoly produces too much, and without more specic information it cannot be said which is the more efcient. The analysis so far has dealt with a monopoly whose Average Cost curve AC was rising throughout the relevant range. Consider next a natural monopoly, where the Average Cost curve AC is falling (as in Figure 8.7). (Average Cost cannot fall forever, since that would violate the Law of Diminishing Returns, but may decline throughout the range of practical interest. If all rms have the same cost function, the rm producing the most would have lowest Average Cost. So ultimately only one rm is likely to survive.)15 15 A falling Average Cost curve does not, strictly speaking, correspond to natural monopoly. A natural monopoly occurs when a single rm can produce any output at lower Average Cost AC than its competitors. A rms Average Cost curve may fall throughout and still leave that rm with costs higher than its competitors. Or Average Cost may be rising and yet the rms Average Costs could remain lower than its competitors costs. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 236 8. MONOPOLIES, CARTELS, AND NETWORKS $/Q DollarsperUnitQuantity D = AR Pm Pz Pc AC MC MR 0 Qm Qz Qc Q Output Figure 8.7. Regulation of Monopoly: Decreasing Cost The regulatory solution (zero economic prot) occurs at Pz , Q z where Average Cost AC equals Average Revenue AR. If this occurs in the range where Average Cost is falling, the regulated output Q z is greater than the prot-maximizing monopoly output Q m but is less than the ideally efcient output Q c where Marginal Cost MC = AR. In comparison with the efcient outcome, the dotted areas represent losses of Consumer Surplus and Producer Surplus due to insufcient output. Since in Figure 8.7 Average Cost AC falls throughout, Marginal Cost MC always lies below it (Proposition 2.2a of Chapter 2). It follows that, as shown in the diagram, the regulatory solution where AC = AR (at output Qz and price Pz ) lies between the monopoly solution (output Qm and price Pm ) and the competitive solution (output Qc and price Pc ). So when Average Cost falls throughout, the regulatory solution improves over the unregulated monopoly: it comes closer to the competitive ideal. The dotted roughly triangular area shows the efciency loss that remains, owing to a regulated output that is still too small. As shown in Figure 8.5, the competitive solution at Qc maximizes the sum of Consumer Surplus and Producer Surplus. But notice that, in Figure 8.7, at Qc Marginal Cost lies below Average Cost. So Average Cost exceeds price violating the longrun No-Shutdown Condition! From an efciency point of view, it is indeed better to have the utility produce the larger output despite any nancial loss.16 In principle, the loss could be covered by a lump-sum transfer of funds to the rm, from customers or from the government, that would leave Producer Surplus and Consumer Surplus unaffected.17 16 17 The justication is as follows. The regulatory solution sets Average Cost = Price Average Revenue, so this is a breakeven situation. Nevertheless, efciency calls for output to increase from Qz to Qc . In the region between Qz and Qc , the demand price (Marginal Value) always exceeds Marginal Cost. The amount consumers are willing to pay for the additional units exceeds the cost of providing those units. Where would the money come from? Perhaps from a government subsidy. Or the consumers themselves may be willing to pay lump-sum fees up front, to allow the rm to remain in business while still charging efcient low prices. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8.3 REGULATION OF MONOPOLY 237 To prevent entry of competitors, the rm must charge a price below the minimum Average Cost of the lowest-cost potential entrant. That remains true even for a natural monopoly with falling Average Cost curve, as in Figure 8.7. Though only a single rm can ultimately survive in the industry, different rms may compete to be the single supplier. Such situations are described as competition for the eld instead of competition in the eld.18 EXAMPLE 8.3 LONG-DISTANCE TELEPHONE SERVICE a A 1982 consent decree between the American Telephone and Telegraph Co. (AT&T) and the U.S. Department of Justice ended AT&Ts effective monopoly of longdistance telephone service in the United States. AT&T had beneted from regulatory decisions of the Federal Communications Commission (FCC) that let it erect barriers against potential entrants. The most important barrier was AT&Ts refusal to allow new entrants to interconnect with AT&Ts huge network of customer lines. If only this barrier could be overcome, rms could prot from entry. The potential prots largely arose from the formula employed for dividing long-distance revenues between the local companies at each end and AT&Ts Long Lines Division; the formula strongly favored the local companies. Though this formula was imposed by local regulators, AT&T had not historically opposed it, rst, because AT&T itself owned many of the local operating companies, and second, because the cross-subsidization generated political support from these local companies for AT&T. But the articially high long-distance rates were very attractive to potential outside competitors. In the 1982 consent decree AT&T divested itself of ownership in the local service companies in order to concentrate on the long-distance market. By eliminating the burden of cross-subsidization, the divestment helped AT&T meet the competition from MCI, Sprint, and other new long-distance providers. In addition, however, AT&T accepted restrictions designed to protect the new entrants from being driven out of business. Since the consent decree became effective in 1984, the long-distance market has become more competitive. AT&T faced competition from other long-distance companies (primarily MCI and Sprint) and from large regional phone companies (primarily Qwest, SBC, and Verizon) that had been freed by regulators to offer long-distance service. In addition, numerous resellers act as wholesalers between these rms and the consumers. AT&Ts share of interstate minutes declined from about 84% in 1984 to about 31% in 2002; the average price for long distance service fell by 43% between those dates.b Faced with such pressures, in 2004 AT&T announced that it is withdrawing from the consumer market for long-distance service. a This discussion is based in part on Giles H. Burgess, Jr., The Economics of Regulation and Antitrust (1995), on Roger G. Noll and Bruce M. Owen, The Anticompetitive Uses of Regulation: United States v. AT&T (1982) in John Kwoka and L. White, eds., The Antitrust Revolution: The Role of Economics (1994), and on Nicholas Economides, The Telecommunications Act of 1996 and Its Impact, Japan and the World Economy, v. 11 (1999). b Economides, pp. 459460, and Federal Communications Commission, Statistics of the Long Distance Telecommunications Industry, 2003. 18 Harold Demsetz, Why Regulate Utilities? The Journal of Law and Economics, v. 11 (April 1968); William J. Baumol, Contestable Markets: An Uprising in the Theory of Industry Structure, American Economic Review, v. 72 (March 1982). P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 238 8. MONOPOLIES, CARTELS, AND NETWORKS CONCLUSION If the Average Cost curve is rising in the relevant range, the regulatory zero-prot solution increases output beyond the monopolists prot-maximizing solution. Such regulation is inefcient, leading to output that is too large in comparison with the monopolists too small output. With a falling Average Cost curve, on the other hand, the regulatory zero-prot solution increases output insufciently. The supposed inefciency of monopoly may be exaggerated, however. The pressure of outsiders anxious to enter the industry limits the monopolists ability to exploit consumers. There is a further problem with regulation, not visible in Figures 8.6 and 8.7. Regulated rms may have little incentive to reduce costs. Indeed, if regulators always maintained the zero-prot condition Average Cost = Price, the rms costs would not affect its prots. Any cost reduction would lead the regulator to lower the allowable price, with no gain for the rm. In practice, regulatory lag somewhat remedies the situation. When costs rise or fall, some time passes before the regulators adjust prices. So the regulated rm does not entirely lack incentive to reduce costs, though the incentive is weakened. 8.4 MONOPOLISTIC PRICE DISCRIMINATION Until now it has been assumed that the monopolist quotes a single price. Sometimes a rm may use more complex discriminatory pricing schemes. A monopolist may divide the market, offering different prices to different classes of buyers (market segmentation). Or, for any given buyer, the monopolist may offer quantity discounts or in other ways charge different prices in accordance with the quantities purchased (block pricing). In the extreme a different price might be charged to each consumer for each unit taken; this is called perfect price discrimination.19 Market Segmentation Suppose the monopolist divides the customers into two or more segments. Japanese auto manufacturers have been accused, for example, of dumping charging lower prices for their cars abroad than in Japan. For market segmentation to work, the monopolist must control possible leakage between segments. If cars are priced at $25,000 in Japan and $20,000 in the United States, and if shipping costs are less than $5,000 per car, Americans could ship their $20,000 cars back to Japan and sell them for $25,000. So any price difference in excess of the shipping cost would tend to disappear.20 Dumping can be protable because demand is generally more elastic in the competitive world market than in the home market. Figure 8.8 pictures a manufacturer who can charge separate prices P1 and P2 in markets 1 and 2. To maximize prot, the rm must equate the respective Marginal Revenues mr1 and mr2 . (If not, prot could be increased by withdrawing some units from the market segment with low Marginal Revenue and selling them in the segment with high Marginal Revenue.) Furthermore, the rm will 19 20 Price discrimination cannot exist under perfect competition. No consumer would pay more than the marketdetermined competitive price, and no rm would sell for less. Even with some leakage, the monopolist could prot from market segmentation. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8.4 MONOPOLISTIC PRICE DISCRIMINATION 239 $/Q P2 d2 MC Price P1 S d1 T U W mr mr 2 mr 1 q 1 q 2 Q 0 Q FirmOutputandSegmentSalesQuantities Figure 8.8. Market Segmentation The market consists of two segments with independent demand curves d1 and d2 ; the corresponding Marginal Revenue curves are mr 1 and mr 2 . The mr curve is the horizontal sum of these separate Marginal Revenue curves. At the prot-maximizing output Q , MC = MR = mr 1 = mr 2 . Of this total output, q 1 is sold to sector 1 at price P1 and q 2 is sold to sector 2 at price P2 . want to set Marginal Cost equal to mr 1 = mr 2 . These conditions can be expressed: MC = mr 1 = mr 2 Market-Segmentation Optimality Condition21 (8.6) From Equation (8.5), and knowing that mr 1 = mr 2 , it follows that: P1 (1 + 1/1 ) = P2 (1 + 1/2 ) (8.7) So if demand is more elastic in market 1 (in algebraic terms, if |1 | > |2 |), the protmaximizing monopolist will set a lower price in that market. PROPOSITION 8.4: Under market segmentation, the segment with more elastic demand will be charged a lower price. In Figure 8.8 notice the curve mr, the horizontal sum of mr1 and mr2 . Equation (8.6) is satised at the intersection of the rms Marginal Cost curve MC with mr at point W, which determines the optimal total output Q . The optimal quantities q 1 and q 2 for the separate markets can be picked off along the horizontal line from W to the vertical axis. Since Q q 1 + q 2 , the distances ST and SU sum to SW. The associated prices 1 P1 and P2 are found along the respective demand curves d1 and d2 . 21 The technical qualication earlier, that MC must cut MR from below, here takes the following form: MC must cut the horizontal sum of the mr curves (the mr curve in Figure 8.8) from below. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 240 8. MONOPOLIES, CARTELS, AND NETWORKS As instances of market segmentation, movie theaters and buses often offer discounts to the elderly or to children (markets segmented by age). Vacation resorts charge different prices in season and off season, and prices usually vary by time of day at restaurants and movie theaters. Since, however, the costs of serving different classes of customers may differ, not all price variations are necessarily instances of monopolistic price discrimination.22 Dinner prices at restaurants may be higher than lunch prices in part because waiters and other employees may demand premium pay for working in the evening. And retail chains may charge higher prices in high-crime neighborhoods becasue the costs of doing business are greater. Discount coupons offered by supermarkets may also represent market segmentation: they let the store charge lower prices to those people willing to take the trouble of collecting coupons. Customers who are retired or unemployed have more free time, and so may be more able to shop around making them more sensitive to discounts, or in other words making their demand more elastic. It is also sometimes thought that discount coupons are particularly aimed at poorer customers, who presumably have lower demand prices (less willingness to pay). But that does not follow. Market segmentation does not depend on the heights of the demand curves, but upon the demand elasticities. Poorer customers typically do have smaller demands but not necessarily more elastic demands. EXERCISE 8.3 A monopolist has its domestic market protected by law from import competition. Its domestic demand curve is Pd = 120 qd /10. The rm can also export to the more competitive world market, where the price is Pe = 80 independent of its export quantity qe. (So the rm is a price-taker in the world market.) Marginal Cost is MC = 50 + Q/10, where Q qd + qe. (a) Find the rms prot-maximizing total output, and its division between the two markets. (b) Compare the prices and demand elasticities in the domestic market versus the world market. A N S W E R : (a) In accordance with equation (8.6), the rm sets mrd = mre = MC. Since the domestic demand curve, Pd = 120 qd /10, is linear, the corresponding marginal revenue is mrd = 120 qd /5. And since the export demand curve is horizontal, mre = Pe = 80. Equating the Marginal Revenues, 120 qd /5 = 80, which implies a domestic output qd = 200. Setting MC = mre leads to 50 + Q/10 = 80, which implies Q = 300. Since Q = 300 and qd = 200, it follows that the export quantity is qe = 100. (b) In the export market the price Pe = 80 is given. Using the equation for the domestic demand curve, Pd = 120 qd /10, since qd = 200 the price is P d = 100. The export demand curve is horizontal, so demand elasticity in that market is e = . In the domestic market, we can use equation (8.4), = ( Q/ Q)/( P / P ), with quantity qd = 200 and price Pd = 100. The value of Q/ P in the formula is the reciprocal of the slope of domestic demand curve, or 10. Substituting, the domestic demand elasticity is d = (100/200) (10) = 5. As expected, price is higher in the domestic market where demand is less elastic. 22 The differences between on-peak and off-peak prices, as analyzed in Chapter 6, are cost-based rather than discriminatory. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8.4 MONOPOLISTIC PRICE DISCRIMINATION 241 EXAMPLE 8.4 PAPERBACKS VERSUS HARDBACKS In the book trade, typically a new title is introduced rst in hardcover, possibly followed by a paperback edition. The physical form of the book, and the timing as well, segment the two markets. (Though sometimes the two versions are issued simultaneously.) Sofronis K. Clerides, making use of a database representing essentially all the titles published in both hardback and paperback editions by Yale University Press in the period 19701995, asked whether the price difference between the two editions exceeded what could be explained in terms of differences in production costs.a For the books studied, on average the prices were (in 1990 dollars) $39.16 for hardbacks and $17.04 for paperbacks. Marginal Costs were much lower, $2.95 and $1.74, demonstrating that the markets for book titles were much closer to monopoly than to perfect competition. (Of course, substantial xed costs were also incurred in setting up a run of print for each book.) Price discrimination between the two book types can be measured by comparing the differences between price and Marginal Cost (the margins). The table indicates that, in percentage terms, margins were lower on paperbacks. The margin would be expected to be smaller (that is, price should be nearer Marginal Cost) in the market segment with more elastic demand. The author obtained a relatively high elasticity estimate, = 3.9, for the more competitive paperback market, so the low margin in that segment is consistent with expectations. Although it is reasonable to expect lesser elasticity in the hardback market, for that segment the obtained elasticity estimate was too extreme strangely, it was actually in the positive range. (Selection effects may provide the explanation. Presumably, books of anticipated higher-than-average quality had both higher prices and higher sales, leading to a misleading statistical association.) Paperbacks versus hardbacks Hardbacks Price Marginal Cost Price Marginal Cost (= margin) $39.16 2.95 (7.5%) 36.21 (92.5%) Paperbacks $17.04 1.74 (10.2%) 15.30 (89.8%) Source: Adapted from Table 2 in Clerides. a Clerides, Sofronis K. Book Value: Intertemporal Pricing and Quality Discrimination in the U.S. Market for Books, International Journal of Industrial Organization, v. 20 (2002). Block Pricing Whereas in market segmentation the seller charges different prices to different customers, in block pricing the seller charges different prices to a single customer. For example, a 1-pound package of detergent might sell for $1.00 while a 2-pound package sold for $1.50. The seller is charging $1.00 for the rst pound bought and $0.50 for the second pound. Figure 8.9 shows the demand curve of a single consumer. Suppose that without price discrimination the monopolist would charge P for each unit sold. Consumer Surplus P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 242 8. MONOPOLIES, CARTELS, AND NETWORKS $/Q InitialBlock Price P1 SecondBlock Price Price P2 = P d q1 q2 0 B q BlockSalesQuantities q Figure 8.9. Two-Part Pricing The monopolist faces the demand curve d for a typical consumer. P is assumed to be the protmaximizing simple price for a monopolist. The monopolist can do better by charging a higher price P1 on an initial block quantity B and charging P2 = P thereafter. This two-part pricing scheme allows the monopolist to capture the portion of Consumer Surplus represented by the rectangle lying within the shaded area. would equal the entire shaded triangle. The monopolist, however, could charge as much as P1 for the rst block of q1 units sold and then sell an additional q2 units at the lower price P . The monopolist could thereby capture the dark-colored rectangle as revenue, rather than leaving it as Consumer Surplus. The rectangle is thus a transfer from the consumer to the monopolist. The monopolist could not usually do this well. The high initial price reduces the disposable income the consumer could spend on buying additional units. (This is the income effect of a price change discussed in Chapter 4.) So only if the income elasticity of demand for this product is zero will the demand curve for additional units be totally unaffected. (The diagram implicitly makes this assumption.) Block pricing, therefore, cannot capture quite as much additional revenue for the monopolist as suggested in Figure 8.9. Differences among consumers also limit the protability of block pricing. The monopolist would like to use a different block price schedule for each buyer. But this is usually impractical. If the same price schedule is used for all, some consumers may be charged too high a price and others too low a price for maximizing the rms prot. As another practical difculty, block pricing entails higher transaction costs for the seller. Discrimination via block pricing may seem quite common. Electric and water utilities often charge a high price for the rst block consumed in any period, and a lower price thereafter. Utility price schedules often have four or ve blocks, and also market segmentation of different classes of customers. Printing shops and furniture movers also commonly use declining-block prices. Indeed, wherever quantity discounts are encountered, block price discrimination may be suspected. The suspicion, however, is not conclusive. As with market segmentation, observed price differences may reect not discrimination but differences in costs. Electric utilities, for example, incur a lump-sum cost to connect a consumer to the main power line, a P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8.4 MONOPOLISTIC PRICE DISCRIMINATION 243 $/Q P1 P2 Price P3 P4 = P d q1 q2 q3 q4 0 q BlockSalesQuantities q Figure 8.10. Four-Part Pricing The monopolist charges P1 for each of the initial q 1 units bought, P2 for each of the additional q 2 units bought, and so on. This four-part pricing scheme leaves only the shaded area as Consumer Surplus. cost that is essentially independent of electricity consumption. Similarly, a printing job not only consumes paper and ink but requires initial setting of the type. In such cases, charges to consumers should ideally include a lump-sum charge independent of use, plus a variable charge that increases with consumption. It may be more convenient to bill for the lump-sum component by charging an extra-high price on the rst few units taken. So what appears to be discriminatory block pricing may be cost-justied.23 Perfect Discrimination At the logical extreme, perfect price discrimination, the monopolist charges a different price for each successive unit bought by each consumer. Figure 8.10 shows a four-part pricing schedule, an extension of the two-part schedule in Figure 8.9. (As in the previous analysis, the income elasticity of demand is assumed to be zero, so that higher prices paid for earlier units do not affect the consumers willingness to pay for additional units.) Such a block schedule can transfer large portions of the Consumer Surplus to the seller; in Figure 8.10, only the small shaded areas remain as Consumer Surplus. Carried to the limit, with different prices for each successive innitesimal unit, essentially all the Consumer Surplus will be transferred from the buyer to the seller. So a perfectly discriminating monopolist can gain for itself all the advantages of trade. Despite the seeming inequity when the seller captures all the benets from trade, perfect price discrimination is efcient! For the last innitesimal unit purchased by each consumer, the monopolist is charging a price equal to Marginal Cost. Thus, under perfect price discrimination as under perfect competition, the rm sets Marginal Cost equal to the price paid. And since each buyers Marginal Value (demand price) then equals the sellers Marginal Cost of production, there can be no efciency gain from producing either a larger or a smaller output. 23 Cost justication is a legal defense for a pricing practice that might otherwise be unlawful. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 244 $/q 8. MONOPOLIES, CARTELS, AND NETWORKS MC DollarsperUnitQuantity P P d d Figure 8.11. A Firms Incentive to Chisel under a Cartel If the competitive equilibrium price is P o , a pricetaking rm would produce output q o . A cartel can drive price up only by having its members cut back production. If this rms assigned production quota were q , and the cartel raised the price to P , the rms gain from chiseling (increase in prot due to exceeding its quota) would be the shaded area. Note that, at the high price P , the rm would nd it protable to produce output q , which is even greater than its competitive output q o . 0 q Output q q q 8.5 CARTELS A cartel is a group of rms behaving as a collective monopoly. Each rm in a cartel agrees to produce less than it would under unrestrained competition. The aim is of course to raise the price so that all can reap higher prots. Cartels have an Achilles heel. However desirable the arrangement for the rms as a group, it pays any single rm to cheat. For the single rm illustrated in Figure 8.11, in perfect competition d o is its horizontal demand curve at the ruling price P o . Assuming the No-Shutdown Condition is met, under perfect competition the rm maximizes prots by producing output q o where MC = P o . A cartel can raise price over the competitive level only by reducing aggregate industry output for example, by assigning production quotas to each cartel member. Suppose a rm agrees to hold its output down to q , and imagine that the cartel successfully raises price to P . The incentive to chisel is evident. The new demand curve as viewed by the rm is d effectively horizontal, just like the d o curve before cartelization. This means that by charging a slightly lower price, any single rm can get as much business as it desires, taking away sales from others. Even at the old competitive price P o the rm would have liked to produce q o , more than the quota q . (Cartel production quotas must be smaller than what competitive rms would have produced, else the market price could not have risen from P o to P .) Once the cartel has raised price, the incentive to chisel is even greater. At price P the rm would want to sell output q . The additional prot capturable by a chiseler, assuming all the other rms abide by the cartel agreement, is indicated by the shaded area in the diagram. Furthermore a cartel might not include all the producers in the industry. A rm outside the cartel will be essentially in the same position as illustrated in Figure 8.11 except that, not being a member of the cartel at all, by producing at level q it isnt even cheating on an agreement. So if a cartel is ever successful, nonmembers do better than members! This fact makes cartels even less viable. CONCLUSION Cartels can raise prices above the competitive level only by cutting industry output. But at the higher prices, a member rm can prot by covertly producing even more P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8.5 CARTELS 245 than at the competitive equilibrium. Nonmembers can do the same and, since they need not disguise their actions, can gain even more. The added production of members and of nonmembers combine to subvert the cartel. EXERCISE 8.4 Suppose 100 identical rms produce in an initially competitive market. Industry demand is P = 10 Q/200; supply is P = 1 + Q/200. (a) Find the competitive equilibrium price, industry output, and rm output. (b) If the 100 rms formed an effective cartel, what would be the price-quantity solution for maximum aggregate prot? (Assume the industry supply curve is simply the horizontal sum of the rm Marginal Cost curves.) (c) At this price, what production quota would be assigned each rm? How much would each rm like to produce at the price set by the cartel? A N S W E R : (a) Equating supply and demand: 10 Q/200 = 1 + Q/200. The solution is Qo = 900, q o = 9, and P o = 51/2. (b) The demand curve is linear, so Marginal Revenue for the industry (the cartel) has double the slope of the demand curve, or MR = 10 Q/100. Since the industry supply curve corresponds to the horizontal sum of the rms Marginal Cost curves, Marginal Cost for the industry is MC = 1 + Q/200. The prot-maximizing solution for the cartel (where Marginal Revenue = Marginal Cost) is Q = 600, P = 7. (c) To achieve the monopoly price P = 7, the typical rms production must decline from q o = 9 to a quota amount q = 6. But at the monopoly price, each rm would like to set its output where Marginal Cost = P , so that 1 + q/2 = 7. This means that, instead of cutting back to q = 6, each rm wants to expand output to q = 12. In dealing with cartels, the laws of different nations vary considerably. Some countries treat cartel agreements as legally enforceable contracts. Other governments take a neutral position: the cartel agreement is lawful, but the courts will not enforce it. In the United States, with a few exceptions, cartels are outlawed as conspiracies in restraint of trade. To be viable when illegal, a cartel would need to enforce its quotas in ways that are both effective and secret an unlikely combination. Even in the United States, the WebbPomerene Act allows American exporters to form a cartel for dealings in foreign markets. More important, the Federal government has encouraged or even insisted upon the formation of cartels aimed at raising prices of certain agricultural products. EXAMPLE 8.5 PEANUTS As described in Example 2.7 of Chapter 2, starting in the 1930s the U.S. government xed support prices for crops with the aim of helping depressed farmers. The initial intention was to buy surpluses in high-production years and then sell them in years of low production, at little or no net cost to the government. But political pressures kept the support prices so high that surpluses accumulated. The Federal agencies attempted to dispose of undesired inventories by diverting them to secondary markets, most importantly dumping them abroad (at a nancial loss to the taxpayers). These approaches in turn became excessively costly or unfeasible in terms of international diplomacy, so the next step was supply management. Typically, to earn the right to a support price, an industry was required to form a cartel that would limit supply usually, by establishing marketing quotas for each supplier. Of course P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 246 8. MONOPOLIES, CARTELS, AND NETWORKS prices could be maintained above competitive levels only because the force of law ruled out both above-quota production and the entry of nonmember suppliers. Randall R. Rucker and Walter N. Thurman studied how such supply management programs affected the peanut industry.a Peanuts are used for two main purposes: there is an edible market (for direct consumption) and a crush market (for peanut oil, cake, and meal). An important feature of the industry is that there are better substitutes for crush (corn oil, cottonseed oil, canola oil, etc.) than for edible peanuts. From 1949 to 1977 the main supply management technique was acreage allotment: only peanuts grown on allotted acres were eligible for the edible market support price. The governments excess accumulations were diverted mainly into crush, so a huge price gap developed between the two branches of the market. But over this period the per-acre yields on allotted acres tripled, as growers employed fertilizers and more sophisticated farming techniques to increase output from their privileged acres. Once again the government having to buy at the high support price and sell at the unsupported crush price suffered heavy losses. So from 1977 on the government has imposed poundage quotas which quantitatively limit supply on the edible market. A supplier could produce over-quota, but only for sale in the crush market. This last feature increased the political acceptability of the program, since it gave crushers a source of supply that would have disappeared had the U.S. production come to be devoted entirely to the high-price edible market. a Discussion based upon Randal R. Rucker and Walter N. Thurman, The Economic Effects of Supply Controls: The Simple Analytics of the U.S. Peanut Program, Journal of Law and Economics, v. 33 (October 1990), pp. 483516. So some cartel agreements have been supported or even dictated by government agencies. As for the anticartel activities of other branches of government, it is often unclear whether these are well-designed or effective. EXAMPLE 8.6 ANTITRUST AND PRICES The Antitrust Division of the U.S. Department of Justice is responsible for prosecuting cartels illegally xing prices. If antitrust prosecutions are effective, detection of a price-xing conspiracy and indictment of its members should be followed by lower prices. For 25 accused industry cartels indicted between 1970 and 1985, Michael Sproul examined price movements after indictment.a In each case he compared the change in price to change in a closely related industry for example, the price movement of potash (indicted) was compared with nitrogen fertilizers (not indicted). The evidence was mixed. The table indicates that for the period before 1976, prices in most cases rose rather than fell after the indictment. In 1976 the legal penalties for price-xing were increased, but even then prices more frequently rose rather than fell after indictment. Indicted industry cartels price movements after indictment Number of cases Before 1976 After 1976 10 15 Prices rose 7 9 Prices fell 1 1 Unclear or mixed 2 5 Source: Estimated visually from Sproul, Figure 2 (pp. 747748). P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8.5 CARTELS 247 Two explanations come to mind: (1) The government may have been harassing innocent rms, so that prosecutions served only to raise the costs of doing business. Or (2) penalties were insufciently severe to induce the rms to abandon the conspiracy. The second explanation is not well supported by the tabulated data, since the after-1976 period (with its heavier penalties) looks similar to the before-1976 period. However, when the author directly examined the effect of severity of penalties for example, whether jail terms were imposed harsher punishments did seem more likely to lead to price reductions. Overall, the study suggested that, at least so far as effects upon consumers are concerned, many antitrust cases alleging cartel behavior are unjustied. a Michael F. Sproul, Antitrust and Prices, Journal of Political Economy, v. 101 (August 1993). A famous cartel is the Organization of Petroleum Exporting Countries (OPEC). The members of that cartel were and are sovereign governments rather than private rms. Nevertheless, over time its power has generally declined, owing to chiselling and to increased production by nonmembers of OPEC. EXAMPLE 8.7 THE OPEC a Before 1960, international oil companies such as Royal Dutch Shell and Standard Oil of New Jersey were often accused of acting as a cartel aimed at keeping prices high. If so they failed as became evident later on when the Organization of Petroleum Exporting Countries (OPEC) came into existence and really raised prices! In fact, it was the attempt of the major companies to cut oil prices that led the oil-exporting nations to establish the OPEC. (At what must have been a low point for intelligent foreign economic policy, the U.S. State Department actively encouraged formation of the OPEC cartel!) Starting about 1960, the main OPEC nations solidied their control over pricing and production, in effect expropriating the private companies whose efforts had discovered and developed their oil resources. Thereafter private oil companies operating in OPEC countries received only what amounted to handling fees for extraction and marketing services. In 1973, for example, the Saudi Arabian government took all but about $0.60 of the $2.59 price per barrel. The problem for the OPEC was and is to limit production. In fact, most OPEC members have not been holding back production. To the extent that the cartel has been viable, it is only because a few major producers, notably Saudi Arabia and Kuwait, have limited their own production. The petroleum trade since formation of the OPEC has gone through several dramatic phases. After Egypt and Syria attacked Israel in 1973, the Arab countries dominating OPEC halted the previous rising trend of oil exports, aiming to inuence the diplomatic policies of the Western nations. Oil prices moved sharply upward. By January 1974 the price more than quadrupled to $11.65 per barrel. During this period the cartel was extraordinarily successful. Presumably, agreement upon foreign policy issues (mainly, opposition to Israel) helped to limit the chiselling that would otherwise have tended to undercut the cartel. For some years afterward OPECs power gradually weakened. Although the ofcial price rose from $11.65 per barrel at the beginning of 1974 to $13.00 ve years later (an increase of about 12%), the U.S. dollar depreciated about 38% over the same P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 248 8. MONOPOLIES, CARTELS, AND NETWORKS period. Thus, by January 1, 1979, the real price of OPEC crude oil was down from its peak. But then, starting in 1979, another round of price increases was triggered by the revolution that paralyzed production in Iran. The ofcial OPEC price rose ultimately to $34 per barrel in late 1981. But by 1985 maintaining these high prices required increasingly severe production cutbacks by the major OPEC producers in particular, Saudi Arabia. Owing to OPEC cutbacks and rising non-OPEC production, the OPEC share of the world market, which had been 56% in 1973, fell to only 30% in 1985. After 1985 Saudi Arabian production began to rise, along with the exports of other OPEC members. In consequence, despite a moderate upward trend in non-OPEC output, the OPEC fraction of the world market has recovered to about 40% in recent years. The price, still at about $28 per barrel in 1985, has since ranged between $15 and $25 per barrel apart from a sharp temporary jump due to Iraqs occupation of Kuwait and the rst Gulf War in 19901991. In some periods the cartel has been hugely successful, thanks in large part to the Middle East wars of 1973 and 19901991 and the Iranian revolution of 1979. In the interludes between these historical shocks, two factors worked against the cartel. First, consuming nations began to use oil more economically and shift toward substitute fuels. Second, the high prices encouraged non-OPEC oil exporters such as Britain, Russia, and Mexico to expand their production and exports. a The data on prices and production used here have been collected from several sources including International Economic Report of the President, Washington, DC: U.S. Government Printing Ofce, February 1974, pp. 110111; Los Angeles Times (March 15, 1983), p. 1; M. A. Adelman, The Genie out of the Bottle: World Oil since 1970 (M.I.T. Press, 1995), especially Figure 6.1 (p. 144), A. F. Alhajji and David Huettner, OPEC and Other Commodity Cartels: A Comparison, Energy Policy, v. 28 (2000), and Energy Information Administration, Monthly Energy Review (July 2003). 8.6 NETWORK EXTERNALITIES A persons demand for a good is usually independent of how much others buy. Sometimes, however, a person values a good more highly the greater the number of other people buying it. Such goods are said to exhibit positive network externalities. The network effect upon demand may be due to direct interaction among consumers. Telephone service would be valueless if no one else had a phone, and in general becomes more useful as the number of subscribers rises. Or, the source of the externality may be informational. If John thinks Mary is a wise shopper, and Mary has just bought a Sony CD player, John is more likely to buy it. Or last, preference for conformity, as in the world of fashion, generates positive network effects. Men may prefer to wear trousers with cuffs only because most other men do.24 Demand for a Network Good In Chapter 4, aggregate industry demand for a good was derived by horizontally summing the separate demand curves of the individual consumers. But a different technique is needed for a network good, where any one persons demand depends also upon the aggregate demand. 24 Nevertheless, some consumers are contrarians, averse to conformity. For them, the network effect would be negative. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8.6 NETWORK EXTERNALITIES 249 Price ($/month) P 20 P 10 P0 DD D 20 D10 D0 10,000 20,000 Internet connections Figure 8.12. Network Effects and Market Demand The horizontal axis measures the number of consumers connecting to the Internet. The more steeply sloped curves show, for any specied price, the numbers of consumers desiring to connect as a function of the number of others they expect to be connected. Owing to the network effect, D10 lies to the right of D 0, D20 to the right of D10, and so on. For consistency however, expectations must be correct. The market demand curve DD, based upon such conrmed expectations, passes through the point on D 0 (where no other people are expected to be connected), the point on D10 (where 10,000 others are expected to be connected), and so forth. So DD is atter (more elastic) than the curves D 0, D10, and D20, etc. In Figure 8.12 the horizontal axis measures the number of consumers connecting to the Internet. The Internet would provide useful informational services even if no other consumer were connected, so a typical person would be willing to pay something even as the sole user. But when others connect, added services such as e-mail become possible. The curve D 0 is the horizontal summation of the individual solo demand curves, which would be applicable if each potential user believes no one else will be connected. The curve D10 is the demand when everyone expects that 10,000 consumers will be connected, the curve D20 is the corresponding summation when each potential buyer expects that 20,000 people will be connected, and so forth. Owing to the network effect, D10 lies to the right of D 0, D20 to the right of D10, and so on. To nd the market demand, assume that consumers expectations are correct and therefore consistent with what actually happens, at least in the long run. The conrmed expectations demand curve DD will pass through the point on D 0 where no people are connected, the point on D10 where 10,000 people are connected, and so on. As is geometrically evident, curve DD is atter (more elastic) than the curves D 0, D10, and D20. Thus, a positive network effect increases the responsiveness of demand to price changes. The diagram also reveals a chicken-and-egg or start-up problem. The choke prices P 0 for demand curve D 0, P10 for D10, P20 for D20, etc. are indicated on the vertical axis. The choke price for the D 0 or solo demand curve is also necessarily the choke price for the overall demand curve DD. If costs of production dictate that the price cannot be lower than P 0, the market is not viable at all. Although under some conditions positive numbers of potential buyers would pay prices above P 0, no point P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 250 8. MONOPOLIES, CARTELS, AND NETWORKS of conrmed expectations lies above that price. Lack of a critical mass of buyers often holds up the introduction of innovative products. To make the market viable, either consumers must more highly value the new product (that is, the conrmed-expectations demand curve DD must rise) or else production costs must fall. Monopoly or Competition? As indicated in the preceding chapter, falling Average Costs AC (increasing returns to scale) often leads to natural monopoly. Other things equal, the largest rm can always produce more cheaply than smaller rms. Network effects may also cause natural monopoly, but the reason lies on the demand side rather than the supply side. Now the leading rm gains not from falling Average Cost but because consumers are willing to pay more for its brand. So, although several rms may initially struggle for market dominance, only one rm will eventually survive. (As a qualication, however, if consumers have varied preferences, a smaller enterprise may survive to serve a niche market.) Network effects and returns to scale may operate in opposite directions. The demandside network externality favoring natural monopoly may be opposed on the supply side by decreasing returns to scale in production (rising Average Cost curves). So, although a network effect on the demand side may suggest that all personal computers should be suppled by a single producer, it appears that rising costs in manufacturing have allowed many producers of personal computers to survive. An important source of network externalities is the convenience of a common standard or format. The format or standard itself could be the basis for a monopoly. But if no one owns that standard, the producing rms can constitute a competitive industry. The more rms adhering to a given format (in cell phones or compact disks or computer operating systems), the more acceptable that format is to consumers. So there is pressure toward convergence upon a single standard. Yet multiple standards do sometimes survive. For one thing, consumers preferences may differ, and some may be willing to pay more to retain their favorite standard. Or, rising costs on the supply side may offset the advantage of rising consumer acceptance on the demand side. Human languages can also be regarded as alternative formats or standards. In the competition among languages, whichever is the most popular and widespread is at an advantage. Yet multiple languages persist. One reason is that not everyone prefers the same language. Another factor is the cost of switching. This relates to the next topic, lock-in. The Lock-in Issue Network effects might possibly lock an industry into an inferior technology. A technologically inferior brand might have been the rst to enter the market, thus gaining a network advantage great enough to attain a monopoly. Or, many rms may be in the market, but all follow a single format that might possibly be technologically inferior. In recording tapes, Betamax was unable to made headway against VHS. In keyboard layouts, QWERTY dominates over Dvorak. But some analysts regard these examples as largely mythical. Betamax may have lost out not because it entered the eld late actually, Betamax preceded VHS in the market but because its product was inferior to VHS. And the Dvorak keyboard does not appear to be notably superior to QWERTY. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 8.6 NETWORK EXTERNALITIES 251 EXAMPLE 8.8 QWERTY AS INEFFICIENT LOCK-IN? The standard English keyboard layout is called QWERTY, after the pattern of letters on the upper-left of the keyboard. At a glance, QWERTY seems to be an inefcient layout. Some very frequently typed letters (such as a) require an awkward nger stretch, while less important letters (such as j) have a better, more central location. The best-known alternative layout, the Dvorak keyboard dating to 1936, was invented to remedy these and other deciencies. The Dvorak International Corporation still actively promotes that keyboard. Nevertheless, QWERTY has maintained its dominance. This situation appears to have the earmarks of an inefcient lock-in. The usual explanation is that QWERTY gained an early lead. The rst successful touch typist, Frank McGurrin, used a QWERTY machine to win a series of typing contests beginning in 1888. Since then, alternative keyboards have faced a chickenand-egg problem. At any moment of time almost all typists are trained on QWERTY, so there is little demand for other keyboards. And it doesnt pay for typists to train on alternative keyboards, when they will almost certainly end up using QWERTY. Although supercially appealing, this explanation does not really hold water. True, it may not pay for an individual QWERTY typist to learn the Dvorak keyboard. But a major corporation such as General Motors, which over many decades has employed tens of thousands of typists, could have easily bought Dvorak keyboards and trained typists to use them. Had the huge benets claimed by Dvorak enthusiasts (for example, a 75% speed increase reported in an often-cited 1944 U.S. Navy study) been valid, these gains would have swamped the switching costs. In fact, though Dvorak keyboards have been commercially available for many years, no major employer of typists has ever switched over. As explanation, the economists S. J. Liebowitz and Stephen E. Margolis have contended that this historical story is largely a myth, and that the Dvorak layout is not demonstrably superior to QWERTY.a Reviewing the U.S. Navy study cited by Dvorak supporters, Liebowitz and Margolis found it poorly designed and biased. (It appears that the tests were conducted by Lt. Cdr. August Dvorak, holder of the patent on the Dvorak keyboard.) The report was never endorsed by the Navy, and a later study by the U.S. Treasury Department did not support changing over to Dvorak. Later comparative tests have usually shown a small superiority for Dvorak. The most signicant recent study was conducted by Leonard J. West, timing the subjects by having them repeatedly type the most common English-language digraphs (twoletter combinations such as th th th th).b To overcome the difculty that most subjects have prior experience using QWERTY, the typists actually used QWERTY keyboards. But, to achieve the effect of typing on a Dvorak keyboard, instead of th the typists were asked to type kj which is where th would appear on the Dvorak keyboard. This was done for all the common digraphs, and in both directions to avoid bias. The overall result was a small (4%) speed advantage for Dvorak, close to the average of previous studies. Despite the ingenuity of the West experiment, the objection remains that speed in repetitively typing digraphs (th th th th) may not be much of an indicator of speed and accuracy in typing regular text. Earlier studies were also subject to a variety of aws and objections. So, in view of the substantial costs of switching, it remains in doubt whether QWERTYs persisting dominance of the market in spite of a P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 252 8. MONOPOLIES, CARTELS, AND NETWORKS Payoff per adopter Technology B Technology B aftercostofs witching Technology A Q Q Numberof adopter Figure 8.13. Network Technology and Switching Cost For each technology, the horizontal axis shows the number of adopters and the vertical axis the payoff per adopter. If the market is small (if there are only a few users), technology A is the better choice. For more than Q users, technology B would be better. But with technology A initially in place, allowing for the cost of switching means that no individual or small group can protably adopt B until the number of potential adopters reaches point Q . Within the range between Q and Q there is lock-in. seeming small speed superiority of the Dvorak keyboard represents an instance of inefcient lock-in. a S. J. Liebowitz and Stephen E. Margolis (1990), The Fable of the Keys, Journal of Law and Economics, v. 33 (April 1990). For a case in favor of the Dvorak keyboard, see Jared Diamond (April 1997), The Curse of QWERTY, Discover Magazine. b Leonard J. West, The Standard and Dvorak Keyboards Revisited: Direct Measures of Speed, Santa Fe Institute Working Paper 98-05-041 (1998). In evaluating whether lock-in is economically inefcient, it is essential to allow for the cost of switching. Retaining a currently dominant format makes economic sense if it is too costly to switch to an alternative even if that alternative would indeed have been hypothetically superior starting from a blank slate. The problem is illustrated in Figure 8.13. The horizontal axis shows the number of adopters of one technology or the other, and the vertical axis shows the payoff per adopter. Initially the market is small, there are few users, and technology A is the better choice. But then the industry grows. At point Q crossover occurs, and technology B becomes better or rather, would have been better starting from a clean slate. But no individual or small group can protably adopt B until the number of adopters reaches point Q . Within the range between Q and Q there is lock-in, but it is not inefcient. Only beyond Q is lock-in inefcient. Inefcient lock-in is possible for two related reasons. People might be myopic and choose or expect others to choose only on the basis of a short-sighted calculation: that if technology A is better today, it will continue to be better in the future. Or, even if all can look ahead and realize that demand is sufcient to make technology B better, switching from A to B calls for coordinated action that may be impossible to achieve. P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 SUMMARY 253 Despite these difculties, a variety of market forces will always be at work to overcome inefcient lock-in. For example, there would be a payoff to inventors who nd ways of reducing switching costs. CONCLUSION Network effects may lock the market into a technology that, although superior initially, becomes inferior once demand grows beyond a certain size. Market forces at work, however, tend to overcome lock-ins. No conclusive examples of inefcient lock-in have yet been demonstrated. SUMMARY A monopoly exists when an industry consists of a single rm. Sometimes a monopoly is conferred by a governmental license or franchise. A natural monopoly occurs when one rm can produce more cheaply than any larger number. Or a rm that is not a natural monopolist may succeed in erecting barriers against competitors. A competitive rm is a price-taker, whereas a monopolist is a price-maker. The monopolist can set either industry price P or industry output Q not both. A monopolist maximizes prots by setting output such that Marginal Cost = Marginal Revenue, where Marginal Revenue MR is less than price. This can be seen from the expression MR = P (1 + 1/), where elasticity (), is negative. Compared to a competitive industry, the higher price and lower output under monopoly are associated with an efciency loss (reduction in Consumer Surplus and Producer Surplus) as well as a transfer from consumers to the monopolist. An additional efciency loss may arise from rent-seeking the struggle to gain and maintain a monopoly positon. Regulation of monopoly commonly aims to reduce price to the lowest level that attracts and retains the resources employed in the industry. Since no economic prots are then earned, Average Revenue must equal Average Cost. If the monopolists Average Cost curve is rising, the intersection of Average Cost and Average Revenue overshoots the competitive equilibrium: there will be an efciency loss due to excessive production in this industry. For levels of output where Average Cost is falling, the regulated solution lies between the monopolists prot-maximizing output and the competitive outcome. Price discrimination may allow a monopolist to earn even higher revenue. (1) Under market segmentation, the monopolist sets overall Marginal Cost of production equal to the Marginal Revenue in each segment. So higher prices will be charged in segments with less elastic demands. (2) Under block pricing, the monopolist charges different unit prices for different quantities sold. (3) Under perfect discrimination the monopolist charges the maximum each consumer would be willing to pay for each successive unit. The monopolist then gains all the advantage of trade: Consumer Surplus is zero. Surprisingly, however, there is no efciency loss. Cartels are associations of rms in an industry that act collectively like a monopolist. But each member is motivated to chisel (produce beyond quota), and producers outside the cartel are induced to increase their production. When consumers value a good more highly the greater the number of other people using it, the good exhibits positive network externalities. Network effects work P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 254 8. MONOPOLIES, CARTELS, AND NETWORKS in a way somewhat parallel to falling Average Costs, making it possible for an initially leading rm to end up as a monopolist. And, although the issue remains subject to debate, network effects might also lock an industry into a leading rms inferior technology. QUESTIONS The answers to daggered questions appear at the end of the book. 1. If a monopolist sells 1,000 portable ultrasonic ghost repellents she will receive $48 per unit. If she sells only 999 units, she will receive a price of $50 per unit. Is the marginal revenue for unit 1,000 greater than, equal to, or less than $48? 2. Why will a monopolists prot-maximizing rate of output always be in the region of elastic demand? 3. A monopolist initially maximizes prots by selling 1,000 panes of glass a year. A salesman then offers to rent a machine that reduces the rms Marginal Cost by $10 at each level of output. Should the rm be willing to pay more or less than $10,000 rent (as a lump sum) per year for the machine? 4. Why is monopoly power over price smaller as elasticity of demand increases? 5. Monopoly is a bad thing for consumers, but a good thing for producers. So, on balance, we cant be sure that monopoly is responsible for any loss in economic efciency. Analyze. 6. A competitive industry may have its equilibrium in the range of inelastic demand. Then the industry would receive more revenue if its output were smaller. Does it follow that such a competitive industry is producing too much of the good in terms of efcient use of resources? 7. Monopoly rms are accused of pursuing nonprot goals to a greater degree than competitive rms. Why might a monopolist be any less interested in prot than a rm in a competitive industry? 8. Compare the prot-maximizing conditions for simple monopoly, market-segmentation monopoly, and perfect-discrimination monopoly. Why is only the last of these said to be efcient? 9. In making efciency comparisons between a monopolized and a competitive industry, the Marginal Cost function of the monopolist was said to correspond to the supply function of the competitive industry. Explain why. 10. When will zero-prot regulation of a monopoly lead to too high a price from an efciency point of view? Too low a price? 11. Show how behavior of a cartels members may threaten its survival. Show how behavior of outsiders may threaten it. For Review For Further Thought and Discussion 1. Movie theaters often offer price discounts to the young. a. Is there likely to be a leakage problem in this form of market segmentation? b. Sometimes youth discounts are explained in terms of differing elasticities of demand. Is this likely to be correct? 2. Explain whether there is a contradiction between the following assertions: (1) the oil industry is an effective monopoly (cartel), and (2) higher prices for petroleum products will do little to discourage demand? P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 QUESTIONS 255 3. Is it better (more efcient) to have a monopolized industry, or no industry at all? 4. a. b. c. In comparison with a simple monopolist, does a perfectly discriminating monopolist possibly or necessarily produce more output? Does a market-segmentation monopolist? A multipart pricing monopolist? 5. Market segmentation is more common in the sale of services (e.g., discrimination by income for medical services, by age for transportation services) than in the sale of manufactured goods. Why? 6. a. b. Are supermarket discount coupons a form of market segmentation? If so, how is leakage controlled? Do consumers who choose to use the coupons have a more elastic demand for grocery products? Explain. 7. Physicians often charge poorer customers lower fees for medical services. They usually explain this as a charitable gesture. Alternatively, can this be an example of market segmentation? 8. It has been said that sellers cartels are more effective in dealing with government agencies as buyers, owing to the public records of transactions in which governments engage. Explain. How might the contention be tested? 9. Governments sometimes auction off the right to monopolize a commodity. (The gabelle, or salt monopoly, of pre-Revolutionary France was an example.) Show in a diagram the maximum amount the government could expect to acquire by auctioning off a monopoly. Is this likely to generate more or less income for the government than the most lucrative excise tax the government might impose? 10. The following contentions about the demand and supply for narcotic drugs are widely believed: (1) that demand is highly inelastic hooked users are practically forced to buy drugs, no matter what the price; (2) that the supply side of the market is dominated by a cartel consisting of a few major providers (Colombian drug lords). Is there a contradiction between these two beliefs? Explain. 11. Show that with price discrimination across two markets, the lower price corresponds to the more elastic demand. [Hint : Figure 5.4 shows how to graphically determine the elasticity along a demand curve.] 12. A monopolist selling a durable good may sometimes be unable to charge more than the competitive price, because it is in competition with itself. Having initially sold some units at a price P exceeding its Marginal Cost MC, at any point thereafter it will want to sell additional units at a slightly lower price P , and so on down to P = MC . Knowing this in advance, buyers will be unwilling to pay more than P = MC to begin with. How could such a monopolist escape this trap? 13. It has been argued that libraries have very inelastic demand for hardback editions of books, and that this inelasticity leads to high prices of certain academic and specialty hardbacks. Is this argument consistent with the evidence discussed in Example 8.4 on Paperbacks versus Hardbacks? 14. If an organization like the Maa effectively monopolized illegal activity, would you expect to observe less crime than under competitive free entry into this industry? P1: OBM/JzG 0521818648c08.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:31 256 P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 9 Product Quality and Product Variety 9.1 Quality 258 Quality under Competition and Monopoly 259 An Application: Suppression of Inventions 263 Cartels and Quality 265 9.2 Variety 266 Product Variety under Monopoly 268 Blending Monopoly and Competition Monopolistic Competition 270 SUMMARY 275 QUESTIONS 276 EXAMPLES 9.1 9.2 9.3 9.4 9.5 9.6 Used-Car Prices 258 Price and Quality: Shopping Hours in Quebec 261 The Japanese Auto Export Cartel 265 Religion: The Value of Variety 267 Advertising and Competition 273 Customization in the U.S. Economy 275 257 P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 258 9. PRODUCT QUALITY AND PRODUCT VARIETY The text so far has focused on how prices and quantities are determined in markets. But rms also can get to choose the nature of the products they offer to consumers. Television networks can air comedies or dramas or news programs, farmers can grow different strains of wheat, barbers can cut hair in different styles, automobile manufacturers can offer sedans or sports utility vehicles. Firms have two main dimensions of choice in determining the nature of the product: what level of quality to offer, and how much variety. Quality, to be taken up in the rst section of the chapter, is something that all consumers want and agree on. Durability, reliability, and safety are always desirable. In contrast, variety, the topic of the second section of the chapter, is a matter of taste. Some people like red roses, some pink, some white; some prefer conservative clothing, others want ash and novelty. 9.1 QUALITY Products vary in many quality dimensions. For simplicity, suppose all consumers are seeking some single service feature from a product. For light bulbs it might be lumens of light output, for hard disks it might be gigabyte capacity, for gasoline it might be mileage. EXAMPLE 9.1 USED-CAR PRICES As cars age, their quality deteriorates. Operating costs rise, and reliability falls off. In addition, consumers may suffer a loss of psychological satisfaction as the vehicles style becomes unfashionable. B. Peter Pashigian, Brian Bowen, and Eric Gould examined how these factors affected used-car prices in the 1990s.a Although all cars fall in value over time, there are differences in the annual rate of price decline with age. The tabulated data show that intermediate passenger cars fell around 22% in value the rst year, an additional 16% the next year, and so forth. In contrast, for pick-up trucks the annual price decrease remained close to 13% per year over the entire range of vehicle life considered (up to 5 years). Also, compare the old-style Volkswagen bus and the new-style vans. For the Volkswagen the initial rate of value decline was only 13%, with even smaller rates of decline later on. (It appears that some consumers derive contrarian satisfaction from owing such a classic machine.) The newer-style vans suffered a much larger rst-year price decline of around 22%, tapering off in following years. The authors interpretation was that the new type of van was valued more for its current stylishness. When no longer quite new, such cars go out of fashion and their prices fall off rapidly. Annual percentage price declines by age, selected vehicle types 12 years Intermediate cars Pickup trucks New vans VW buses 22 13 22 13 23 years 16 13 14 12 34 years 14 13 12 11 45 years 13 13 11 12 Source: Estimated visually from Pashigian et al., Figure 2 (p. 287). a B. Peter Pashigian, Brian Bowen, and Eric Gould, Fashion, Styling, and the Within-Season Decline in Automobile Prices, Quarterly Journal of Economics, v. 38 (October 1995). P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 9.1 QUALITY 259 $/z $/z DollarsperUnitofService MC (qn = q o ) n MCq ( n = o) n MCz Sz Po z Po z Dz 0 zo n z 0 Z o Z QuantityofService Panel(a) IndustryQuantityofService Panel(b) Figure 9.1. Marginal Cost of Quantity versus Quality, and the Market for Service In Panel (a) the dashed and dotted curves MC and MCq show the Marginal Cost of producing more service output by increasing quality of product and quantity of product, respectively. Panel (b) shows market equilibrium at price Po and service amount Z o . The industry supply curve, Sz , is the horizontal z sum of the rms MCz curves. Quality under Competition and Monopoly The key idea in analyzing quality is to distinguish between the product that is sold in the market and what consumers are really interested in the underlying service. Consumers buy gasoline, but they are really interested in the road mileage they can get from the gasoline. The quality of an offered good is the service provided per physical unit. For gasoline, it would be miles per gallon (mpg). So service (mileage) is quantity (gallons) times quality (mpg). Suppose there are a xed number N of competitive rms, say oil reneries. The nth renery produces quantity qn gallons of gasoline at quality (mpg) level n . So that rms output of the service zn can be written zn n qn (9.1) A renery producing q n = 1,000,000 gallons of gasoline per day, at quality level n = 20 miles per gallon, is effectively generating z n = 20,000,000 units of mileage service for consumers. How about price? If users are fully informed, the price of each rms product will reect its quality. Although consumers pay a direct dollar price Pn for the physical product of rm n, what underlies that price is the price of the service, denoted Pz . The prices of different brands must reect the product quality offered: Pn n Pz (9.2) If one brand of gasoline has 10% better mpg than another brand, and assuming mpg is the only dimension of quality, then in equilibrium the price of the superior-quality brand must be 10% higher. What determines the underlying price Pz of the service? Under conditions of pure competition, the answer, as usual, is supply and demand. In Panel (b) of Figure 9.1, the P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 260 9. PRODUCT QUALITY AND PRODUCT VARIETY height of the demand curve Dz shows what consumers are willing to pay for amounts of service Z (mileage) offered on the market. The supply curve Sz shows, for each price Pz , the amounts of service (mileage) that the rms in aggregate are willing to provide. Chapter 6 showed how the competitive rm determines its prot-maximizing output q by setting the Marginal Cost of its product equal to market price P. But when products can differ in quality, in effect each rm chooses the prot-maximizing amount of the service (mileage) to offer. It does so by setting the Marginal Cost MCz of the service it generates equal to Pz , the going market price of the service: MCz = Pz (9.3a) The rms Marginal Cost of service MCz depends upon both the quantity qn it produces and the level of quality n that it chooses to offer. Panel (a) of Figure 9.1 shows o an initial situation where rm n provides quantity q n (gallons of gasoline) at quality o o o o n (mpg). The service output (mileage) generated is thus z n q n n . The diagram shows three different Marginal Cost curves. The dotted curve MCq shows the cost of providing more mileage by varying quantity alone (holding quality constant at o ). The dashed curve MC shows the cost of providing more mileage n o by varying quality alone (holding quantity constant at q n ). Last, the third Marginal Cost curve MCz shows the balanced (lowest-cost) way of generating additional units of o the service. Quality and quantity are shown as balanced at service output z n , where the o o rms chooses quality n and quantity q n . At that point it is equally costly to generate another small unit of service by expanding quantity as by improving quality, so all three Marginal Cost curves intersect. PROPOSITION: For any amount of service generated, the rms quality and quan- tity choices are correctly balanced when the Marginal Cost of expanding service by increasing quantity (MCq ) and the Marginal Cost of expanding service by improving quality (MC ) are equal. The true (lowest) Marginal Cost MCz of providing the service is the same as MCq and MC when these are equal.1 EXERCISE 9.1 Suppose a rms cost function is C = q 2 + q 2 . Initially the rm chose q = = 10, so its service output is z q = 100. (a) As an approximation of Marginal Cost, how much more will it cost to expand service output to z = 101: (i) by increasing q only, (ii) by increasing only, and (iii) by the lowest-cost (balanced) increase in q and ? (B) What is the incremental cost of a bigger increase in service output, form z = 100 to z = 200? A N S W E R : (a) At the initial q = = 10, the cost of producing z = 100 was C = 10(102 ) + 102 (10) = 2,000. (i) Holding quality xed at = 10, producing z = 101 requires that q z/ = 101/10 = 10.1. The associated cost is therefore C = 10.1(102 ) + 10.12 (10) = 2,030.1. The cost increment is approximately MCq = 30.1. 1 Mathematical Footnote: In terms of derivatives, the Marginal Costs of expanding service produced by providing more quantity or by providing more quality are: MCq = dC dq dq dz and MC = dC d d dz P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 9.1 QUALITY 261 (ii) Owing to the algebraic symmetry of the cost function, MC is also 30.1. (iii) To produce z = 101 with a balanced increase of quantity and quality, again the symmetry of the cost function means that q and must remain exactly equal. The solution is q = = 10.05 approximately. The associated Total Cost is about 2,030.075, so Marginal Cost of the service, MCz , is approximately 30.075. As expected, a balanced increment of quality and quantity is cheaper than expanding z by raising either q alone or alone. (b) Although the difference between 30.1 and 30.075 is small, the disparity is magnied for larger changes. To produce z = 200 while holding quality xed at = 10 means that q = 20, the Total Cost being 6,000. To produce z = 200 while holding quantity xed at q = 10 means that = 20, so again the Total Cost is 6,000. In contrast, a balanced increase of quality and quantity to q = = 14.142 generates a service output of z = 200 at a substantially lower cost of 5,656.9. This principle of balance enters into the rms prot-maximizing choice, which now involves the condition (9.3a) together with: MCz = MCq = MC (9.3b) In Panel (a) of Figure 9.1, at the service price Po the rms prot-maximizing service z o output is z n .2 In line with the analysis in Chapter 6, the MCz curve is the rms supply curve for the service. Summing horizontally over all the rms in the industry leads to the industry supply curve Sz (the aggregate amounts of the service Z provided at each price Pz ),3 as pictured in Panel (b) of the diagram. Firms in a competitive industry need not all produce the same level of quality. Depending upon their cost functions, some could specialize in high-quality products and others in low-quality products. The key point is that, since consumers are really buying the underlying service, quality differences will be fully reected in higher or lower prices. EXAMPLE 9.2 PRICE AND QUALITY: SHOPPING HOURS IN QUEBEC In July 1990 the Quebec laws governing retail hours were relaxed, and a number of stores began to remain open on Wednesday evenings and on Sundays. This represented improved quality of retail service. Georges A. Tanguay, Luc Vallee, and Paul Lanoie studied how the change affected supermarkets price margins for several standard commodities.a Taking chicken as an example, for the period when the earlier law was in effect the authors estimated the relation between the stores costs and the prices charged consumers by the equation: P = 1.68 C 0.851 Here P is the retail price of chicken per kilogram and C is the stores wholesale cost per kilogram. The equation means, for example, that when the stores cost was $1.50 2 3 The qualications to the MC = P rule covered in Chapter 6 also apply here: (i) the MCz curve must be rising and (ii) Pn ACz (the No-shutdown condition). Setting aside possible external economies and diseconomies, and also changes in the number of rms (entry or exit), as discussed in Chapter 7. P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 262 9. PRODUCT QUALITY AND PRODUCT VARIETY per kilogram, the estimated average retail price for chicken was P = 1.68(1.500.851 ) = $2.37. For the period after the closing law was relaxed, the multiplicative constant rose from 1.68 to 1.76. This meant that, under the more relaxed law, when the stores cost was $1.50 per kilogram the average retail price would now be $2.49. So the longer shopping hours appear to have raised the stores average margin, given a wholesale cost of $1.50 per kilogram, from $0.87 to $0.99 about 12%. Similar results were obtained for other products: beef, bananas, apples, and onions. Presumably the higher margins reected consumers willingness to pay for the increased convenience of the extended shopping hours. Margins might possibly also have increased owing to higher operating costs in keeping stores open longer. But, the authors found, costs per kilogram appeared to rise very little, if at all. True, there are additional costs incurred in staying open longer hours, but on the other hand the stores were able to manage their inventories better. For one thing, there was less wastage of perishable produce. So it appears that the increase in price margins was indeed due to the improved quality of service offered to consumers. a Georges A. Tanguay, Luc Vallee, and Paul Lanoie, Shopping Hours and Price Levels in the Retailing Industry: A Theoretical and Empirical Analysis, Economic Inquiry, v. 33 (July 1995). So far only competitive industries have been studied. What about monopoly and quality? Chapter 8 showed that a monopolized industry would provide a smaller quantity of product than a competitive industry. Is there any reason to expect it to offer lower quality as well? Taking laundry detergent as an illustration, suppose quality can be dened in terms of cleaning power per ounce. Again, the crucial point is to appreciate that the rm, whether a monopolist or a competitor, is really providing consumers with levels of service Z. Since the consumers demand for service is surely negatively sloped, a monopolist would offer a smaller service output Z than would a competitive industry. In fact, the familiar monopoly equation will apply. The monopolist will set its Marginal Cost equal to its Marginal Revenue, both now dened in terms of amounts of service: MCz = MRz (9.3c) The only question is, will this smaller Z be associated with both lower quality (weaker detergent) and less quantity (fewer pounds of detergent)? Or would the change be only in one dimension? Or might the quality actually improve, accompanied by an even greater cut in quantity? The answer is already evident in equation (9.3b), which indicated that changes in service output are best achieved by balanced adjustments of both quantity and quality. In fact, equation (9.3b) applies for any type of rm, whether a competitor or a monopolist. Consequently, the smaller service output Z of the monopolized industry should logically involve some combination of reduced quantity and lower quality. The monopolist would produce a weaker detergent, and produce fewer pounds. CONCLUSION A monopolist produces a smaller service output Z than a competitive industry, and generally does so by some combination of reduced quantity and lower quality. P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 9.1 QUALITY 263 Cz Cz Figure 9.2. A Quality-Improving (Cost-Reducing) Invention A monopolist is considering an innovation that costlessly doubles the quality of its product. Since the horizontal axis represents amount of service Z, the original Total o Cost curve C z shifts to C z service output is doubled at each level of cost. Fully informed consumers are interested only in amount of service, and so the Total Revenue function R is unchanged. The monopolist will necessarily increase prots by adopting rather than suppressing the invention. In the situation pictured, the prot comparison is > o . Consumers also benet, because more service is produced to be sold at a lower price. $ Rz Dollars 0 Zo Z Quantityofservice(Mileage) Z An Application: Suppression of Inventions Monopolists are sometimes accused of suppressing useful inventions. A useful invention is a discovery permitting production of a higher-quality product at given cost, or of a given quality of product at lower cost. As will be seen, if buyers are adequately informed it is never protable for a monopolist to suppress such an innovation. Consider gasoline, where as before consumers are interested only in the service generated (road mileage). Suppose the monopolist discovers how to produce its existing quality of gasoline at half the cost. Obviously, it will never suppress (fail to make use of) such a cost-reducing discovery. Now suppose instead that the discovery lets the rm double the quality (mpg) with no increase in production costs. To the rm, such a quality-improving invention is equivalent to the cost-reducing invention. The rm would not suppress either invention. Figure 9.2 illustrates the equivalence of cost-reducing and quality-improving inventions. Suppose the invention doubles quality (miles per gallon) of gasoline without changing the cost of producing the physical product (gallons of gasoline). Assuming consumers are fully informed, the demand curve for mileage service remains unchanged. (Consumers dont care about gasoline as such, they will only pay for what concerns them mileage.) So it follows that the Total Revenue curve, showing R z Pz Z as a function of Z, remains unchanged. On the cost side, although the Total Cost curve in terms of gasoline output Q would remain unchanged, here it is service output Z that is shown on the horizontal axis. Since Z Q , the doubling of quality shifts the Total Cost curve of producing Z from C o to C a horizontal stretching to the right by a factor of 2. So a quality-improving invention is indeed equivalent to a cost-reducing invention. The prot-maximizing level of service output was Z o before the invention and became Z after the invention. The associated prots are o and . (The postinvention prots are of course larger.) In the situation illustrated, the monopolists protmaximizing service output increases ( Z > Z o ) but does not quite double ( Z < 2 Z o ). This means that, although the rm generates more service output, it does so while actually producing fewer gallons of gasoline. So consumers benet from the invention, P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 264 9. PRODUCT QUALITY AND PRODUCT VARIETY $/z MCz MC o z AC o z ACz DollarsperUnitofService Dz MRz Z Zo Z QuantityofService Figure 9.3. A Quality-Improving (Cost-Reducing) Invention Adverse to Consumers A quality-improving invention is equivalent to a reduction in the Average Cost of producing the service, and so the new ACz curve lies everywhere below the original ACzo curve. Nevertheless, as shown here, there may be a range in which the new Marginal Cost MCz is higher than the original MCzo . As a result, the new MCz = MRz intersection may determine a prot-maximizing level of service z that is smaller than the initial level z o . If so, consumers will be worse off for the invention. which allows them to consume more service Z (mileage), and the rm saves cost by producing a smaller physical quantity Q of output (gallons). It is also possible, if the revenue and cost curves have somewhat different shapes, that the service output Z that maximizes prots could more than double ( Z > 2 Z o ). Consumers would then benet even more. The rm would incur higher costs, but would nevertheless earn higher prots. Last, although this may seem paradoxical, Figure 9.3 shows that it is also logically possible for the output of service in the postinvention solution to fall ( Z < Z o ). The monopolist does not suppress the invention, but the consumers end up worse off! This surprising possibility is more easily visualized in a diagram like Figure 9.3, a diagram in average-marginal units as opposed to the total units used in Figures 9.1 and 9.2. The demand curve, or Average Revenue curve, in terms of service output Z remains unchanged. Since this is a cost-reducing invention, the postinvention Average Cost curve AC z is lower throughout than the original Average Cost curve AC zo . Nevertheless, it is possible (as shown in the diagram) for the postinvention Marginal Cost curve MC z actually to be higher than the original Marginal Cost curve MC zo in the relevant range. If so, as shown in the diagram, the new intersection of Marginal Revenue and Marginal Cost can occur at some Z < Z o . In that case the rms prot-maximizing output of service is smaller, the monopoly price is higher, and consumers lose out. Such a result requires very special shapes of the Marginal and Average Cost curves specically, there must be a range where Average Cost falls while Marginal Cost rises. This is probably very unusual. The assumption that consumers are fully informed is essential to this entire analysis. If the invention really improves product quality but consumers do not believe that is the case, they will initially be unwilling to pay more for the higher-mileage gasoline. That P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 9.1 QUALITY 265 would eliminate the monopolists incentive to introduce the innovation. Still, the cost of informing consumers is a real economic cost. It is not really suppression when an invention, even though a genuine quality improvement, cannot be put on the market except at a cost including the cost of convincing consumers that it really is a quality improvement that is too great in comparison with the benet received. CONCLUSION If consumers are fully informed, a quality-improving innovation is equivalent to a cost-reducing innovation. Neither would be suppressed by a prot-maximizing monopolist. Normally consumers also gain, except in exceptional circumstances. Cartels and Quality Chapter 8 showed that each member of a cartel is motivated to chisel to produce beyond its assigned production quota. If rms can vary quality as well as quantity, then to remain effective the cartel would have to control cheating in both dimensions. But it is often difcult to dene or measure quality unambiguously. This difculty was what led to the sandwich wars among international airlines in the 1970s. In that period international cartel agreements xed international coach fares. To limit quality competition, the agreements also banned full on-ight meals. However, the airlines were permitted to offer their customers sandwiches. The result: sandwiches grew more and more elaborate, eventually becoming sumptuous meals in themselves. EXAMPLE 9.3 THE JAPANESE AUTO EXPORT CARTEL With the aim of protecting manufacturers of American cars, in 1981 the United States induced Japan to limit its automobile exports to the United States. (In these negotiations little attention was paid on either side to the interests of U.S. consumers!) The agreement effectively converted the Japanese auto industry into a highly profitable export cartel. Japanese auto manufacturers, previously unable or unwilling to agree on export quotas, had competed with one another in quoting relatively low prices for cars exported to the United States. Thanks to the successful American diplomatic prodding, Japans Ministry for International Trade and Industry agreed to limit exports by assigning export quotas to the various Japanese auto manufacturers. The effect upon the protability of Japanese auto companies was drastic. Corporate shares in Japanese auto rms rose by an average of around 24% in the single month when the arrangement was announced.a The reduced numbers of Japanese cars available raised the U.S. prices of Japanese cars in comparison with those of American-made cars. But there was also a quality effect. Since the export controls limited only the numbers of Japanese cars sold in the United States, the cartelized Japanese exporters still competed with one another in the quality dimension. According to a study by Robert C. Feenstra, though the price index of Japanese cars in the United States rose by 48.3% in the period 19801985, the quality index also rose by 25.4%. So the increased quality offered to consumers of imported Japanese cars offset about half the observed price increase.b a Arthur T. Denzau, Made in America: The 1981 Japanese Automobile Cartel, Center for the Study of American Business, Washington University (August 1986). b Robert C. Feenstra, Quality Change under Trade Restraints: Theory and Evidence from Japanese Autos, Department of Economics, University of California, Davis (May 1986). P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 266 9. PRODUCT QUALITY AND PRODUCT VARIETY Red Violet Orange Smallest Largest Blue Green Yellow Panel(a) LinearPreferences:Size Panel(b) CircularPreferences:Color Figure 9.4. Linear versus Circular Preferences For a characteristic such as size, individual consumer preferences range from smallest to largest. For a characteristic such as color, individuals preferences may be thought of as distributed around a ring. For simplicity, assume the preference distribution is uniform over the linear range in the one case, or around the circle in the other case. 9.2 VARIETY How do product markets respond to variations in consumer tastes or needs? Just as quality has several possible dimensions, variety has many possible aspects. Manufacturers of womens dresses, for example, attempt to meet consumer requirements by offering many combinations of size, fabric, color, and cut. Imagine a single dimension of variation for example, clothing size or color. Sizes vary from large to small. Consumer size preferences can be imagined as distributed over a line-segment as in Panel (a) of Figure 9.4. A consumer preferring a small size can be regarded as located toward the left; a consumer preferring a large size toward the right. Size has a lower limit and an upper limit. It will be more convenient here to think of a product attribute such as color, which can be illustrated as a ring in Panel (b) of the diagram. Imagine that as many people prefer red as yellow as green and so on. So consumers can be thought of as distributed uniformly around the color circle. As a geographical analogy, the product characteristic (color) most desired by any consumer can be thought of as a specic point on the ring; call this point the consumers consumption locale. Similarly, any variety produced and sold can be regarded as a production locale. The distance around the circle between the two locales measures the extent of imperfect matching between preferences and products. For example, a consumer looking for a true blue dress (consumption locale) may nd that only greenish-blue or reddish-blue garments (production locales) are available on the market. The loss suffered from imperfect color matching is the economic equivalent of having to pay the cost of (metaphorically) transporting the good from point of sale to point of consumption. The value of variety is illustrated in Figure 9.5. Here the limiting (highest) aggregate consumer demand function D represents the ideal case. Imagine there are an innite P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 9.2 VARIETY 267 P Pc Figure 9.5. Aggregate Demand as Related to Number of Producing Plants D1 , D2 , . . . , D show the rising aggregate effective demand, as viewed by a monopolist seller, achieved by increasing the number of plants (production locales) spaced evenly around the ring of Figure 9.4. Effective demand increases with the number of plants, because consumer preferences are better matched (there is less wastage in transport costs). However, demand grows at a decreasing rate. D D10 D1 0 D2 Output number of production locales spread evenly around the ring ( N = ), so every consumer can be located at a production locale. Then there are no transport losses, so consumer desires for the product are fully reected in the D demand curve. At the opposite extreme, curve D1 shows the aggregate demand when there is only a single production locale at some arbitrary point on the circle. Here the most distant consumer must pay for shipment halfway around the ring. The average loss of value (transport cost) per consumer then corresponds to a quarter-circle of circumference about the ring. Similarly, D2 is the effective demand curve with two production locales, located 180 apart. The average consumer is then separated by an eighth-circle from the nearest production locale, and so forth. Note that the curve of aggregate demand shifts upward, but at a decreasing rate, as the number of production locales rises that is, as the assortment of products on the market more closely approximates the distribution of consumer preferences. EXAMPLE 9.4 RELIGION: THE VALUE OF VARIETY In countries with an established church, religion is somewhat like a monopoly. At the extreme, if all other religions were prohibited, there would be only one production locale. But most countries, with or without an established church, are characterized by varying degrees of competition among different sects and denominations. Laurence R. Iannaccone studied the religious worship records of Protestant denominations in several Western countries where Protestants constituted the major religious group.a The table relates weekly religious attendance to the degree of concentration of church membership. Concentration could range from 100% (if there was only one church) to practically 0% (if each person had his or her own denomination). The table indicates that high concentration is associated with low religious attendance. The range is from the United States (2% concentration, 43% attendance) to Denmark (94% concentration, 3% attendance). It appears that consumers have varied preferences for religions, as they have for clothing or automobiles. So a single predominant religion will be a poor t for many consumers, who in consequence opt out of religious observance. P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 268 9. PRODUCT QUALITY AND PRODUCT VARIETY In addition, with more competition religious organizations will likely strive harder to meet the needs of present and prospective members. Religious attendance and concentration (Protestant denominations) % attendance United States Canada Netherlands Switzerland W. Germany Australia New Zealand Britain Norway Sweden Finland Denmark 43 31 27 25 21 21 20 14 8 5 4 3 Concentration (%) 2 3 10 21 23 18 21 40 85 72 92 94 Source: Estimated visually from Iannaconne, Figure 1 (p. 158). a Laurence R. Iannaconne, The Consequences of Religious Market Structure, Rationality and So- ciety, v. 3 (April 1991) Product Variety under Monopoly A monopolist must decide on the prot-maximizing assortment of products to offer consumers. Its rst problem is how many varieties to produce. In the geographical metaphor this becomes the number N of distinct production locales (manufacturing plants) to establish around the ring of Figure 9.4. (A nearly production source is, for a consumer, analogous to a product that closely matches his or her needs.) The next decisions for the monopolist are how much of each variety to produce (the scale of output at each production plant) and what prices to charge. An increase in the number of varieties (production locales around the ring) reduces the average gap between what the consumer wants and what he or she nds in the market. The smaller the average gap, the higher will be the average price consumers will be willing to pay. (Consumers would be willing on average to pay more if shirts were offered in sizes 28, 30, 32, . . . , 50 rather than only Small, Medium, and Large.) What prevents carrying this process to the limit attaining the D demand curve is economies of scale. Over some range, Average Cost per plant may fall as plant output expands. So the monopolist must balance the savings in production costs from offering fewer varieties against the additional revenue that a more varied assortment of products would make possible. Suppose that costs of production are the same regardless of location around the ring, and that consumers are uniformly distributed around the ring. Then the rm should locate its producing plants (whatever their number) evenly around the circle. The price at the factory (the so-called f.o.b. price) must then also be identical at each producing P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 9.2 VARIETY 269 Figure 9.6. Monopoly Total Revenue and Total Costs, as Related to Number of Plants The aggregate Total Revenue curves TR1 , TR2 , . . . correspond to the aggregate demand curves (curves of Average Revenue) D1 , D2 , . . . in the previous diagram. As the number of plants N rises, Total Revenue TR N also rises but at a decreasing rate. The Total Cost curves TC1 , TC2 , . . . show the aggregate cost of producing any output Q with 1, 2, . . . plants. Under the assumption of an identical linear cost function each plant, TC N shifts upward by a constant amount as N rises (because an additional Fixed Cost is incurred each time a new plant is brought into production). The bold vertical segments show the highest achievable prot for each N; the greatest of these is the prot maximum , which occurs here at N = 4. Maximumprofit TC5 TC4 TC3 TC2 TC1 Dollars TR1 0 TR2 Output TR3 TR4 TR5 Q plant. Continuing with the geographical metaphor, each consumer will pay the f.o.b. price plus the transport cost from the nearest plant. Figure 9.5 showed how demand is affected by the number of production locales in this case, the number of plants N that the monopolist distributes around the preference ring. Now consider the cost side. Suppose the production costs for the monopolists nth production plant is: C n = A + Bq n (9.4) Here A is the xed cost of each plant, and B is the constant Marginal Cost. Let the number of identical plants be N, so that aggregate output is Q Nqn . Then overall Total Cost is: TC N = NCn = N ( A + Bq n ) = NA + BQ (9.5) How Total Cost varies with the number of plants N is shown by the dashed lines TC1 , TC2 , . . . in Figure 9.6. Since a xed cost of A is incurred per plant, the Total Cost of producing any aggregate output Q rises as the number of plants N increases. However, the Marginal Cost remains B per unit wherever that unit is produced. Figure 9.6 also shows Total Revenue functions for different numbers of plants. The Total Revenue curve with only one producing plant (corresponding to demand curve D1 in the previous diagram) is TR1 ; similarly TR2 is the Total Revenue curve with two plants (corresponding to D2 ), and so on. For any given number of plants N, the monopolist chooses the f.o.b. price P m and the associated quantity Q m by using the familiar condition Marginal Cost = Marginal Revenue. For each possible number of plants N, the rms prot is the maximum vertical distance between the TRN and TCN curves, shown in the diagram by bold linesegments. As plotted, initially increases as N rises. (The bold line-segment between the TR2 and TC2 curves is longer than the segment between the TR1 and TC1 curves.) This means that the revenue gain from better matching of products to consumers desires exceeds the increased cost arising from a larger number of production locales. But the gains from increasing N taper off. Meanwhile costs rise steadily as N grows, because an P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 270 9. PRODUCT QUALITY AND PRODUCT VARIETY additional xed cost A is incurred for each additional plant. There will, consequently, be an optimum number of plants. In Figure 9.6 the largest prot is achieved at N = 4: having exactly four production locales represents the best compromise between production costs and transport costs. Blending Monopoly and Competition Monopolistic Competition What happens to overall variety when competitors can enter, producing closely similar products? Assume now a number of rms, with free entry and exit. Furthermore, suppose each rm produces just a single variety of product. So a monopolistic element remains in the picture: each rm is the sole supplier of its own particular product. The market structure representing such a mixture of monopolistic and competitive elements is called monopolistic competition. Each rm offers a unique product that best satises its clientele: those customers whose preferences (consumption locales) closely match its product (production locale). A city, for example, may have a dozen supermarkets closely competing in many respects. Yet any single store, given its geographical location and other possibly unique features, may face a downward-sloping demand curve. That is, it might be able to raise prices slightly without losing all of its customers. So each rm under monopolistic competition is a price-maker, not a price-taker. Still, the store is not a monopolist. If it raises prices, customers can switch to some more or less similar store (some nearby production locale). How do the assortment of products and their associated prices under monopolistic competition compare with the monopoly situation? The question can be separated into two parts: (i) If the range of products offered were the same, would prices be lower (and the quantities offered therefore larger) under monopoly or under monopolistic competition? (ii) Which of the two market structures will offer consumers more varieties to choose from? In Figure 9.7 the demand curve D N and the associated Marginal Revenue MR N represent the situation of a monopolist with N plants. Since each plant serves a fraction 1/ N of the total demand, a single plants share of the overall demand is Dn D N / N . Similarly, Marginal Revenue for each plant is MRn MRn / N . If N = 4, the per-plant Dn and MRn curves would represent a quarter of the quantities along the corresponding D N and MR N curves. Given the assumed constant Marginal Cost MC = B , in the diagram the prot-maximizing solution is Q for a monopolist controlling all the N plants. This translates into production of q n at each of its separate plants. Thus aggregate output Q must satisfy MC = MR N . Or equivalently, the per-plant output level q N N satises MC = MRn . Either approach determines the same monopoly price P m . Now suppose the industrial structure changes from monopoly to monopolistic competition. Each of the monopolists production plants has become an independent rm. Increased competition, it can be anticipated, will lead to greater output and lower f.o.b. prices. But how does this work out? In Figure 9.8 the independent rms perceived demand curve dn is more elastic (atter) than the monopolists per-plant demand curve Dn . The curve dn is more elastic than Dn because, by lowering price relative to its neighbors, each rm can win some customers away from them. (Whereas, when the industry was one single rm, the monopolist P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 9.2 VARIETY 271 $/q DollarsperUnitQuantity Pm DN B Dn MRn 0 qn MRN N QN MC DN N MRN q, Q PlantOutputandAggregateOutput Figure 9.7. Monopoly Solutions: Aggregate and Plant For a given number of plants N, the monopolists effective aggregate demand curve is D N . Curve Dn = D N / N is the pro rata plant demand curve. MR N and MRn = MR N / N are the associated Marginal Revenue curves. Marginal Cost is assumed to be constant at the level B. The prot-maximizing aggregate output is Q (where MC = MR N ), and plant output is q n (where MC = MRn ). Of course, N Q n = Nq n . For either the plant or the rm solution, the same prot-maximizing price P m is found along the associated demand curve. $/q DollarsperUnitQuantity Pm P H dn MC mrn Dn B MRn 0 qn q qn PlantorFirmOutput Figure 9.8. Monopoly Plant versus Monopolistic-Competition Firm, at Monopoly Solution The solution for the monopoly plant, where MC = MRn at output q n and associated monopoly m price P is the same as in the preceding diagram. However, once the monopoly plant becomes an independent rm, at price P m the rms perceived demand curve is dn . This curve is more elastic than the pro rata demand curve Dn , because the rm can win customers from its neighbors if it lowers its price. The rm will therefore attempt to achieve the solution H at output q n , where Marginal Cost MC cuts the curve mr n . P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 272 $/q 9. PRODUCT QUALITY AND PRODUCT VARIETY DollarsperUnitQuantity Figure 9.9. Monopoly Plant versus Monopolistic-Competition Firm, at Monopolistic-Competition Equilibrium Pm P S dn MC mrn Dn B MRn qn q qn Curve mrm is the Marginal Revenue associated with the perceived (atter) rm demand curve dn . With N rms, point S in the diagram represents a monopolistic-competition equilibrium. Each rm is maximizing prot since MC = mrn . This outcome is consistent with equilibrium of the industry as a whole, because the combination of output q n and price P constitutes point on the pro rata demand curve Dn . Price is lower and output greater than in the monopoly case. 0 PlantorFirmOutput would not allow its separate plants to cut price at one anothers expense.) Corresponding to the more elastic rm demand curve dn is a higher perceived Marginal Revenue curve mrn .4 The rm in Figure 9.8 therefore maximizes prots at point H, producing output q n , where mrn = MC B . Since the rm produces an output q n that exceeds the monopoly per-plant output q n , it would have to set an f.o.b. price P lower than the m monopoly price P . Figure 9.8 suggests, correctly, that the output of a rm under monopolistic competition is greater than the per-plant output of an ordinary monopolist. The argument as presented, however, is awed: the solution with output q n sold at price P is not possible as an overall equilibrium of the industry. Since the rms are assumed identical, no single rm can sell more than its pro rata share of the overall demand the Dn curve in the diagram. The atter dn demand curve is therefore an illusion (just as the strictly horizontal demand curve faced by the rm in pure competition is an illusion). Any single rm can hope that, if it cuts price, it can expand output along dn . And indeed, if its competitors kept their prices unchanged, it could do so. But in equilibrium the N identical rms will all charge the same price. So if a rm cuts its price, others will do the same; sales per rm will expand less than expected. The rms all together will move along the steeper pro rata demand curve Dn curve rather than along their illusory dn curves. The nal equilibrium is represented in Figure 9.9 by point S on the pro rata demand curve Dn . The rm still perceives an illusory demand curve dn and its relatively at associated mrn curve. Now, however, the rms optimum MC = B = mrn leads to the price-quantity combination P , q n , which lies along the pro rata demand curve Dn . So the rms solution is now consistent with its pro rata share of the overall consumer demand. Each rms output, though not as large as Figure 9.8 had suggested, still exceeds the output the monopolist would set at each of its plants (q n > q n ). And the price to m consumers is lower ( P < P ). 4 Since MR P (1 + 1/), as the demand elasticity becomes greater (takes a larger negative value), Marginal Revenue is higher approaching P as goes to . P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 9.2 VARIETY 273 $/q DollarsperUnitQuantity Figure 9.10. Long-Run Equilibrium: Representative Firm in Monopolistic Competition The short-run equilibrium conditions of the preceding diagram continue to hold: MC = mr n , and the representative rms price-output combination at L lies on the true pro rata demand curve Dn . The additional long-run condition is that entry or exit takes place until the representative rm earns zero prot (price equals Average Cost AC n ). P L dn B Dn mrn ACn MC 0 q qn FirmOutput What about long-run equilibrium, for which entry and exit have to be taken into account? Depending upon the xed costs, in the short-run equilibrium of Figure 9.9 the typical rm might either be earning an economic prot (which would induce new rms to enter) or suffering an economic loss (which would induce some old rms to exit). Let us assume that the short-run equilibrium is protable, so that new rms enter. The true pro rata demand curve Dn D N / N then shifts inward (to the left); so does the illusory dn as viewed by an existing rm.5 Figure 9.10 shows the long-run solution for the representative rm as point L. Here all three equilibrium conditions are satised: (1) each rm chooses the level of output that maximizes prots (MC = mrn ); (2) the aggregate quantity that rms supply equals the quantity that consumers demand (the rms price-output combination is consistent with the pro-rata demand curve Dn ); and (3) no rms want to enter or exit (each rm earns zero economic prot). (The zero-prot condition is represented in the diagram by the tangency of the rms perceived demand curve dn with its Average Cost curve ACn at point L.) So the equilibrium output is Q n and price is Pn . At this equilibrium, total industry output is greater than what would be produced by a monopolist who owned all the different plants. Price under monopolistic competition is therefore lower than under monopoly. EXAMPLE 9.5 ADVERTISING AND COMPETITION The competitive element in monopolistic competition is greater, and the monopolistic element smaller, the greater the elasticity of demand. One inuence upon elasticity is the degree to which consumers know prices. If consumers are poorly 5 This shift is due to dividing the aggregate demand curve DN horizontally by a larger N. However, a larger number of varieties allows a better match to consumer desires. So as N rises, DN will also rise (see Figure 9.5). However, in the ratio DN /N that denes the Dn curve, the numerator rises less than the denominator. When the number of rms increases from 2 to 3, N increases by 50%. But, in general, consumers demand prices will increase by a smaller percentage. So the Dn curve must, at least eventually, shift inward as N rises. The same holds for the dn curve. P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 274 9. PRODUCT QUALITY AND PRODUCT VARIETY informed and do not know they can get better prices elsewhere, the demand curve facing each rm is less elastic so rms can charge higher prices. A natural experiment to test this hypothesis arose in New York in 1979. Because of a strike, the three major newspapers in New York City (the Times, Post, and Daily News) suspended publication from August 10 to October 5. A newspaper in neighboring Long Island, Newsday, continued publishing. Lacking their regular newspapers, shoppers in New York City had less access to supermarket food advertisements in comparison with residents of the suburban areas served by Newsday. Amihai Glazer studied prices for six products (peaches, grapes, lettuce, watermelon, chicken, and ground beef) in Queens County within New York City, in comparison with neighboring Nassau County outside the city.a He found that over the period August 1418, the rst week of the strike, prices in Queens supermarkets increased by 3.4% more than in Nassau supermarkets. In contrast, over the period August 23October 6, which saw the reappearance of the Post in New York City, Queens prices changed by about 8.8% less than in Nassau. These differential price changes were observed for supermarkets, which do normally advertise in newspapers, but were not observed for prices charged by small fruit and vegetable stores, which do not generally advertise in newspapers. Another study by Jeffrey Milyo and Joel Waldfogel examined changes in Rhode Island liquor prices after a Supreme Court ruling in 1996 permitting advertising of liquor prices.b Once advertising was allowed, stores cut prices of advertised liquors about 20%. But prices of other products, at both advertising and nonadvertising stores, did not change. a Amihai Glazer, Advertising, Information and Prices A Case Study, Economic Inquiry, v. 19 (October 1981). b Jeffrey Milyo and Joel Waldfogel, The Effect of Price Advertising on Prices: Evidence in the Wake of 44 Liquormart, American Economic Review, v. 89 (December 1999). A second question is: under monopolistic competition will consumers be offered more variety (in comparison with a multiplant monopolist)? In terms of the ring model, would the number of independent rms (each serving its own clientele) under monopolistic competition be greater or smaller than the number of separate production locales under monopoly? It turns out that the result could go either way. When the plants operated by a monopolist become independent competing rms, the per-plant prot declines. But these prots may still be positive. If so, new rms will enter, increasing the variety offered to consumers. On the other hand, when the separate plants become independent rms, what was a positive per-plant monopoly prot could turn into a per-rm loss. If so, some rms would exit, reducing variety. CONCLUSION Under monopolistic competition, aggregate output is greater and price is lower than under multiplant monopoly. But the number of independent rms under monopolistic competition, each offering its own unique variety, could be either larger or smaller than the prot-maximizing number of varieties offered by a monopolist producer. Thus, though consumers benet from a lower price under monopolistic competition, they may or may enjoy not a better assortment of varieties. P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 SUMMARY 275 EXAMPLE 9.6 CUSTOMIZATION IN THE U.S. ECONOMY In recent years the United States has seen an astounding increase in the range of product varieties offered consumers. A study by W. Michael Cox and Richard Alm documented this development,a as summarized in the table. Product choices in the U.S. economy Product type Vehicle models Vehicle styles Personal computer models Software titles Websites Movie releases Airports Amusement parks McDonalds menu items National soft drink brands Milk types Levis jean styles Running shoe styles Womens hosiery styles Contact lens types Bicycle types Early 1970s 140 654 0 0 0 267 11,261 362 13 20 4 41 5 5 1 8 Late 1990s 260 1,212 400 250,000 4,000,000+ 458 18,292 1,174 43 87 19 70 285 90 36 31 Source: Selected from Cox and Alm, Exhibit 1. Variety has increased not only for new products such as computers but even for long-established goods and services including movie releases, soft-drink brands, womens hosiery, bicycles, and milk. The authors emphasize that, by failing to allow for the value of variety, standard national income measures such as GNP drastically understate the real increases in consumer well-being that have taken place in recent decades. a W. Michael Cox and Richard Alm, The Right Stuff: Americas Move to Mass Customization, Federal Reserve Bank of Dallas, 1998 Annual Report. In the preceding Example, most of the tabulated products and services are probably generated by industries whose market structures more closely t the monopolistic competition model than the pure monopoly model. So, though a direct test is unavailable, there is ground for doubting despite the theoretical possibility that monopolies offer more variety. SUMMARY Firms can sometimes choose the characteristics of the product offered to consumers, including product quality and product variety. Quality refers to a characteristic like durability or reliability that is unambiguously desirable. Firms then effectively offer consumers some underlying service z generated by the product, with z equal to the physical output times the quality per unit of output. P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 276 9. PRODUCT QUALITY AND PRODUCT VARIETY In a competitive market, supply and demand for the service will determine its implicit price Pz . The rm will set its Marginal Cost of providing service equal to that price: MCz = Pz . In doing so it will balance generating more service by increasing quantity q and by improving quality . Varying production conditions can cause different rms to produce goods of differing qualities. In any case, the price of the nth rms product must be proportional to its quality: Pn = n Pz . A monopolistic rm would set MCz = MRz . So it would produce a smaller amount of the desired service than a competitive industry, and would generally do so by reducing both the quantity and the quality offered. A monopolist would always adopt an invention that reduces cost without hurting quality. Also, if consumers are fully informed, a monopolist would always adopt an invention that improves quality without raising production costs. If, however, consumers are initially imperfectly informed, rms have to consider whether it is worth while building a reputation for producing a superior product. The problem of variety arises when consumer tastes are distributed over some dimension such as size or color. A monopolist would choose a product assortment and associated prices and quantities so as to maximize its overall prot. Under monopolistic competition, each variety is produced by an independent rm. Each separate rm has some monopoly power (faces a demand curve that is not perfectly elastic). The competitive element in monopolistic competition is provided by rms producing similar though not identical products, to whom customers can transfer their business. In comparison with ordinary monopoly, monopolistic competition leads to greater aggregate output and lower price, but may not lead to more product variety. QUESTIONS The answers to daggered questions appear at the end of the book. 1. How does monopolistic competition differ from pure competition? From pure monopoly? 2. In monopolistic competition, why is the rms perceived demand curve atter than the true demand curve? 3. Why is the rms perceived demand curve in monopolistic competition analogous to the horizontal demand curve faced by the rm in pure competition? 4. If a monopolist normally produces a smaller quantity of a product than a competitive industry, is it correct to presume that the monopolist would normally also offer a product of lower quality? For Review 5. a. b. c. Would a monopolist ever suppress an invention that lowered the cost of producing its product without reducing quality? Would it ever suppress an invention raising quality with no increase of cost? Will consumers in either case necessarily be better off if the invention is adopted? 6. What conditions make it more protable for a rm to produce high-quality rather than low-quality products? 7. What is the trend toward mass customization in recent decades? What does it imply for the ability of GNP to measure real increases in consumer well-being? P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 QUESTIONS 277 8. A common criticism of markets is that sellers spend resources on advertising, an allegedly wasteful use of resources, which they recover by raising prices to consumers. Do advertising expenditures necessarily lead to higher prices? Why or why not? For Further Thought and Discussion 1. Some analysts assert that there is excessive competition among hospitals. Allegedly, too many hospitals acquire expensive diagnostic machinery such as CAT scanners, which remains idle much of the time. These analysts propose that in each community just one or a very few hospitals should obtain such devices; anyone validly needing to use them could be directed to those hospitals. Comment, in the light of the discussion in the text, about the quality of service likely to be provided by monopolized versus competitive industries. 2. Is there a reason to expect monopolistic competition (rather than pure competition) to emerge when the desired commodity is really a single quality characteristic contained in the marketed good? Explain. 3. Would the price-quantity equilibrium under monopolistic competition tend to lie between that achieved under pure monopoly on the one hand, and pure competition on the other? Explain. 4. Suppose that every peach looks good in the store, but half of them turn out to be inedible. Given that fact, suppose the consumers demand curve for peaches on the shelf is P = 100 2 Q . What would the demand curve be if all peaches were good? 5. Could a quality-improving invention in a competitive industry ever reduce consumer welfare? 6. It is sometimes argued that only relatively high-quality products can bear the cost of shipment to distant locations. Thus, California oranges shipped to New York are (on average) of better quality than those consumed by Californians at home. Does this follow from the analysis in this chapter? [Hint: Does it cost much more to ship high-quality oranges than low-quality oranges?] 7. Would imposition of a xed per-unit tax (e.g., 10 cents per gallon of gasoline) tend to increase or decrease the equilibrium quality of gasoline (miles per gallon) offered on the market? 8. Mr. A says: A monopolist will produce a product of higher quality, since cut-throat competition must lead to a decline in quality. Mr. B says: A monopolist produces a smaller quantity of product than would a competitive industry, and by the same logic will also produce a product of lesser quality. Is either correct, or are they both wrong? 9. In an attempt to reduce tobacco production and thereby raise prices received by tobacco farmers, a government program introduced in 1933 allotted quotas to farmers that xed the number of acres that could be planted. Over the years production expanded anyway, since the farmers responded by applying more fertilizer, irrigating more intensively, etc. In 1965 the program was reformed, replacing acreage limitations with quotas that xed the number of pounds that each farmer could sell. Would you expect the original and the reformed programs to have different effects upon the quality of tobacco produced by American farmers? Explain. 10. Suppose that in an initial period rms choose machinery and product designs that commit them to a particular level of quality for ve rather than two years. Explain why this increases the rms incentives to produce a high-quality product. 11. We stated in Section 9.1.2 that a quality-improving invention need not lead the monopolist to reduce Q, the amount of physical product produced. Prove this. [Hint: Convert Figure 9.2 (where the vertical axis is in total units) to a diagram like Figure 9.3 (where P1: JZP 0521818648c09.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:33 278 9. PRODUCT QUALITY AND PRODUCT VARIETY the vertical axis is in average-marginal units). The stretching of the Total Cost curve o from C z to C z in the total diagram implies that the MCz curve in the averagemarginal diagram is lower over some range. A lower MCz , together with a (nearly) level MRz , means that the prot-maximizing service output Z could be more than twice the preinvention amount.] 12. Explain why the various DN curves in Figure 9.5 eventually become parallel to the D curve. [Hint: Transport costs can be regarded as a tax upon consumption, but the tax is effective only for consumers who are not choked out of the market.] 13. Example 9.1 indicated a decline in the average selling price for used cars as the age of the car being sold increases. Suppose that we can observe the selling prices only of used cars that the owner wants to get rid of. Do you think that the decline in average selling price with age is a good measure of the decline in quality of the average car (whether sold or not) as it ages? P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 10 Competition Among the Few: Oligopoly and Strategic Behavior Strategic Behavior: The Theory of Games 280 Patterns of Payoffs 280 An Application: Public Goods Two-Person versus Multiperson Prisoners Dilemma 282 Pure Strategies 283 Mixed Strategies 286 10.1 10.2 Duopoly Identical Products 288 Quantity Competition 289 Price Competition 293 An Application: Most-Favored-Customer Clause 295 10.3 Duopoly Differentiated Products 297 Quantity Competition 297 Price Competition 298 10.4 Oligopoly, Collusion, and Numbers 300 An Application: The Kinked Demand Curve 300 Oligopoly and Numbers 302 SUMMARY 304 QUESTIONS 304 EXAMPLES 10.1 10.2 10.3 10.4 10.5 Mixed Strategies in Tennis 287 Pioneer Oligopoly Experiment 292 Standard Oil and John D. Rockefeller 294 Oligopoly and Price Rigidity 301 Concentration and Market Prices in Sweden 303 279 P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 280 10. COMPETITION AMONG THE FEW: OLIGOPOLY AND STRATEGIC BEHAVIOR An industry that consists of only a small number of rms is called an oligopoly. If there are just two rms, the term duopoly is used. Oligopoly stands between pure competition (many suppliers) and pure monopoly (a single supplier). Facing only a few competitors, each rm is in a strategic situation. In choosing its own price or output, it needs to consider how its rivals will individually react.1 The best price for rm A to charge depends on what rms B and C are charging, and similarly the best choices for B and C depend upon what rm A does. This chapter introduces the theory of games, the method used by economists to predict the likely outcomes when decision-makers nd themselves engaged in strategic choices.2 10.1 STRATEGIC BEHAVIOR: THE THEORY OF GAMES A game, in the mathematical sense, is a way of picturing social interactions. Two distinct elements must be kept in mind: (a) the pattern of payoffs, and (b) the protocol of play. The pattern of payoffs reects the mix of shared versus opposed interests. If a particular outcome is good for John, is it also good for Mary? Or can John make himself better off only by making Mary worse off? The other element, the protocol of play, corresponds to the rules of the game. Do the parties take turns, or do they move simultaneously? Can a chosen move be revoked? Are the players allowed to communicate? Both elements, the pattern of payoffs and the protocol of play, enter into all game-theory solutions. Patterns of Payoffs Table 10.1 is an illustrative payoff matrix reecting Paul Reveres famous ride. The redcoats had to come by land or by sea, and their choice could be observed from the steeple of Bostons Old North Church. Paul Reveres task was to carry the message (signalled by lanterns in the church steeple One if by land, two if by sea) to the American defenders at Lexington and Concord. In Table 10.1 the rows represent possible Attacker (British) strategies; the columns represent Defender (American) strategies. In each cell, the paired numbers are the payoffs: the rst number is the payoff to the Row player, the second the payoff to the Column player. If Defender correctly matches the point of attack, Attacker loses 10 and Defender gains 10. But if Defender makes the wrong choice, Attacker gains 25 and Defender loses 25. Notice that in this table the numbers vary from cell to cell, but within each cell they add up to a xed sum (zero). Such a pattern of payoffs, representing a situation of totally divergent interests, Table 10.1 Zero-sum game: land or sea? Defenders choice of strategy Land Attackers choice of strategy Land Sea 10, +10 +25, 25 Sea +25, 25 10, +10 1 2 Monopolistic competition (discussed in the preceding chapter), like oligopoly, falls between pure competition and pure monopoly. But in monopolistic competition there are, by assumption, enough rms so that no supplier has to consider the possible reactions of any single competitor. The path-breaking book on the theory of games, by the mathematician John Von Neumann and the economist Oskar Morgenstern, is titled Theory of Games and Economic Behavior. P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 10.1 STRATEGIC BEHAVIOR: THE THEORY OF GAMES 281 Table 10.2 Mutuality of interests: the coordination game Bs choice of strategy Right As choice of strategy Right Left +15, +15 100, 100 Left 100, 100 +10, +10 is called a constant-sum game. (Or in this case, more specically a zero-sum game, since the winners gain exactly equals the losers loss.) Table 10.2 pictures the opposite extreme, a pure Coordination Game. Here the players interests are in complete accord. Imagine two cars moving in opposite directions on an otherwise empty highway. Each driver can choose to drive on the right or to drive on the left. If they coordinate their choices to both choose Right, by assumption they obtain their best payoffs 15,15. Coordinating on Left is (as assumed here) not quite so good, with payoffs 10,10. (Perhaps the drivers nd it easier to drive on the right.) But the crucial point is that if they fail to coordinate, each loses 100 (the cars crash). Once again the numbers may vary from cell to cell, but now within each cell the payoffs are identical for the two players. Their interests are in complete harmony. Complete harmony of interests and total divergence of interests are the extreme cases. Intermediate situations can blend opposed and parallel interests in many different ways. An important class of situations, the Prisoners Dilemma, is illustrated in the payoff matrix of Table 10.3. Starting with Panel (a), suppose the police have apprehended two men, accomplices in a crime, but the evidence against them is weak. Lacking a confession, the authorities will be able to impose only a minor penalty. But if either prisoner confesses, conviction on a major count is guaranteed. Isolating the prisoners from one another, the district attorney offers to let either one go free in return for his turning states evidence provided that the other does not also do so. (If both confess, each will receive a reduced punishment.) In Panel (a) each prisoner has the strategy options Confess or Dont Confess. The degree of shared interests is indicated by the identical second-best payoffs (1 each) in the upper-left cell and their identical second-worst payoffs (24 each) in the lowerright cell. But the prisoners also have opposed interests, as shown in the other two cells: the best outcome for each (0) goes along with the others very worst outcome (36). Table 10.3 The Prisoners Dilemma: two versions Months of imprisonment Dont confess Panel(a) Dont confess Confess 1, 1 0, 36 Confess 36, 0 24, 24 Rank-ordered payoffs Small output Panel(b) Small output Large output 3, 3 4, 1 Large output 1, 4 2, 2 P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 282 10. COMPETITION AMONG THE FEW: OLIGOPOLY AND STRATEGIC BEHAVIOR Table 10.4 Farm drainage as a public good: a Prisoners Dilemma Pump Pump Dont pump 2, 2 5, 3 Dont pump 3, 5 0, 0 The dilemma here is that each does better confessing, regardless of what his accomplice does even though they could gain by both refusing to confess. Panel (b) of Table 10.3 is equivalent to Panel (a), except that the numbers in the cells indicate only the rank ordering of the outcomes. For each player 4 is best, 3 second best, 2 next, and 1 is worst. Any situation described by this rank ordering of payoffs corresponds logically to a Prisoners Dilemma. The rank-ordered pattern of payoffs in Panel (b) can be applied to chiselling in cartels (Chapter 8). If both rms abide by the cartel agreement and restrict output, the outcome is the second-highest payoff for each: 3,3. But, regardless of what the other rm does, each does better violating the agreement. If rm A abides by the agreement and limits its output, rm B can gain its best outcome of 4 by producing without restriction. And if rm A is a violator and does not limit its output, rm B does better for itself if it also produces without restriction (payoff of 2 rather than 1). International armaments represent another Prisoners Dilemma situation. All countries together might be better off in a disarmed world. But if other nations disarm, a single armed nation could successfully attack any of the others. And when all others are armed, no single nation is likely to expose itself by disarming unilaterally. The upshot is that all nations, or at rate the great majority of nations, continue to arm themselves. An Application: Public Goods Two-Person versus Multiperson Prisoners Dilemma A commodity is called a public good if its consumption by any one person does not reduce the amount available to others. If a public good is provided to any consumer, that makes it available to every consumer. A radio signal intended for receiver A can equally well be picked up by receivers B , C , D , . . . . An Internet website intended for one class of customer can equally well be visited by anyone else.3 Imagine a group of farmers attempting to improve marshy soil by drainage. In pumping excess water from his own eld, each individual farmer nds himself also partially draining his neighbors elds he is providing them with a public good. In that case it may not pay any single farmer to pump even if, were everyone to pump, all would be better off. In Table 10.4 the rank ordering of the payoffs is consistent with Panel (b) of Table 10.3. So this situation is once again a Prisoners Dilemma. For each farmer the strategy options are Pump and Dont Pump. Numerically, the table sets the per-farmer cost of pumping at 8, while the per-farmer benet is 5 multiplied by the number of pumpers. 3 A radio broadcast could be coded to exclude undesired users, and a website might require a password. When such exclusionary devices are effective, the commodity is no longer a public good. P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 10.1 STRATEGIC BEHAVIOR: THE THEORY OF GAMES 283 Table 10.5 Farm drainage as a multiperson Prisoners Dilemma Number of other farmers pumping Farmer As choices Pump Dont pump 0 3 0 1 2 5 2 7 10 3 12 15 4 17 20 So each farmer is individually better off choosing Dont Pump, even though the resulting 0,0 payoffs are worse for both sides than the 2,2 achievable if they were both to pump. Table 10.5 shows how the logic of the Prisoners Dilemma extends to more than two decision-makers. As before, for any single farmer A the choices are Pump and Dont Pump. The columns represent the number of other farmers, apart from A, who might also be pumping (and thereby helping to provide the public good). Under the assumptions here, the payoffs are such that Dont Pump always remains the better choice for farmer A regardless of the number of others who are pumping. And since farmer A is typical of all the others, no single farmer will provide the public good of drainage. So Table 10.5 represents a Multiperson Prisoners Dilemma. The Prisoners Dilemma payoff pattern is a kind of social trap. All the farmers would benet from an enforceable contract whereby each would provide his share of pumping, in consideration of everyone else doing the same. But each individual farmer has an incentive to cheat on such a contract. Later chapters will deal with Prisoners Dilemma and other possible social traps, together with ways of escaping them. Pure Strategies In game theory a solution is a prediction of the strategies that rational players will select in the light of opponents possible choices. Solutions depend upon both the pattern of payoffs and the protocol of play. For a given pattern of payoffs, the protocol (rules of the game) can vary in many ways. Consider one possible difference in the rules: whether the parties move simultaneously or in sequence. If the players move sequentially, the rules must also specify who goes rst and who goes last. [Note: Simultaneity in game theory refers not to clock times but to equivalent states of information. Choices are considered simultaneous even if A makes his choice rst in time, provided that B has to make her decision without knowing As.] In the Coordination Game (Table 10.2) under the sequential protocol of play, whoever moves rst should choose Right. The second mover will then rationally match the rst movers choice, so the solution is the strategy-pair (Right, Right) with payoff 15 to Row and 15 to Column. The solution concept just employed is called the perfect equilibrium.4 Each player makes a rational decision, on the assumption that the opponent will choose rationally when it comes to his or her turn. SEQUENTIAL PLAY 4 Or, more explicitly, the subgame-perfect equilibrium concept. P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 284 10. COMPETITION AMONG THE FEW: OLIGOPOLY AND STRATEGIC BEHAVIOR Table 10.6 The Entry-Deterrence game Player B (monopolist) Resist Player A (potential entrant) Enter Stay out 10, 30 0, 100 Tolerate 20, 80 0, 100 With regard to sequential-move solutions, two important questions are: (1) Who does better, the rst mover or the second mover? (2) Are the results efcient? That is, does some other pair of choices yield payoffs better for both parties, or at least better for one side without being worse for the other? In the Land or Sea game of Table 10.1, if the protocol calls (say) for Row as Attacker to move rst, there are two perfect equilibria: (Land, Land) and (Sea, Sea), each with payoffs 10,+10. The advantage is to the second mover. Although biased in this sense, the result remains efcient. No other strategy combination yields a better outcome for both players. In the general Prisoners Dilemma pattern pictured in Panel (b) of Table 10.3, the perfect equilibrium leads to payoffs 2,2 regardless of who moves rst. So there is neither a rst mover advantage nor a last mover advantage in Prisoners Dilemma games. But here the perfect-equilibrium solution is not efcient. If both players were instead to choose Dont Confess, their payoffs would be 3,3 rather than 2,2. Up to now all the illustrations have been of symmetrical games: each players situation is the mirror image of the others. Table 10.6, the Entry-Deterrence game, represents an asymmetrical situation. Suppose a monopoly currently exists, but a competitor threatens to enter. If entry occurs, the incumbent monopolist could Resist (by waging a price war to drive out the newcomer) or else might Tolerate the intrusion (so as to retain a share of its former monopoly prot). Suppose the protocol is sequential, with the potential entrant (Row) moving rst. Under the numerical assumptions here, the perfect-equilibrium strategy-pair is (Enter, Tolerate) with payoff 20 to the new entrant and payoff 80 to the former monopolist. But suppose the monopolist were to threaten the potential competitor: If you enter I will resist, which means you will get 10 rather than +20. So you had better stay out. If this threat were credible, Row should rationally stay out. Under the protocol assumed here, however, the threat is not credible. Given that entry has occurred, the monopolist loses by carrying it out. To make such a threat credible, the monopolist would have to somehow change either the payoffs or the rules of the game. Here is one possibility. The monopolist might say: You are not the only potential entrant I will be facing. I expect to be dealing repeatedly with potential competitors like you. This means that the payoff numbers in Table 10.6 are incorrect they dont tell the full picture. Because, if I give in to you now, others will expect me to do the same. To achieve a tough reputation and thereby deter others, I will simply have to resist if you enter. The monopolist is saying that the (Enter,Tolerate) payoffs are not 20,80 but perhaps something more like 20,0. If these were indeed the payoffs, the monopolist would rationally respond to Enter with Resist. Knowing this, the Row player should rationally choose Stay Out. (Possible disagreement or uncertainty about the payoffs will be taken up in the Information chapter that follows.) P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 10.1 STRATEGIC BEHAVIOR: THE THEORY OF GAMES 285 Table 10.7 Prots in duopoly Output of rm B Zero Output of rm A Zero Small Large 0, 0 1500, 0 2000, 0 Small 0, 1500 1300, 1300 1400, 800 Large 0, 2000 800, 1400 500, 500 EXERCISE 10.1 Table 10.7 shows the payoffs (prots) for duopolists who can each choose among the three strategies Zero, Small, or Large levels of output. (i) The protocol is sequential: rm A moves rst, then rm B. Find the perfect equilibrium. Is there a rst-mover or last-mover advantage? Is the solution efcient for the two rms together? (But recall that an efcient outcome for the two rms could hurt consumers.) (ii) Answer the same questions, but now assume that after rm B responds to As initial choice, rm A can then revise its own decision. (Thus rm A has both the rst move and the last move.) A N S W E R : (i) As best choice is Large output. B would respond with Small, and the payoffs are 1400,800. The rst mover has the advantage. The solution is efcient, since no other cell yields higher payoffs for both rms. (ii) It might seem here that rm A would benet from having both the rst move and the last move. But not so! Firm B should ignore As initial choice, which makes no difference for the nal outcome. Instead, rm B should act as if its own choice were the rst move, and choose Large. The nal outcome would be the strategy-pair (Small, Large) with payoffs 800,1400. (So what is involved here is really not a rst-move advantage but rather a last-move disadvantage.) SIMULTANEOUS PLAY Under the simultaneous-move protocol each player must make his or her choice without knowing what the opponent has decided to do. In the Prisoners Dilemma of Table 10.3, the Row player did better choosing the less cooperative strategy (Confess) no matter what Column chose. This means he does not have to know what choice Column might be making in order to pick his own best move. And Column can reason in exactly the same way. In game-theory terminology, in Table 10.3 the less cooperative strategy dominates the other strategy for both players. So the (Confess, Confess) strategy-pair is a dominant equilibrium. To see what happens when one side has a dominant strategy but the other doesnt, consider the Entry-Deterrence game in Table 10.6. Tolerate does not always give Column a strictly higher payoff than Resist. But Tolerate always yields at least as much and sometimes more. So it is natural to extend the previous reasoning and say that Column should always choose even such a weakly dominant strategy. Row, in contrast, has no dominant strategy. But, making the inference that Column will choose her weakly dominant strategy (Tolerate), Rows best move is clearly Enter. So the solution is (Enter, Tolerate). When neither side has a dominant strategy, a broader solution concept for the simultaneous-move protocol is the Nash equilibrium. (A dominant equilibrium, if it P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 286 10. COMPETITION AMONG THE FEW: OLIGOPOLY AND STRATEGIC BEHAVIOR exists, will also be a Nash equilibrium.) To nd the Nash equilibrium, look for a cell in the payoff matrix such that, even if the opponents strategy were revealed, neither party would benet from a unilateral change of move. In Table 10.2, for example, there is no dominance. But the (Right, Right) and (Left, Left) strategy-pairs are both Nash equilibria. If either of these were somehow arrived at, neither player would ever want to deviate into a 100,100 payoff situation. EXERCISE 10.2 Using Table 10.7, now assume a simultaneous-move protocol. Are there one or more dominant equilibria? Nash equilibria? A N S W E R : By inspection, there is no dominant equilibrium. But the strategy-pairs (Large, Small) with payoffs 1400,800 and (Small, Large) with payoffs 800,1400 are both Nash equilibria. Mixed Strategies Returning to Table 10.1, that payoff matrix has no dominant equilibrium. Furthermore, if the players are restricted to using only the pure strategies shown, there is no Nash equilibrium either. But a Nash equilibrium does exist in mixed strategies. A player choosing a mixed strategy in effect tosses a coin (the coin having known probabilities, not necessarily even, of coming up one way or the other) and moves accordingly. Let Attacker (Row) play Land with probability pR ; let Defender (Column) play Land with probability pC . That implies that Row plays Sea with probability 1 p R and Column plays Sea with probability 1 p C . Given these probabilities and the payoff numbers in Table 10.1, it is possible to calculate the average or expected payoff for each of the two possible strategies, for each player. For example, when Row plays Land he will receive 10 if Column plays Land and 25 if Column plays Sea. So the expected payoff is (10) p C + 25(1 p C ). Similarly, Rows expected payoff from playing Sea is 25 p C 10(1 p C ). The essential idea of mixed strategies is: Keep the opponent in doubt! With this aim, Column as Defender wants to choose a pC that makes neither Land nor Sea a clearly superior choice for the attacker. So she will choose a pC that makes Rows average payoff the same whichever strategy he chooses. Setting (10) p C + 25(1 p C ) equal to 25 p C 10(1 p C ), her solution is p C = 0.5. By corresponding reasoning, the solution for Row is p R = 0.5. So, the prediction is, the players will each randomly mix the two pure strategies on a 50:50 basis. More generally, the solution depends upon the payoff numbers, so it will not generally involve a 0.5, 0.5 mixture. For a payoff matrix in the general symmetric form of Table 10.8, algebra shows that the mixed-strategy equilibrium has Row choosing his rst (top) strategy with probability pR and Column choosing her rst (left-hand) strategy with probability pC in accordance with: P R = PC = d c a bc +d (10.1) P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 10.1 STRATEGIC BEHAVIOR: THE THEORY OF GAMES 287 Table 10.8 General symmetric payoff matrix Left Top Bottom a, a b, c Right c, b d, d One might think that mixed strategies are a purely academic idea with no practical application. On the contrary, mixed strategies can be observed whenever intelligent play involves keeping the opponent guessing. EXAMPLE 10.1 MIXED STRATEGIES IN TENNIS Tennis serves are usually aimed to the receivers left or right. (Center serves are unusual, at least in championship play.) Since the server needs to keep the receiver guessing, rational play dictates a mixed strategy. The best mixture will depend upon many factors: whether the players are right-handed or left-handed, possible weaknesses of forehands or backhands, individual peculiarities of play, the current point score, the direction of the sun, possible referee bias, and more. Despite these complications, the test of an optimal mixed strategy is that all the pure strategies being played must on average be equally protable. (If they were not, it would pay to choose the more protable option more often.) In particular, for the player with the service, serves to the left and serves to the right should have equal success rates. Mark Walker and John Wooders obtained data on all rst serves in 10 important professional tennis matches most of them nal championship matches.a If the players were choosing rationally, in a given match there might be a large disparity between the percentages of left and right serves, but left and right serves should have been, on average, equally likely to win points. Mixed strategies in championship play Mixture (%) Match Server Left 93 37 61 84 37 25 26 63 56 63 39.0% Right 7 63 39 16 63 75 74 37 44 37 Win rates (%) Left 71 70 61 67 73 63 80 72 61 73 10.4% Right 60 66 56 53 69 71 63 65 85 63 74 Wimbledon Rosewall 80 Wimbledon Borg 80 US Open McEnroe 82 Wimbledon Connors 84 French Lendl 87 Australian Edberg 88 Australian Wilander 88 Masters Becker 95 US Open Sampras 97 US Open Korda Average of differences Source: Adapted from Walker and Wooders, Table 1. The results reported here refer to the service choices of the ultimate match winner when the score was at deuce. The left-right mixtures are percentages that sum P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 288 10. COMPETITION AMONG THE FEW: OLIGOPOLY AND STRATEGIC BEHAVIOR to 1, since center serves (only about 6%) were not counted. The win rates for both left serves and right serves are all well above 50%, reecting the advantage at tennis of having the serve. (Winning was dened here as gaining the point, whether earned on the initial service as an ace or only after additional strokes.) The imbalance between left and right service proportions was sometimes very great. Rosewall at Wimbledon in 1974 served left 93% of the time. That was the extreme, but the percent differences between the proportions of left and right serves were generally quite large averaging about 39%. In contrast, the win rates for the two types of service were close together, diverging on average by only around 10%. The authors interpretation was that, unconsciously perhaps, championship tennis players appreciate the need to mix their strategy choices, and do so in a way close to the theoretical optimum. a Mark Walker and John Wooders, Minimax Play at Wimbledon, American Economic Review, v. 91 (December 2001). In warfare as in tennis, it is essential to keep the opponent in doubt. Military writers sometimes advise generals always to go round the enemys anks, never to make a frontal attack. But that cannot be right, since then the enemy could leave his center bare and place all his strength on the anks. General William Tecumseh Sherman, in his march through Georgia in 1864, usually preferred to attack the Confederates on one or the other ank. But at Kennesaw Mountain he made an unsuccessful frontal attack, a choice criticized by military historians. The critics failed to realize that, to remain unpredictable, Sherman had to follow a mixed strategy which dictated that he make frontal attacks some of the time. CONCLUSION In the sequential-play protocol, the perfect equilibrium concept has each player make a rational (payoff-maximizing) choice on the assumption that the opponent will do the same when it comes to his or her turn. A perfect equilibrium always exists, though it may not be unique. In the simultaneous-play protocol, a dominant strategy one that is better in the strong or weak sense no matter what the opponent does should be chosen if available. A dominant equilibrium exists if even only player has such a strategy available (since then the other player can predict what his opponent will do). In the absence of a dominant equilibrium, the Nash equilibrium concept applies. At a Nash equilibrium, no player has an incentive to alter his or her decision, given the others choice. There may be one, several, or no Nash equilibria in pure strategies. If mixed strategies probabilistic mixtures of pure strategies aimed at keeping the opponent guessing are also permitted, a Nash equilibrium always exists. 10.2 DUOPOLY IDENTICAL PRODUCTS Apart from the discussion in the preceding Chapter 9 (Product Quality and Product Variety), most of the analysis in the text has assumed that rms in an industry are offering identical products. The same simplifying assumption is used here in this section of the chapter. Section 10.3, which follows, will then take up the more realistic assumption that the products offered by competing oligopolists vary from rm to rm. P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 10.2 DUOPOLY IDENTICAL PRODUCTS 289 Table 10.9 Duopoly solutions, industry demand curve: P = 100 (q1 + q2 ), zero cost of production q1 Symmetrical Collusive Cournot Competitive Asymmetrical Stackelberg Threat 25 1 33 3 50 50 50 q2 25 1 33 3 50 25 0 Q 50 2 66 3 100 75 50 P 50 1 33 3 0 25 50 1 1,250 1 111 9 0 1,250 2,500 2 1,250 1 1,111 9 0 625 0 For a monopolist providing a single uniform product, the same prot-maximizing optimum can be achieved either by choosing the most protable price or the most protable quantity. (Because along the industry demand curve, the chosen price will determine the quantity that can be sold and vice versa.) But in oligopoly or duopoly, it makes a difference whether the rms engage in quantity competition or price competition. These will be taken up in turn. Quantity Competition Consider two duopolists producing an identical product. Firm 1 chooses a level of output q 1 and rm 2 chooses q 2 . Suppose the industry demand curve is P = 100 Q , where industry output Q is the sum of the two rm outputs: Q q 1 + q 2 . And imagine, for extreme simplicity only, that the Total Cost, Average Cost, and Marginal Cost functions are all zero throughout. (This unlikely assumption might be approximated by a situation where each rm owns a mineral spring gushing forth costlessly in unlimited volume.) A monopolist would set Marginal Revenue equal to Marginal Cost. Numerically, here, the MR = MC condition would be 100 2Q = 0,5 implying Q = 50. The monopolist, though able to produce any amount without cost, would offer only Q = 50 units at price P = 50. Its Total Revenue would be R P Q = 50 50 = 2,500. And, since costs are zero, the monopolists prot is = R = 2,500. What happens when the industry is a duopoly instead? Table 10.9 summarizes several of the possible outcomes.6 The upper part of the table shows possible symmetrical outcomes for rms operating under a simultaneous-move protocol. First, the Collusive solution occurs when the two rms act together as a collective monopolist or cartel, sharing the gain equally. (By assumption, the chiselling problem has somehow been solved.) Since joint prot is maximized when Q = 50 and P = 50, the rms separate outputs are q 1 = q 2 = 25. The prots are 1 = 2 = 50 25 = 1,250. If the rms cannot collude, several other possibilities arise. Skipping to the third line of the table, the opposite extreme is the Competitive solution. This holds if the rms behave as price-takers, each using the decision rule Marginal Cost = Price. Since Marginal Cost = 0, a price-taking rm would be willing to produce an indenitely large amount at any price P even innitesimally greater than zero. So, in effect, the 5 6 Recall that if P = A BQ, then MR = A 2BQ. The discussion here is based in part on M. Shubik, Information, Duopoly, and Competitive Markets: A Sensitivity Analysis, Kyklos, v. 26 (1973), p. 748. P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 290 q2 q2 OutputofFirm2 10. COMPETITION AMONG THE FEW: OLIGOPOLY AND STRATEGIC BEHAVIOR A Figure 10.1. Duopoly Reaction Curves Identical Products, Quantity Competition C q2 q2 B D E RC1 0 RC2 q1 Given any output q 2 of rm 2, rm 1 can determine its prot-maximizing output q 1 . Considering all possible levels of q 2 , a Reaction Curve RC1 for the rst rm is dened. Similar reasoning (based on taking q 1 as given) leads to the construction of RC2 , the Reaction Curve of the second rm. The intersection of the two Reaction Curves determines the NashCournot equilibrium. A hypothetical dynamic process A B C D suggests how the equilibrium at E might eventually be attained. q1 q1 OutputofFirm1 competitive supply curve runs along the horizontal axis with equation P = 0. Combining this with the demand curve P = 100 Q implies that at competitive equilibrium P = 0 and Q = 100. Revenue and prot will be zero for both rms. On the second line of the table, lying between the Collusive and the Competitive outcomes, is the Cournot solution. Here the underlying assumptions are as follows: (1) Each rm recognizes that increasing its own output will reduce the market price P. (2) However, in making its own output decision each rm assumes its competitors output is xed. That is, each decision-maker chooses the highest available payoff given the decision of the other. (The Cournot solution corresponds therefore to the Nash equilibrium in game theory.) The rationale for the Cournot solution goes as follows. For any output q2 chosen by the second rm, the rst rm has some prot-maximizing q 1 . In effect, rm 1 is a monopolist over the remaining demand not satised by the second rms output q 2 . Plotting rm 1s optimal q 1 as a function of all of its rivals possible outputs leads to the Reaction Curve RC1 shown in Figure 10.1. Firm 2 has a corresponding Reaction Curve RC2 . The Reaction Curves are mutually consistent only at the point of intersection, which therefore denes the Cournot equilibrium. (When the rms are both on their Reaction Curves, each is responding optimally to the others decision, so neither will want to change.) The NashCournot solution lies between the two extremes represented by the Collusive and Competitive solutions. Figure 10.1 also illustrates a possible dynamic process leading to the Cournot equio librium. Suppose rm 2 initially produces q 2 . The curve RC1 indicates that rm 1 will then want to produce q 1 in response (point A in the diagram). But if rm 1 produces q 1 , rm 2 reacts by moving to point B on its Reaction Curve RC2 to produce q 2 . Firm 1 responds further by moving to point C; rm 2 then moves to point D, etc. The result is that both rms end up at the intersection of the two Reaction Curves.7 7 There will be a stable equilibrium if the cobweb of dynamic reactions spirals inward (as shown in the diagram) rather than outward. If the labels of the two RC curves were interchanged, there would be an outward rather than an inward spiral in which case one of the rms would end up with a sole monopoly of the industry. P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 10.2 DUOPOLY IDENTICAL PRODUCTS 291 q2 100 Figure 10.2. Linear Reaction Curves Identical Products, Quantity Competition The straight-line Reaction Curves correspond to the data of Exercise 10.3. The rms demand curves are P1 = P2 = 100 q 1 q 2 , and production is assumed costless (MC1 = MC2 0). OutputofFirm2 RC1 50 E (331/ 3,33 1/ 3) RC2 50 OutputofFirm1 100 q1 EXERCISE 10.3 Use the numerical assumptions of Table 10.5 to nd the equations for the Reaction Curves RC1 and RC2 . Verify that their intersection is indeed the Cournot solution shown in the table. A N S W E R : If rm 1s output q1 is given, the demand equation for rm 2 is P = (100 q1 ) q2 , with rm 2 regarding q1 as constant. Since this is a linear demand equation, rm 2s Marginal Revenue is MR2 = (100 q1 ) 2q2 . To obtain rm 2s best choice of q2 as a function of rm 1s different possible choices of q1 , set MR2 = MC2 . Since Marginal Cost MC2 is zero, the equation becomes 100 q1 2q2 = 0, so that q2 = 50 q1 /2. This is the equation for RC2 . Similar reasoning yields q1 = 50 q2 /2 as the equation for RC1 . Solving the two Reaction Curve equations simultaneously, the solution is q1 = q2 = 33 1/3, as shown in Table 10.9 and pictured in Figure 10.2. Zero Marginal Cost is of course an extreme assumption. The exercise that follows employs a more normal Marginal Cost function. EXERCISE 10.4 Use the same industry demand function P = 100 Q as before, where Q q1 + q2 . But now suppose the rms Marginal Cost functions are MC 1 = 20 + q1 and MC 2 = 20 + q 2 . Find the Reaction Curves and the Cournot solution. A N S W E R : For rm 1, setting MR1 = MC1 implies 100 2q1 q2 = 20 + q1 , which reduces to 80 3q1 = q2 . This is the equation for RC1 . By similar reasoning, rm 2s Reaction Curve is 80 3q2 = q1 . Solving simultaneously, the equilibrium outputs are q1 = q2 = 20. Therefore Q = 40, the equilibrium price is P = 60, and prots are 1= 2 = 600. (The positive costs of production make the outputs and prots smaller than for the corresponding Cournot solution in Table 10.9.) P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 292 10. COMPETITION AMONG THE FEW: OLIGOPOLY AND STRATEGIC BEHAVIOR EXAMPLE 10.2 PIONEER OLIGOPOLY EXPERIMENT The economist Lawrence E. Fouraker and the psychologist Sidney Siegel jointly conducted one of the rst controlled economic experiments.a The experiment simulated a duopoly situation. Each subject, paired with an unknown counterpart, was asked to choose an output. The prot earned depended upon the quantities offered by the two sellers together. One group of trials was conducted under conditions of complete information: each subject knew the counterparts output choice and prot schedule. A second group of trials was conducted under incomplete information: each subject knew only the quantity decision of the other player. There were 28 trials 14 for each of the two informational conditions. In the complete-information case, 5 results were closest to the Collusive solution, 71/2 to the Cournot solution, and 11/2 to the Competitive solution. (The fraction represented a tie.) In the incomplete-information case, all 14 trials most closely approximated the Cournot solution. COMMENT This experiment suggests that the NashCournot solution, where each participant takes as given the quantity decision of the other, is likely to describe outcomes in oligopoly situations especially in the absence of additional information. Consistent with the NashCournot model, the subjects usually failed to achieve the Collusive arrangement. On the other hand, they seemed aware of how their separate output decisions would affect price, and so were usually able to avoid the disastrous Competitive outcome. The sensitivity of the experimental observations to the informational conditions was also an important nding. Later studies showed that other details of the market process for example, whether prices are secretly negotiated or openly posted affect how closely the nal outcome approaches the collusive or the competitive end of the spectrum of possibilities.b a L. E. Fouraker and S. Siegel, Bargaining Behavior (New York: McGrawHill, 1963). b Charles R. Plott, Industrial Organization Theory and Experimental Economics, Journal of Eco- nomic Literature, v. 20 (December 1982). In the lower portion of Table 10.9 the rms payoff functions remain symmetrical, but the protocol is asymmetrical. Suppose that rm 1 moves rst and is aware of the other rms Reaction Curve RC2 . These conditions correspond to the Stackelberg8 solution in the table, the rst mover having the advantage. More specically, suppose the leader (rm 1) sets an output and commits to it. If so, the follower (rm 2) does best by choosing the corresponding point along its Reaction Curve RC2 . Of course, the leader will choose that output q1 which, when combined with the followers correctly predicted output q2 , leads to the most protable outcome for itself. 8 Heinrich von Stackelberg, 20th-century German economist. P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 10.2 DUOPOLY IDENTICAL PRODUCTS 293 EXERCISE 10.5 Verify the Stackelberg solution shown in Table 10.9. A N S W E R : Since rm 1 is the leader, it chooses the most protable output for itself, knowing that rm 2 will respond along its Reaction Curve RC2 . In Exercise 10.3 rm 2s Reaction Curve was found to be q2 = 50 q1 /2. Substituting in the industry demand curve, P = 100 (q1 + q2 ), leads to the net demand curve facing rm 1: P = 50 q1 /2. Since this is linear, the Marginal Revenue equation for the Stackelberg leader is MR1 = 50 q1 . Setting MR1 = MC, where MC = 0 as assumed here, the leaders optimal output is q1 = 50. The other values shown in Table 10.9 for the Stackelberg solution can then be veried. Last, the Threat solution in Table 10.9 has the leader respond to entry by carrying out a threat to make q1 so big as to lower the price to zero. Seeing no way to make a prot, the second rm would stay out. Here the leader rm does as well as if it had the sole monopoly of the industry. As in the Entry-Deterrence Game (Table 10.6), such a threat is not credible under the protocol and payoff assumptions used. The symmetrical Collusive solution is also not achievable under these assumptions, owing to the chiselling problem. These solutions might, however, be realized under protocols not considered here, for example ones in which a threatener can guarantee to carry out his threat. The threatener might, for example, post a bond to be forfeited if he fails to follow through. (Ones reputation can sometimes serve as such a bond.) But posting a bond or staking ones reputation would then have to be listed as additional strategy options, making for a different game. Price Competition Rather than just supplying quantities to the market, rms more usually compete by quoting prices to consumers.9 It turns out that price competition is more severe than quantity competition. The reason is that, if the products are identical, a rm that quotes a price lower than its competitors takes away not just part of the market but all of it. Suppose that Marginal Cost is MC = 0 for both rms, and that rm 1 quotes some positive price P1 . Firm 2 will then set its P2 just a trie lower. But then rm 1 can go still lower, and so on until the nal stopping-point where P 1 = P 2 = 0! More generally, when duopolist rms choose prices, the Nash outcome (called the Bertrand10 solution, analogous to the Cournot solution under quantity competition) is the same as the Competitive equilibrium: P 1 = P 2 = MC . The following exercise uses the more realistic nonzero Marginal Cost of Exercise 10.4 to obtain a solution that involves positive prices P1 and P2 . 9 10 To illustrate the distinction, a shareholder can sell stock by placing a market order for a specic number of shares with his broker. Placing a market order means that the seller will accept whatever is the current market price. Alternatively, the shareholder can place a limit order that species a minimum acceptable price. Joseph L. F. Bertrand, 18221900, French mathematician. P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 294 10. COMPETITION AMONG THE FEW: OLIGOPOLY AND STRATEGIC BEHAVIOR EXERCISE 10.6 Using the same data as in Exercise 10.4, nd the NashBertrand solution. A N S W E R : Each rm will undercut the others price as long as it gains from so doing. So in equilibrium they must charge the same price P 1 = P 2 = P . Furthermore, these prices must be equal to the respective Marginal Costs MC1 and MC2 . The condition MC 1 = P becomes 20 + q1 = 100 q1 q2 . The corresponding equation for rm 2 is 20 + q2 = 100 q1 q2 . Solving simultaneously gives q1 = q2 = 26 2/3. Since total output is Q q1 + q2 = 53 1/3, the equilibrium price is 46 2/3. This checks with the numerical values of MC1 and MC2 . The preceding exercise illustrates the assertion that price competition is more severe than quantity competition. The outcome under price competition is less favorable for the rms but more favorable for the consumers (output is larger and price is lower) than the corresponding Cournot solution for quantity competition obtained in Exercise 10.4. Consider next the Stackelberg solution, assuming price is the decision variable and the rms have the same costs of production. The follower (second mover) will always do better than the leader (rst mover). If the leader sets a price leaving him any prot at all, the follower will quote a price a bit lower and take away all the business. Since neither rm will want to be the Stackelberg leader, we would not expect to observe Stackelberg equilibria under these conditions. In contrast, the asymmetrical Threat solution is still valid when price is the decision variable. Here rm 1 as leader would announce that if rm 2 attempts to do any business at all, by either matching or undercutting the leaders price, rm 1 will quote a price so low as to drive out its competitor. If rm 2 believes this threat, it may as well stay out of business completely. Firm 1 gains all the prot, as shown on the bottom line of Table 10.9. Once again, however, to make such a threat credible either the payoff structure or the protocol of the game, or both, must have changed. EXAMPLE 10.3 STANDARD OIL AND JOHN D. ROCKEFELLER Predatory price-cutting corresponds to the Threat solution of Table 10.9, with price rather than output as the decision variable. A ruthless rm with sufcient resources might always stand ready to wage a price war to drive out any competitors. Having achieved a reputation for doing so, such a predator would not need to execute its threat very often. Occasional punishment meted out to foolish interlopers would sufce to deter others. John D. Rockefellers old Standard Oil Company dissolved in 1911 as a result of a landmark antitrust decision is often described by historians as a predator. Standard Oil had acquired, before that date, substantial monopoly power in oil rening through merger and acquisitions. It is widely believed that these mergers and acquisitions were mainly secured by predatory price-cutting. But a study by John S. McGeea demonstrated that Standard Oil rarely if ever started costly price wars to achieve its monopoly. Rather, it bought out its competitors. However, Elizabeth Granitz and Benjamin Kleinb showed that the competitors were willing to sell out at prices favorable to Standard Oil only because of indirect P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 10.2 DUOPOLY IDENTICAL PRODUCTS 295 pressures that Standard exerted through railroad rates. Before the 1870s, the three major railroads that transported petroleum products from the Pennsylvania oil regions had repeatedly attempted to form a cartel. The familiar chiselling problem led in each case to breakdowns and rate wars. Standard Oil found an innovative way to enforce the railroad cartel. Once the roads had agreed upon shipment quotas, Standard served as an evener. If any single railroad secretly cut prices, its trafc would visibly increase. So Standard would simply reduce its own shipments on that road. For its services to the cartel as an evener, Standard was given preferential shipping rates. In 18741979 Standard received a 10% rebate, plus a commission on all shipments (not just on Standards own oil) received through Standards pipeline collection network. For example, while the regular rate in 1878 for shipments to New York was $1.70 per barrel, Standard paid only $1.06. This handicap induced many of the independent oil reners to sell out to Standard. The discovery of new elds in Ohio (1885) and especially in Texas (1901) weakened Standards position. Several new reners entered, other railroads were transporting oil, and Standard had no established transport network in the new areas. So Standard lost its effective monopoly of the petroleum industry. a J. S. McGee, Predatory Price Cutting: The Standard Oil (NJ) Case, Journal of Law and Economics, v. 1 (October 1958). b Elizabeth Granitz and Benjamin Klein, Monopolization by Raising Rivals Costs: The Standard Oil Case, Journal of Law and Economics, v. 39 (April 1996). CONCLUSION When duopolists produce identical products, the possible outcomes depend upon the nature of the payoffs (as determined by the market demand curve and the rms cost functions) and the protocol of play, together with the assumed behavior of the decision-makers. If quantity is the decision variable and the simultaneous-move protocol applies, at one extreme the rms may behave as a joint monopolist (the Collusive outcome) and at the other extreme as price-taking competitors (the Competitive outcome). The Nash solution is the intermediate Cournot equilibrium: each rm chooses optimally, given the other rms production quantity. When price is the decision variable instead, the Nash solution is called the Bertrand equilibrium: each rm chooses a prot-maximizing price, given the others price. Price competition is more severe than quantity competition, and so leads to worse outcomes for the rms (but better outcomes for the consumers). For the sequential-move protocol, the Stackelberg leader (the rst mover) is at an advantage under quantity competition but at a disadvantage under price competition. An Application: Most-Favored-Customer Clause11 Oligopolists might collude by offering buyers price guarantees. Imagine that only two rms, A and B, sell steel in a small country. For simplicity, suppose each rm considers only two possible price quotations, High and Low. The prot payoffs of Table 10.10 11 This analysis is based largely upon Steven C. Salop, Practices That (Credibly) Facilitate Oligopoly Coordination, in Joseph E. Stiglitz and G. Frank Mathewson, eds., New Developments in the Analysis of Market Structures (Cambridge, MA: M.I.T. Press, 1986). P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 296 10. COMPETITION AMONG THE FEW: OLIGOPOLY AND STRATEGIC BEHAVIOR Table 10.10 The Prisoners Dilemma: oligopoly prots Firm 2 price High Firm 1 price High Low 100, 100 140, 10 Low 10, 140 70, 70 indicate that the duopolists are once again caught in a Prisoners Dilemma. If both choose High, each rm can attain its second-best outcome (numerically, a prot of 100). Yet for either rm Low yields higher prot regardless of what the other does. So the two are likely to end up at their next-to-worst outcome the Prisoners Dilemma equilibrium strategy-pair (Low, Low) yielding a prot of 70 each. Each rm could charge the high price provided the other did the same. But suppose such agreements are illegal or unenforceable. The Most-Favored-Customer clause is a subtler way of achieving the same effect. Imagine that the duopolist generously guarantees each customer that, if it were ever to offer a reduced price to anyone else, the rst customer would get the same low price. It may seem that the rms clientele ought to be happy about the Most-Favored-Customer clause. But notice in Table 10.11 how the payoffs have changed in comparison with Table 10.10. The assumption here is that, if the rm were ever to cut price, the cost of carrying out its guarantee would be 50 units. Thus, for each rm the prot from pricing Low when its competitor is pricing High falls from 140 to only 90. Thus the strategy-pair (Low, Low) with payoffs 70,70 is no longer a dominant equilibrium. True, it remains a Nash equilibrium, but so is the mutually more protable strategy-pair (High, High) with payoffs 100,100. The rms are likely to be able to coordinate on this superior solution. This is an instance of a more general paradox often encountered in strategic situations. A player is sometimes better off sacricing an opportunity. Here the sacrice arranging to lose rather than to gain prot by cutting price makes it likely that neither rm will want to cut price. A different arrangement with somewhat similar consequences is the Meet-or-Release clause. The seller would guarantee a buyer who has not yet taken delivery that any lower price on the market will be matched, else the customer is released from the obligation to buy. (The Most-Favored-Customer clause guarantees that buyers will get the advantage of the sellers own later price cuts, if any; Meet-or-Release guarantees that buyers will get the advantage of other rms lower prices.) The Meet-or-Release clause has the side effect of encouraging the buyer to report when competitors cut prices, thus reducing the likelihood of secret discounts and chiselling. Table 10.11 The Most-Favored Customer clause Firm 2 price High Firm 1 price High Low 100, 100 90, 10 Low 10, 90 70, 70 P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 10.3 DUOPOLY DIFFERENTIATED PRODUCTS 297 One ought not, however, jump to the conclusion that the Most-Favored-Customer clause or the Meet-or-Release clause or similar arrangements are used only to keep prices high. They may have other uses, for example, to protect buyers from price discrimination. Therefore, such clauses are not conclusive evidence of anticompetitive collusion. 10.3 DUOPOLY DIFFERENTIATED PRODUCTS In the preceding analysis the duopolists provided identical products. That assumption simplied the analysis, since in equilibrium the rms prices have to be the same. Moving on now to the more typical situation in which the products differ, in equilibrium the prices need not be equal. Nevertheless, the same underlying forces operate.12 Quantity Competition Previously, the assumed industry demand function was: P = 100 q 1 q 2 (10.2) To allow for differentiated products, let s be an index of the similarity of the two rms distinct products, where s ranges from 1 (the products are indistinguishable) down to 0 (the products are so different neither has any effect upon the market for the other). As a numerical illustration, the demand functions might be: P1 = 100 q 1 s q 2 and P2 = 100 s q 1 q 2 (10.3) When s = 1, equation (10.3) reduces to the preceding (10.2). In the opposite limiting case where s = 0 instead, the two rms are not competing at all. They would be independent monopolists, each in its own industry. Under quantity competition, the exercise that follows illustrates the nature of the solution. EXERCISE 10.7 In equations (10.3) suppose s = 1/2, and for simplicity assume again that costs of production are zero throughout. (i) Find the rms Reaction Curves and the Nash Cournot solution. (ii) What happens as s approaches 0? (iii) What happens as s approaches 1? A N S W E R : (i) Following the same reasoning as in Exercise 10.3, the Marginal Rev- enues now become MR1 = (100 sq2 ) 2q1 and MR2 = (100sq1 ) 2q2 . Setting s =1/2, the Marginal Revenues equal to the zero Marginal Costs, and solving, the Reaction Curves become: q1 = 50 q2 /4 and q2 = 50 q1 /4 The Reaction Curves intersect at q1 = q2 = 40 and the implied equilibrium prices are P 1 = P 2 = 40. (ii) As s approaches zero, the two demand curves become less 12 In the analysis here the oligopoly rms are producing products of xed, although distinct, characters. The issues taken up in Chapter 9, as to the types of products (quality and variety) offered on the market, also arise under oligopoly. These topics are set aside here. P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 298 10. COMPETITION AMONG THE FEW: OLIGOPOLY AND STRATEGIC BEHAVIOR q2 200 RC 1 OutputofFirm2 150 100 50 q2 (40,40) RC 2 q1 50 150 100 OutputofFirm1 200 q1 Figure 10.3. Linear Reaction Curves Differing Products, Quantity Competition The Reaction Curves correspond to the data of Exercise 10.7. The products are no longer identical, and the demand curves are P1 = 100 q 1 s q 2 and P2 = 100 s q 1 q 2 , where s (the coefcient of similarity) is 1 . As s 0, the Reaction Curves swing toward the respective dashed horizontal and 2 vertical lines, showing the optimal outputs if each rm were an independent monopolist. and less interdependent. At the limit where s = 0 the two rms would be separate monopolists each producing q1 = q2 = 50 at prices P 1 = P 2 = 50. (iii) As s approaches 1, the rms demands become more and more interdependent. At the limit where s = 1 the same solution as in Exercise 10.3 is obtained: q1 = q2 = 33 1/3 and P 1 = P 2 = 33 1/3.13 The results of the preceding exercise are illustrated in Figure 10.3. As s approaches 0 the Reaction Curve RC1 pivots about the horizontal intercept at q 1 = 50 to become more and more vertical. RC2 would similarly pivot about the vertical intercept at q 2 = 50 to become more and more horizontal. Thus, if the rms were independent monopolists (s = 0) the intercept values would indicate the respective outputs. (Although omitted from the diagram to avoid excessive clutter, as s approaches 1 the two Reaction Curves would pivot in the opposite directions, approaching limiting shapes corresponding to the RC1 and RC2 equations of Exercise 10.3.) Price Competition What would happen if price were the decision variable instead? Figure 10.4 pictures the outcome under price competition for the demand data of Exercise 10.7. The crucial point is that the Reaction Curves now slope upward. In quantity competition, when 13 Although with nonidentical products the prices P1 and P2 do not have to be the same, they equal one another in this exercise since the cost and the demand conditions are completely symmetrical. P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 10.3 DUOPOLY DIFFERENTIATED PRODUCTS 299 P2 RC1 50 PriceQuotedb yFir m2 RC2 (331/3,33 1/3) 25 25 50 PriceQuotedb yFir m1 P1 Figure 10.4. Linear Reaction Curves Differing Products, Price Competition The Reaction Curves are based on the data of Exercise 10.7, but the rms are assumed to compete in terms of price rather than quantity as the decision variable. The Reaction Curves now have positive slopes: each rm rationally raises price if the competitor does and similarly follows a price reduction but by less than 1:1 in either case. As the similarity index approaches s = 0, the Reaction Curves swing toward the respective and vertical dashed lines, indicating the optimal prices if each rm were an independent monopolist. rm 1 produces more, rm 2 will rationally produce less. But in price competition, if rm 1 raises its price, rm 2 benets by raising its own price. The slopes of the Reaction Curves, however, indicate that each rm responds by less than 1:1 to a price change on the part of its competitor (else there could be no equilibrium). Also, as suggested in the diagram, as s approaches 0 the Reaction Curves pivot toward the limiting horizontal and vertical dashed lines at P 1 = P 2 = 50 (the price solutions when the two rms are independent monopolists). For the data of Exercise 10.7 the solution is P 1 = P 2 = 33 1/3, which implies outputs q 1 = q 2 = 44 4/9. Note that, consistent with the result for identical products, outputs are greater and prices lower under price competition than under the quantity competition. CONCLUSION When duopolists produce differentiated products, the Cournot and Bertrand solutions will be a function of s, the index of similarity between the two products. At one extreme (s = 1) the rms produce identical products. At the other extreme (s = 0) the two rms are independent monopolists. For intermediate values of s, when quantity is the decision variable the Reaction Curves slope downward. When price is the decision variable the Reaction Curves slope upward. So for differentiated as for identical products, price competition is more severe than quantity competition; the outcomes are less favorable to the rms and more favorable for the consumers. This last conclusion suggests the question: Why do oligopoly rms more typically engage in price competition, when they would do better collectively under quantity P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 300 10. COMPETITION AMONG THE FEW: OLIGOPOLY AND STRATEGIC BEHAVIOR competition? The answer turns upon the fact that consumers are interested only in the prices quoted, not the quantities manufactured by the suppliers. So suppliers trying to compete on a quantity basis, simply offering produced quantities for sale, would have to rely upon some kind of market or auction mechanism to translate the quantities offered into the prices that the consumers need to see. Market mechanisms are necessarily imperfect, as will be discussed in Chapter 14. Rather than rely upon them, more usually oligopolist rms nd it more protable to quote prices directly to consumers. 10.4 OLIGOPOLY, COLLUSION, AND NUMBERS What circumstances help oligopolists to collude? First and most obviously, rms can more easily police one another the fewer of them there are. Second, secret price cuts are more likely to be offered to large than to small buyers. A chiselling deal with a single big customer could be kept quiet; trying to get the same increase of business from 10 small customers is stretching secrecy too far. Third, enforcement of collusion should be much easier if rms products are identical since, otherwise, price cuts can take the hard-to-penetrate guise of better quality. (However, even where the physical commodity is the same for all rms, it may be possible to chisel by offering better credit terms or delivery.) Fourth, the more unstable the conditions of the industry, the harder it will be to negotiate and maintain agreements. An Application: The Kinked Demand Curve In the early 1900s, prices in the American steel industry were remarkably stable. The industry had few rms and so t the pattern of an oligopoly. The kinked demand curve, representing a kind of partial collusion, was proposed to explain why such oligopolies might be characterized by unusually stable prices. Figure 10.5 pictures a single oligopolist rm initially charging price P . If that rm tried to expand sales by cutting price, then (allegedly) all the other oligopolists will meet the price cut so the original price-cutter sells very little more at the lower price. In other words, in the region below the initial P the rms demand curve is steep. What if the rm were to raise its price? Then, allegedly, competing oligopolists would not meet the price increase, so the rm loses a lot of sales. Above P , therefore, the rms demand curve is relatively at.14 This hypothesis is not a complete theory. It does not say how the original price P was determined. But it has a testable implication: the prices arrived at by oligopolistic sellers should be relatively stable. In Figure 10.5, notice that the kink in the rms demand curve generates a vertical jump in the corresponding Marginal Revenue curve. This is evident geometrically in the special case where the two branches of the demand curve are straight lines. For any linear demand curve, the Marginal Revenue curve bisects the horizontal distance from the demand curve to the vertical axis. With two separate linear branches of the demand curve, there must then be a vertical break or jump in the Marginal Revenue curve, as shown. For the price P to be optimal for the rm, Marginal Cost must equal Marginal Revenue at q . Geometrically, the MC curve must cut through the vertical jump of MR. 14 The argument presumes differentiated products, since only then could any price divergence persist. P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 10.4 OLIGOPOLY, COLLUSION, AND NUMBERS 301 $/q Figure 10.5. Kinked Demand Curve: Nonidentical Products Suppose the rm currently produces output q at price P . If the rm cuts its price, the other oligopolists will meet the price reduction, so the price cutters sales gain will be small. If the rm raises price, the others will not follow the increase and the sales loss will be large. These assumptions dene a kink in the rms demand curve d that is associated with a vertical jump in the Marginal Revenue curve MR. The equilibrium price will be relatively stable, because even after small changes in the demand and cost curves, the MC curve likely continues to cut through the vertical jump of the MR curve. DollarsperUnitQuantity P MC d MR 0 q FirmOutput q Suppose cost conditions were to change. If the effect on Marginal Cost is not too large, the MC curve might shift up or down but continue to intersect MR within the vertical gap in MR. So the rm will continue to produce q at price P . And similarly, a change in demand for the rms product could shift the demand curve a little to the right or to the left. But if its rivals continue to follow the assumed pattern of reaction, the changed demand curve will still be kinked at P . If the demand shift is not too great, the MC curve will once again cut through the vertical jump of MR. If so, while the rms output q may change, its price P will remain the same. EXAMPLE 10.4 OLIGOPOLY AND PRICE RIGIDITY Some Canadian market areas are served by only a single daily newspaper (monopoly), whereas others are served by several (oligopoly). Timothy C. G. Fisher and Jerzy D. Konieczny compared the frequency of price changes in these two types of markets during the period 19651990.a The newspapers typically quoted different prices for various classes of customers: single copy (newsstand) sales, weekly carrier sales, mail subscriptions, and so forth. The table indicates that, consistently across all these classes, newspaper prices in oligopoly markets changed less frequently than monopoly prices. And, as follows logically, the oligopoly price changes when they did take place were on average larger. Price changes for Canadian daily newspapers Average time between changes (mos.) Category Single copy Weekly carrier Carrier Dealer Mail rate Monopoly 40.5 21.9 22.0 37.1 21.9 Oligopoly 41.8 25.9 29.0 42.0 26.6 Average price change (%) Monopoly 26.2 13.1 12.8 25.5 20.5 Oligopoly 29.0 16.6 16.3 30.2 28.0 Source: Selected from Fisher and Konieczny, Table 1. P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 302 10. COMPETITION AMONG THE FEW: OLIGOPOLY AND STRATEGIC BEHAVIOR In this generally inationary period, any price xed in nominal dollar terms was gradually eroding in real value. As a result, the price changes tabulated typically represented attempts to catch up with ination. To avoid the costs and disruption of frequent changes, the newspapers compensated for the gradual decline in real value by making only occasional discrete upward adjustments. But any paper making such an adjustment risked losing customers. The oligopolist newspapers, facing competitors in the same market, were evidently more reluctant to raise prices. a Timothy C. G. Fisher and Jerzy D. Konieczny, The Relative Rigidity of Oligopoly Pricing, Economics Letters, v. 49 (July 1995). Oligopoly and Numbers Even in the absence of collusion, oligopoly prices would be lower the larger the number of competitors. How this comes about can be illustrated by extending the data of Exercise 10.3, for the case of quantity competition with identical products, to allow for increasing numbers of rms N. Under the conditions of Exercise 10.3 each rm has zero costs. The market demand curve is P = 100 Q , where Q is the sum of the quantities produced by the oligopoly rms. Thus: Q q1 + q2 + + q N Now dene Q1 as the sum of all the outputs except that of rm 1, so that: Q q 1 + Q 1 (10.5) (10.4) And let qo represent the output of each and every rm other than rm 1, all assumed to make identical choices. Then the industry demand curve can be written: P = 100 [q 1 + (n 1)q o ] Since this is a linear demand curve, rm 1s Marginal Revenue MR1 is: MR1 = 100 (n 1)q o 2q 1 (10.7) (10.6) Setting this Marginal Revenue equal to rm 1s MC1 = 0 leads algebraically to the condition: q 1 = 50 N1 qo 2 (10.8) This is the Reaction Curve for rm 1, responding to the quantity choices of any typical other rm. Given that the rms are identically situated, their outputs must be equal. So it must be that q1 equals qo . Making the substitution and solving algebraically leads to the results P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 10.4 OLIGOPOLY, COLLUSION, AND NUMBERS 303 (where q now signies the output of any single rm): q = 100 N+1 N Q = 100 N+1 100 P = N+1 (10.9) For two rms ( N = 2), this conrms the Exercise 10.3 result that each rm has output 33 1/3. Aggregate output is 66 2/3 and price is 33 1/3. With N = 3, each rm has output q = 25, aggregate output rises to Q = 75, and price falls to P = 25. This special case illustrates the general forces at work. As the number of oligopoly rms in a given market increases, each single competitor will produce less. But, in aggregate, all the rms together will produce more. So as N increases the outcome moves in the direction of the solution under perfect competition. EXAMPLE 10.5 CONCENTRATION AND MARKET PRICES IN SWEDEN Marcus Apslund and Richard Friberg studied how retail grocery food prices in local Swedish markets responded to the number of competing stores during the period 19931997.a The data were based upon twice-annual surveys conducted by the Pensioners National Organization. The results reported here indicate that a larger number of stores was indeed associated with lower prices. Retail food prices in Sweden Number of stores 1 2 3 4 5 ... 10 15 20 Median price 103.9 102.9 101.8 101.7 100.8 ... 97.8 96.3 93.2 Source: Selected from Apslund and Friberg, Table 3. Although the tabulated differences might appear small, competition in retailing services can narrow only the margin between stores food acquisition costs and what consumers pay. The retail margin often accounts for only a small fraction of the products cost to consumers. Apart from the price effect, consumers also gain convenience and variety (as discussed in Chapter 9) as the number of retail stores in a local market increases. a Marcus Apslund and Richard Friberg Food Prices and Market Structures in Sweden, Scandinavian Journal of Economics, v. 104 (December 2002). P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 304 10. COMPETITION AMONG THE FEW: OLIGOPOLY AND STRATEGIC BEHAVIOR SUMMARY Oligopoly is competition among a small number of rms in an industry. With small numbers, the best action for each competitor depends upon what the others are doing. So the rms are involved in strategic situations, as studied in the theory of games. In game theory the outcome depends upon the pattern of payoffs and the protocol of play (the rules of the game). Payoffs may range from completely opposed interests (a constant-sum game) to completely parallel interests; most economic situations fall in between. An important protocol distinction is between sequential-move versus simultaneous-move play. (When one player moves later than the other, but without knowledge of the opponents choice, the two moves are considered simultaneous.) For sequential-move play the perfect equilibrium solution assumes that each player chooses rationally, in the belief that players moving later will also play rationally. A perfect equilibrium always exists, though it may not be unique. In simultaneous-move play there may be a dominant equilibrium, where one or both players has a strategy that is best no matter what the other player does. A more general solution concept is the Nash equilibrium, in which no player can gain by revising his or her choice even after knowing the opponents choice. A Nash equilibrium may or may not exist in pure strategies, but if not it will exist for probabilistically mixed strategies. In the payoff context known as the Prisoners Dilemma, the players could mutually gain from cooperating. But rational self-interested choices lead to a less cooperative outcome, which is a dominant equilibrium in simultaneous play and is also a perfect equilibrium in sequential play. The problem of chiselling in oligopoly is a typical Prisoners Dilemma. Oligopolists can engage in price competition or quantity competition. Price competition is more severe, since at stake are not fractions of the market but the whole market. In equilibrium, however, price differences can persist only if the oligopolists products differ. Under quantity competition the Nash equilibrium is called the Cournot solution; under price competition it is called the Bertrand solution. For oligopolists producing differentiated products, one particular type of assumed strategic interaction leads to a kinked demand curve for any single rm. If the other producers will meet any price cut, the rms demand curve below the current price will be steep; if the others will not meet any price increase, above the current price the rms demand curve will be at. The effect is to discourage price changes. With increasing numbers of rms in an industry, the NashCournot (and Nash Bertrand) solutions, as would be expected, move in the direction of the outcomes in pure competition. QUESTIONS The answers to daggered questions appear at the end of the book. 1. What is strategic behavior? Why are suppliers more likely to engage in strategic behavior when there are only a few of them? 2. What is the Prisoners Dilemma? Do the participants in this game have an unexploited mutual gain from trade, and if so, why? For Review P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 QUESTIONS 305 3. Distinguish oligopoly from monopolistic competition. 4. Justify the statement in the text that the Cournot oligopoly outcome is a special case of the Nash equilibrium in the theory of games. 5. Explain the Cournot solution to the duopoly problem. 6. Why is collusion more likely if the rms expect to remain in the industry in the future? 7. Diagram the Reaction Curves for the asymmetrical Stackelberg and Threat cases (letting output be the decision variable). 8. a. b. Why does a kinked demand curve tend to lead to rigid prices? How might a kinked demand curve for any single oligopolist result from the behavior of others designed to enforce a collusive agreement? 9. In American football, the quarterback of the team on offense can call a running play or a passing play. If the team on defense knew which kind of offensive play would be called, it could prepare for the play and have a better chance of defeating it. If the quarterback follows an optimal mixed strategy, on average do you expect the offense to benet more on passing plays or on running plays? How does your answer relate to Example 10.1 on mixed strategies in tennis? For Further Thought and Discussion 1. It seems strange that different duopoly solutions are obtained depending on whether price or quantity is the decision variable. Which outcomes are different, and why? 2. Under the Cournot model, in making its output decision each duopolist rm assumes that the others output is xed. Over time, however, each would surely learn that this assumption about the others behavior is not valid. What would then be likely to happen? 3. In deterring entry, a monopolist faces the problem of making his threat that he will always produce enough to drive out the entrant credible. The difculty lies in the fact that, once a newcomer has entered, it may be more protable to share the market than to engage in a costly price war. How might a monopolist make his threat more credible? 4. Can a kinked demand curve arise under homogeneous duopoly? If so, what would be its shape? 5. Do small numbers inevitably imply cartel-like collusion? 6. Consider the argument that predatory price cutting to enforce the Threat solution will rarely be observed because the symmetrical Collusive solution is typically better for both parties. a. Is this necessarily correct? Is it ever correct? b. Under what circumstances will predatory price cutting be likely to emerge, if ever? 7. Construct a payoff table in which two duopolist rms both offer consumers a Meet-orRelease clause. Show that this permits them to escape from the Prisoners Dilemma in order to charge higher prices. 8. Verify that there are no dominant strategies in the payoff matrices shown in Tables 10.1 and 10.2. 9. For the payoffs shown in Tables 10.1 and 10.2, under the sequential protocol: a. Who has the advantage, rst mover or last mover? b. Are the results inefcient in the sense introduced in Chapter 7 (that is, is there another outcome whose paired payoffs are better for at least one party without being worse for the other)? 10. (Mathematically challenging) Using the values of Exercise 10.7, but assuming price competition, justify the shapes of the Reaction Curves in Figure 10.4 What happens when s approaches 0? When s approaches 1? P1: OBM/JZG 0521818648c10.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:35 306 10. COMPETITION AMONG THE FEW: OLIGOPOLY AND STRATEGIC BEHAVIOR 11. Discuss sources of possible outward spiral in the duopoly cobweb of dynamic reactions. 12. In price competition with a Stackelberg leader, the text describes the solution with zero costs of production. What if costs are positive? (To isolate the leader versus follower distinction, assume the two rms cost functions are identical.) Is the leader still at a disadvantage? Will it necessarily earn a prot of zero? 13. Using the Marginal Cost functions for Exercise 10.4, nd the Collusive and the Competitive solutions. P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 11 Dealing with Uncertainty The Economics of Risk and Information 11.1 Decisions under Uncertainty 308 Expected Gain versus Expected Utility 308 Risk Aversion 309 Risk-Bearing and Insurance 312 11.2 11.3 The Value of Information 316 Asymmetric Information 317 Adverse Selection The Lemons Problem 317 Conveying Quality through Reputation 321 Do Prices Signal Quality? Information as a Public Good 323 Conveying Information Advertising 325 11.4 11.5 Herd Behavior and Informational Cascades 325 Copyright, Patents, and Intellectual Property Rights 328 SUMMARY 332 QUESTIONS 334 EXAMPLES 11.1 11.2 11.3 11.4 11.5 11.6 11.7 Risk Aversion and Executive Stock Options 315 Adverse Selection in Dental Insurance 319 Racehorses Can Be Lemons 320 Restaurant Hygiene 322 Fads and Cascades in Television Programming 327 The Napster Story 330 Pharmaceuticals Creation versus Utilization 331 307 P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 308 11. DEALING WITH UNCERTAINTY THE ECONOMICS OF RISK AND INFORMATION Up to now consumers have been assumed to be entirely aware of their incomes and personal preferences, and suppliers fully informed as to the technology and costs of production. Although assuming complete certainty is not realistic, most of the results obtained so far for example, that demand curves are negatively sloped hold even when people are less than perfectly informed. Nevertheless, uncertainty is often crucial. Without uncertainty there would be no insurance industry, no need for consultants, no litigation, no advertising, no reason to engage in scientic research. Another crucial aspect of uncertainty is that some market participants are likely to be better informed than others. A jeweler usually knows a lot more about the quality of a diamond offered for sale than do potential buyers. This chapter introduces the tools necessary to deal with imperfect information and with unbalanced distributions of knowledge. 11.1 DECISIONS UNDER UNCERTAINTY Expected Gain versus Expected Utility Suppose an airline must decide whether to send off a ight from Los Angeles to Chicago, despite being unsure about the weather at OHare Airport in Chicago by the time the ight arrives. The plane already has 100 people aboard. If the ight is dispatched and OHare is open, suppose the airline will gain $40,000. If the airline holds the ight until the weather clears, the disruption in the schedule will make its gain smaller, say only $20,000. But if the ight departs and nds Chicago snowed under, returning the plane to Los Angeles and reboarding the passengers later on will cause a loss of $30,000. Suppose also that the airline estimates that the chance of OHare Airport being closed is 25%. What should the airline do? As a rst step the airline might ask, which of the possible actions would maximize its mathematical expectation (or expected value) the probability-weighted average of its dollar gain. The mathematical expectation of gain if the ight is dispatched would be: Expected Gain if Dispatch = (0.75 $40,000) + (0.25 $30,000) = $22,500 And since by assumption there is no uncertainty if the ight is held: Expected Gain if Delay = $20,000 So, in terms of mathematical expectation of gain, the airline should dispatch the plane. The general rule for choosing among different actions on the basis of mathematical expectation of gain is: For any single action that might be undertaken, take the value of each possible outcome, multiply it by the probability of that outcome occurring, and sum all these products. The result of that calculation is the expected value of that particular action. Repeat the calculation for each of the available actions, and select the action with greatest expected value. Algebraically, suppose state 1 occurs with probability 1 , state 2 with probability 2 , state 3 with probability 3 , and so forth. (The probabilities, when all possible states are counted, necessarily sum to 1.) Consider some specic action ai . The values associated with action ai in the possible states (numbered from state 1 to state S) can be denoted P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 11.1 DECISIONS UNDER UNCERTAINTY 309 Vi 1 , Vi 2 , . . . , Vi S . So the expected value of taking action ai can be written: E [V (ai )] = 1Vi 1 + 2Vi 2 + + SVi S (11.1) And the decision rule is: Among all the available actions a1 , a2 , . . . , choose the action that yields the highest E [V (ai )]. Risk Aversion If a decision, like that of the airline here, will be repeated many times over, achieving the highest dollar gain on average makes sense. The law of large numbers cancels out the risk. But sometimes situations arise in which risk cannot be ignored. Suppose Helen has two job offers. A job in Iowa pays a straight salary at a rate of $40 an hour. (At 2,000 hours a year, that would be $80,000). A job in Nebraska offers a lower assured salary of $30, but theres a possibility of an annual bonus equivalent to $20 an hour. Suppose Helen thinks there is a 60% chance she will get the bonus. Then the expected per-hour compensation on the riskier job is (0.4)($30) + (0.6)($50) = $42. If she cared only about the mathematical expectation of dollar income, she would take the risky job in Nebraska. But choosing a job is not an action that will be repeated many times, and furthermore it might involve a large fraction of her lifetime wealth and income. So Helen might be willing to pay something to avoid the risk of ending up with low income in the bad state of the world. If so, she could be well advised to take the job with the guaranteed salary of $40 an hour. A way of expressing her possible willingness to sacrice income to avoid risk is to describe her as desiring to maximize expected utility rather than expected income. Using the cardinal utility interpretation of Chapter 3, a person associates a utility number with each level of income.1 Expected utility is the probability-weighted average of the utilities attached to all the possible outcomes. Suppose the utilities that Helen assigns to different possible weekly incomes are U ($30) = 2, U ($40) = 3, and U ($50) = 3.5. Then her expected utility for the riskier job is (0.4)(2) + (0.6)(3.5) = 2.9. Since this is less than U ($40) = 3, Helen should choose the job with the xed salary. For any action ai , the mathematical expectation of utility is: E [U (ai )] = 1 Ui 1 + 2 Ui 2 + + S Ui S (11.2) The decision rule is: Choose the action ai with highest expected utility. Equation (11.2) is identical to equation (11.1), except that the cardinal utility values are entered into the calculation instead of the dollar measures of gain. In Figure 11.1 the horizontal axis represents income I and the vertical axis represents utility U. The utility function shown is concave: it becomes atter at higher incomes. Since utility is rising with income at an always-decreasing rate, this decision-maker has diminishing marginal utility of income. It is diminishing marginal utility of income that leads to risk aversion. In the diagram, points A, B, and C represent Helens assumed utilities U ($30) = 2, U ($40) = 3, and U ($50) = 3.5. As previously calculated, for the risky job 2 her expected 1 As explained in Chapter 3, ordinal utility only ranks the outcomes, telling us in this case only that the individual prefers more income to less. Cardinal utility means that the decision-maker can quantitatively scale the desirability of different levels of income. The justication for using cardinal utility in dealing with choices under uncertainty is discussed in more advanced economic treatises. P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 310 11. DEALING WITH UNCERTAINTY THE ECONOMICS OF RISK AND INFORMATION Utility (U ) 4 3.5 3 2.9 B N M C Utility 2 A 1 0 10 20 30 38 42 40 50 60 Income (I ) Figure 11.1. Certainty-Equivalent Income Points A and C are the possible outcomes of Helens risky job; point B represents the safe job. Since the probability of the good outcome C is 0.6, the expected utility of the risky job is shown by point M, 6/10 of the distance from A towards C. Since M is lower on the utility scale than point B, Helen should prefer the safe job. The sure salary that would give Helen the same utility as the risky job is shown by point N, whose vertical coordinate is the same as point M. utility is 2.9. To nd the expected utility geometrically, connect points A and C with a line segment. Since the probability of the good outcome C is 0.6, on this line nd the point 6/10 of the distance from A towards C. Call this point M. The height of M is necessarily (0.4)(2) + (0.6)(3.5) = 2.9, conrming the previous calculation. Geometrically, point M lies lower on the utility scale than point B, which represented the 3.0 utility of the safe job 1. So the geometry conrms that, given Helens degree of risk aversion, she would prefer the safe job in Iowa. What sure salary would give Helen the same utility as the risky Nebraska job? That is shown by point N, which has the same height as point M. Point N corresponds to a weekly salary of $38. So Helen is indifferent between receiving $38 for sure and receiving $30 with probability 0.4 and $50 with probability 0.6. In other words, $38 an hour is the certainty-equivalent for Helen of the risky salary. The difference between $38 and (0.4)($30) + (0.6)($50) = $42 is the risk premium. Helen is willing to give up income of $4 an hour in income to avoid the risk entailed by the Nebraska job. [Note: It would be wrong to infer that Helen would never accept any risk. A riskaverse person will accept a risky option, if the terms are sufciently favorable. That is, if the difference in expected income exceeds his or her risk premium. Or put another way, if the riskier option is associated with a higher certainty-equivalent income.] The concave curve in Figure 11.1 was associated with diminishing Marginal Utility of income, which is the normal case. (Compare Chapter 3, Figure 3.2.) It is also possible to construct a utility function that is not concave but instead convex (becoming steeper P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 11.1 DECISIONS UNDER UNCERTAINTY 311 IR 110 100 A 90 CertaintyLine 80 70 60 50 D 40 38 G U2 F 20 U1 30 10 45 0 10 20 30 38 40 50 60 B 70 80 IP Figure 11.2. The Risk Premium The horizontal axis measures income IP under Prosperity; income IR under Recession is shown on the vertical axis. Line AB shows all the possible combinations of state-contingent incomes in Prosperity and Recession whose expected value is the same as the sure income represented by point D along the certainty line. The risky job offer is represented by point F along AB. Point F lies on the same indifference curve as point G, lower down on the certainty line. The monetary difference between point F and point G is the risk premium the additional expected income that Helen requires to make her indifferent between the risky job and the job with guaranteed income. moving to the right). Then the decision-maker has increasing Marginal Utility of income. Such a person, over a certain range at least, prefers a risky option over a safe one with the same average income. The risk premium is negative; that is, the person is willing to sacrice some sure income in order to incur the risk. Last, if the utility function is neither concave nor convex but is instead a straight upward-sloping line (constant Marginal Utility of income), the individual is risk-neutral and the risk premium is zero. As a different way of representing risk aversion, now think in terms of two distinct states of the world such as Prosperity and Recession. In Figure 11.2, income in the P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 312 11. DEALING WITH UNCERTAINTY THE ECONOMICS OF RISK AND INFORMATION Prosperity state, denoted IP , is measured along the horizontal axis. Income in the Recession state, IR , is scaled along the vertical axis. (These are the state-contingent incomes.) Any given level of expected income is associated with a straight line such as AB whose slope reects the probabilities of the different states. Suppose the probability of Prosperity is P and of Recession is R 1 P . Then for some specic expectation of income E [ I ], the equation of the line is: E [ I ] = R I R + P I P (11.3) With IP on the horizontal axis and IR on the horizontal axis, the slope of the line is P /R . The line shows all the possible probabilistic combinations of state-contingent incomes in Prosperity and Recession associated with any given mathematical expectation of income. Returning to Helens situation, if the bonus will be paid only in the Prosperity state of the world, for the risky job Helens expected income is E [ I ] = (0.4)($30) + (0.6)($50) = $42. In Figure 11.2 the line AB reects this expected income. The probabilistic income combination represented by her risky job in Nebraska ( I R = $30 and I P = $50) appears as point F. Were Helen able to choose among all possible income combinations with an expectation of $42, then line AB would be a budget line, just like those discussed in Chapter 4. The only difference is that Chapter 4 dealt with a consumer choosing between ordinary goods such as shoes and hats, whereas here the two goods are amounts of the respective state-contingent incomes. Indifference curves such as U1 and U2 between the various income combinations can also be drawn on axes IR and IP . A person whose earnings are the same in Prosperity and Recession receives those earnings with certainty. Any such sure income would be a point on line OC the certainty line. The certainty line necessarily has a slope of 45 , reecting the fact that I R = I P . In the diagram, the sure salary of $40 associated with Helens riskless job offer in Iowa is shown as point D. D lies on a higher indifference curve than does point F. This shows, in another way, that Helens risk-aversion leads her to prefer a guaranteed income of $40 over the risky income combination at point F even though point F lies on the budget line representing a higher expected income of $42. The risk premium can also be shown in Figure 11.2. Point G lies on the same indifference curve as point F, but G lies on the 45 certainty line and so represents riskless income. The difference between the expected income at point F ($42) and the expected income at point G ($38) is the risk premium how much more expected income Helen would require to bear the risk associated with accepting the risky job in Nebraska over the riskless job in Iowa. Risk-Bearing and Insurance Joe has wealth of $300,000. One-third of his wealth is tied up in an Old Master painting worth $100,000. With probability 40%, art thieves will steal his painting this year. (This unrealistically high probability gure is used here for numerical convenience only.) For Joe the two states of the world are Painting stolen (state S) and Painting not stolen (state N ). Joes initial situation or endowment is represented by point E in Figure 11.3, consisting of his possible contingent wealth levels WN = $300, 000 (measured on the horizontal axis) and WS = $200, 000 (measured on the vertical axis). Joe is initially in a risky position, off the 45 certainty line. Suppose, however, that for a P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 11.1 DECISIONS UNDER UNCERTAINTY 313 WS 700,000 650,000 600,000 A 500,000 CertaintyLine 400,000 300,000 A F 200,000 E B 100,000 45 100,000 200,000 300,000 B 433,333 400,000 500,000 600,000 WN Figure 11.3. Fair and Unfair Insurance Opportunities The horizontal axis measures wealth WN in the state of the world Painting not Stolen; wealth WS in the state Painting Stolen is shown on the vertical axis. Point E represents Joes initial situation, off the certainty line. With insurance at fair rates, Joe could move anywhere along budget line AB. His optimal point is F on the certainty line, where he fully insures against his potential loss. The line A B represents an unfair insurance opportunity, so Joes indifference curve tangency would necessarily lie below and to the right of the 45 line. This means that Joe would not fully insure. premium of $40,000 Joe can buy insurance in the amount of $100,000 (the indemnity) against the risk of theft. At this point it is useful to dene a fair2 gamble or insurance contract.3 DEFINITION: A gamble is fair if the mathematical expectation of net gain, E [G ], is zero. Suppose the probability of winning is and of losing is 1 , and let the winning payoff be a wealth gain of H and the losing payoff be a wealth loss of F. So a gamble is 2 3 Fair in probability theory is only a technical term. It does not mean moral or just. Whether a contract is a gamble or insurance depends upon the point of view. A risk-reducing insurance arrangement for a purchaser is a risk-increasing gamble for the insurance company. P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 314 11. DEALING WITH UNCERTAINTY THE ECONOMICS OF RISK AND INFORMATION fair if: E [G ] = H + (1 )( F ) = 0 From this equation it immediately follows that, as a condition for a fair gamble: 1 H = F (11.4) That is, the ratio of payoffs must be inversely proportional to the ratio of probabilities. On this denition the offered insurance contract is a fair gamble. As Joe sees it, the gamble succeeds if the painting is stolen. If Joe loses the gamble (the painting is not stolen) he is out the $40,000 premium. If he wins, his net gain on the contract is $60,000 (the $100,000 indemnity, less the $40,000 premium that the insurance company keeps). That the premium is fair is shown by: $60,000 0.6 1 H = = 1.5 = = F $40,000 0.4 Since E [G ] the mathematical expectation of income gain or loss is zero for fair gambles, it follows that all fair gambles or fair insurance contracts leave the individuals mathematical expectation of income unchanged. Referring back to Figure 11.3, the line AB represented all possible combinations of state-contingent incomes for Helen with a mathematical expectation of $42. Figure 11.4 here represents a similar situation for Joe. The mathematical expectation of his endowment in dollar terms is (0.6)($300, 000) + (0.4)($200, 000) = $260, 000. So his budget line has the equation 0.6WN + 0.4WS = $260, 000. If Joe accepts the offered fair insurance contract, he would move along this budget line to the 45 certainty line, ending up with wealth $260,000 for sure. If he fails to insure, he will remain in a risky position southeast of the 45 line. This analysis now allows a more precise denition of risk aversion: DEFINITION: A person is risk averse if, offered a choice of fair gambles (or fair insurance contracts), he always prefers to end up at a position on the 45 certainty line. It follows that an individual endowed with any given amount of riskless wealth or income would never accept a fair gamble. Doing so would move him away from the 45 line. If instead his endowment already contains some risk, so that his initial position lies off the 45 line, he would accept a gamble tending to offset the risk inherent in his endowment. That is what insuring means. This denition has an important implication for the shape of the indifference curves. If Joe is risk-averse, as shown in the diagram he would move along the budget line to the tangency position F on a higher indifference curve. More generally, risk aversion means that the individual would end up at a certainty position along any fair-gamble budget line, whenever offered such an opportunity. So the individuals indifference curves must all be tangent to fair-gamble budget lines precisely where each such line crosses the 45 line out of the origin. But what if, as is more common, an insurance contract is unfair in probability terms? After all, insurance companies have costs of doing business, so on average must do better than break even on the coverage they offer. In Figure 11.3 the hypothetical P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 11.1 DECISIONS UNDER UNCERTAINTY 315 dashed budget line A B is atter than the fair budget line AB that is, the H/F ratio of equation (11.4) is numerically smaller than the fair ratio (1 )/ = 0.6/0.4 = 1.5. Along A B the tangency with Joes indifference curve would necessarily lie to the southeast of the 45 line. This means that Joe would not fully insure. The diagram has been constructed so that at Joes endowment, point E, an indifference curve is tangent to the budget line A B meaning that Joe maximizes utility there and will stand pat with his initial gamble. If instead the tangency point falls between point E and the certainty line he will want to go only part of the way in purchasing insurance underinsuring in order to bear part of the risk himself. And a tangency lying along A B in the opposite direction from the certainty line would mean that Joe nds the insurance terms so attractive that he would like to buy more insurance. He might do so by buying a second painting with the intention of also insuring that one. EXAMPLE 11.1 RISK AVERSION AND EXECUTIVE STOCK OPTIONS Stock options are rights to purchase corporate shares at a specied exercise price. A stock option may pay off handsomely if the companys stock rises above the exercise price, but is worthless otherwise. In recent decades Boards of Directors have increasingly been granting executives stock options as part of their pay packages. The idea is that the options will motivate executives to take actions that will benet the corporation and lead therefore to a higher stock price. (Or so the companys directors presumably hope.) Since stock options are so risky, the valuation that an executive places upon this form of pay will depend importantly upon his or her overall nancial situation and degree of risk aversion, together with the underlying riskiness of the stocks themselves. Brian Hall and Kevin J. Murphy estimated certainty-equivalent values for an executive offered a 10-year nontradable stock option with an exercise price of $30.a The row headings of the table represent differing assumptions as to the executives degree of risk aversion r (a theoretical measure called the constant of relative risk aversion) and as to his or her exposure to risk (measured by the percent of the executives personal wealth already held in the form of the companys stock). As each of these factors increases, the certainty-equivalent of a stock option decreases as compared with straight cash. The column headings show various assumed levels of the stock price at the time of granting an option with the xed exercise price of $30. If the exercise price is below the current stock price the option is already in the money that is, it has an immediate conversion value in addition to its option value. Such an option is of course also less risky. The data in the cells show the value of an option to buy a single share. The rst data cell shows that for an executive with the stated characteristics (r = 2, and 50% of wealth already in company stock), if the current stock price is $15 an option to buy a share 10 years from now at the exercise price of $30 is worth only $2.50 today. Moving to the right in any row, the option values increase simply because the stock is already worth more today. But moving down the columns, the option values decrease as the executives risk aversion r rises, and also decrease as the executives risk exposure (proportion of wealth already held in company stock) grows. The key conclusion is that the value of stock options for executives, after allowing for risk aversion, is typically considerably less than might at rst appear. P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 316 11. DEALING WITH UNCERTAINTY THE ECONOMICS OF RISK AND INFORMATION Certainty-equivalents of an option to buy a share at $30 Current stock price r r r r = 2, = 2, = 3, = 3, 50% in stock 67% in stock 50% in stock 67% in stock $15 2.5 2.0 1.8 0.6 $30 12 8 7 3 $45 22 17 13 9 $60 32 25 22 15 Source: Estimated visually from Hall and Murphy, Figure 2 (p. 42). a Brian Hall and Kevin J. Murphy, Stock Options for Undiversied Executives, National Bureau of Economic Research Working Paper No. 8052, December 2000. 11.2 THE VALUE OF INFORMATION If you will be getting better information before you have to lock in your decision, it may pay to defer making a nal choice. Suppose you see an ad for a computer, at a special price today of $800. The sale is for one day only. If you wait for tomorrow, you are unsure what the price will then be. Lets say you estimate there is a two-thirds chance the price will rise to $950, but a one-third chance the price will decline to $700. Should you buy today or wait? Suppose you are risk-neutral, which means you only need to take into account the mathematical expectation (the probability-weighted average) of the dollar amounts. If you wait, the expected price is (1/3)($700) + (2/3)($950) = $866.67, which exceeds the $700 you would pay for the computer today. So if you were sure you wanted the computer, even at a price of $950, you should buy it today at the sale price of $800. But now suppose your demand price (see Chapter 7), the most you would be willing to pay for the computer, is Pd = $810. So if you buy today your Consumer Surplus will be $810 $800 = $10. If you wait and the price falls to $700, you would buy the computer and receive a larger Consumer Surplus, $810 $700 = $110. But if the price rises to $950 you would not buy at all, in which event Consumer Surplus is zero. Thus, if you wait, the mathematical expectation of your Consumer Surplus is E (CS) = (1/3)($110) + (2/3)($0) = $36.67. Since this exceeds the $10 Consumer Surplus on an immediate purchase, on average waiting is better than buying the computer today. And waiting is better even though todays price is lower than the mathematical expectation of tomorrows price. How can this be? Postponing the decision gives you the option of varying your nal action in accord with information you will receive tomorrow. Since the future is never entirely knowable, option value enters into the worth of any durable asset. When buying a car today, an element in its value is that you could resell it if used-car prices rise or if not, you can retain it for continued use. It is option value that makes information useful. Acquiring knowledge is worthwhile only if it might change a decision you would otherwise have made. Continuing with the example, now suppose your willingness to pay for a computer exceeds $950. If so, as seen above, you should buy the computer today at the sale price of $800, which is less than the expected later price of $866.67. But suppose you can subscribe to a marketing P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 11.3 ASYMMETRIC INFORMATION 317 service that can reliably tell you today whether the price tomorrow will be $700 or $950. If the report arrives in time so that you could still buy at the sale price today, how much would you pay for that information? The reasoning goes as follows. Your demand price Pd is some value greater than $950. If you dont invest in the information you should buy the computer today, paying $800. Your Consumer Surplus would be CS = Pd 800. If you do buy the information, with probability 1/3 the marketing service will report that the future price will be $700. If so, you will wait to buy the computer tomorrow, paying $700. Or, with probability 2/3 you will learn that tomorrows price will be $950 but in that case you will buy the computer today at its sale price of $800. Thus, the mathematical expectation of Consumer Surplus due to having the information about future prices would be E [CS] = (1/3)( Pd 700) + (2/3)( Pd 800) = Pd $766.67. If you do not subscribe to the service, you will buy the computer today so that Consumer Surplus is Pd $800. The difference is the value to you of the information, which is the maximum you would be willing to pay to subscribe to the marketing service: $33.33. In terms of symbols, let the two possible states of the world be s 1 and s 2 . Let CS o denote the expected Consumer Surplus of the best uninformed action; CS is the expected Consumer Surplus of the best informed action. For simplicity suppose that the number of actions matches the number of states, and that a1 is the better action in state 1 and a2 is the better action in state 2. Suppose f is the probability you attach to state 1, so that 1 f is the probability of state 2. Let CS(a1 |s 2 ) signify Consumer Surplus when the action is a1 and the state of nature is s 2 . Similar interpretations apply to CS(a1 |s 1 ) and so on. In the absence of information, the chosen action cannot be adapted to the state of nature. Therefore, whichever of a1 or a2 generates a higher benet should be chosen. Let it be a1 . Then: CS o = f CS(a1 |s 1 ) + (1 f )CS(a1 |s 2 ) Given the information, however, the chosen action can be adapted to the state of the world, so: CS = f CS(a1 |s 1 ) + (1 f )CS(a2 |s 2 ) Since by assumption a2 is the better action in state s 2 , CS must exceed CS. The difference represents the worth of the information, the most you should be willing to pay for the marketing service. On the other hand, if your decision would not be affected the information has no value to you. For example, suppose your willingness to pay for a computer is only $600. Then you wouldnt buy the computer at todays price of $800, you wouldnt buy it if the price later rose to $950, and you wouldnt buy it if the price later fell to $700. So you gain nothing from learning whether the price will be $950 or instead $700. 11.3 ASYMMETRIC INFORMATION Adverse Selection The Lemons Problem In any transaction the better-informed party has an advantage. Suppliers usually know more about their product than do buyers. A patient may not know which physician or dentist is the best qualied, a prospective buyer may not know that a used car has a P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 318 11. DEALING WITH UNCERTAINTY THE ECONOMICS OF RISK AND INFORMATION Price( P ) L De P K G Cars Sold qL q n ma r dP s ice (In fo r d me Bu y ) ers H p Su P ply r ic es edB u ) y ers N Dem and Pr ic nin es(U f orm Cars Not Sold qH Quality (q ) Figure 11.4. The Lemons Problem GH shows the reservation supply prices of the existing owners of used cars, ranked upwards from the lowest-quality car to the highest-quality car. KL shows what the corresponding demand prices of the potential buyers would be, if buyers were perfectly informed about quality. Assuming equal numbers of owners and potential buyers, each wanting to sell or to buy a single unit, all the cars would be sold. But when buyers can observe only the average quality of the cars currently offered, their demand prices for any quantity on the market are shown by the lower curve KN. Point N is the buyers demand price for a car of average quality in the entire population of cars. KN intersects GH at quantity q between qL and qH . In equilibrium only the cars with quality below q will be sold. The equilibrium price is P , where the reservation price of the marginal seller equals the reservation price of the marginal uninformed buyer. broken transmission, an employer cannot be certain how well an applicant will perform on the job. All such instances create a problem of adverse selection. Low-quality goods or services (lemons) may destroy the market for high-quality goods (peaches).4 Consider used cars. The potential seller, Sally, may know that her car stalls intermittently, that the air-conditioning frequently fails on hot days, or that the car accelerates poorly on mountains. But potential buyers, like Bob, do not generally know about these problems. Were customers fully informed, good cars would sell at a higher price than bad cars. But if buyers cannot determine a cars condition before purchase, good cars and bad cars end up selling at the same price. That is the heart of the problem. In Figure 11.4 the horizontal axis represents used-car quality q ; the vertical axis represents price P. Suppose the qualities of all the cars offered for sale are distributed 4 George A. Akerlof, The Market for Lemons: Quality Uncertainty and the Market Mechanism, Quarterly Journal of Economics, v. 84 (1970), pp. 488500. P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 11.3 ASYMMETRIC INFORMATION 319 evenly from a low of qL to a maximum of qH . For simplicity, let there be equal numbers of existing owners and potential buyers, each wanting to sell or to buy a single unit. The rising curve GH shows the reservation supply prices of the existing owners, ranked upward from the lowest-quality car to the highest-quality car. It is drawn for convenience as a straight line. The curve KL (also drawn for convenience as a straight line) shows what the corresponding demand prices of the potential buyers would be, if buyers were perfectly informed about quality. Since KL lies entirely above GH, by assumption here every available car has at least one customer willing to pay more for it than the reservation price of its present owner: Bob, for example, is willing to pay Sally enough so that she would want to sell the car. So ideally, all the cars should be sold. But buyers are not perfectly informed. Suppose Bob and other buyers can observe only the average quality of the cars currently offered for sale at the going price. The curve KN shows the demand prices that buyers would offer for the average visible quality in the market, starting from the bottom. Since at the low end only the single car of lowest quality (qL ) is on the market, at that point the average quality in the market and the actual quality of the single offered car are identical. That is why the KL and KN curves coincide at point K. But when price is so high that all the cars are offered for sale, the height of point N is the buyers demand price for a car of average quality in the overall population of cars halfway between qL and qH . So the height of point N is half the vertical distance between points K and L. As drawn, KN intersects the GH curve at the quantity q between qL and qH . In equilibrium all the cars below q will be sold, at a price P that equates the reservation prices of the marginal seller and the marginal buyer. For the marginal seller, say Sally, the reservation price is the minimum she will take to part with the car. For the marginal buyer, say Bob, it is the maximum he is willing to pay for the average quality of the cars in the market, that is, the average of qualities ranging from qL to q . Cars of quality higher than q are not sold. They are worth more to their present owners than any potential buyer, knowing only the average quality of cars in the market, is willing to pay. So long as point K (showing what some buyer would pay for the lowest-quality car) lies above point G (showing what that cars owner would be willing to accept), the lowest-quality lemons will always remain in the market. What of the highest-end peaches? The diagram shows that they might be frozen out of the market. But this is not inevitable. If the gap between the buyers demand prices and the sellers reservation prices is sufciently great, the mutual advantage of trade is large and the KL curve lies considerably above the GH curve. In that case even the KN curve could lie always above GH, so that in the diagram no interior q intersection would exist. But for the peaches to remain on the market, owners of the highest-quality cars must be willing to sell them for no more than cars of merely average quality. EXAMPLE 11.2 ADVERSE SELECTION IN DENTAL INSURANCE Adverse selection is a serious problem for the insurance industry. People who face the greatest risks, or are the most likely to make claims, are the ones most anxious to buy insurance. But these are the very people that the insurance companies are least happy to welcome as customers. Martin Godfried, Hessel Oosterbeek, and, and Frank Van Tulder examined the role of adverse selection in the purchase of dental insurance in the Netherlands.a In 1995 P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 320 11. DEALING WITH UNCERTAINTY THE ECONOMICS OF RISK AND INFORMATION the Netherlands government decided to exclude dental services from the standard health insurance package covering 60% of the Dutch population. Individuals, formerly automatically covered, now had to choose whether or not to purchase dental insurance. If voluntary dental insurance has to be offered on the same terms to all, regardless of the condition of teeth, adverse selection is inevitable. Conversely, adverse selection will be moderated to the extent that insurers can charge differential rates. For some time after the policy change in the Netherlands, private insurance suppliers were under political pressure to charge the same rates to everyone regardless of the condition of their teeth. Moreover, no applicants were to be refused. In these circumstances, adverse selection could be expected. Statistically, the authors found poorer quality of teeth raised the probability of becoming insured. Also, individuals who customarily visited dentists more frequently were found to be more likely to choose insurance. Among those who chose to insure after the change in policy, 93% customarily visited the dentist twice a year. Among those who chose not to insure, it was only 82%. So people whose teeth were of poorer quality, or people more anxious about dental health, were indeed more likely to purchase the insurance. a Martin Godfried, Hessel Oosterbeekand, and Frank Van Tulder, Adverse Selection and the Demand for Supplemental Insurance, De Economist, v. 149 (2002), pp. 177190. EXAMPLE 11.3 RACEHORSES CAN BE LEMONS Credible information about quality helps overcome the lemons problem. For thoroughbred racehorses in the United States, auction houses provide information as to quality, where quality refers to potential race earnings. Horses offered for sale may or may not be certied. Certication means that the horse has been physically inspected by the auction house and found to be in good shape. A noncertied horse could be of any level of quality. Understandably, owners seeking to sell high-quality horses arrange to have them certied. Bradley S. Wimmer and Brian Chezum examined a sample of 3,376 thoroughbreds born in 1993.a Overall, the average price in noncertied sales was $13,268 compared to $93,437 in certied sales. That certication was a reliable process is evidenced by the fact that average race earnings turned out to be $48,475 for horses sold in certied sales, as compared to $27,188 for horses in noncertied sales. The most denitive test for adverse selection is to compare the prices of certied as against uncertied horses when all other publicly determinable factors age, pedigree, and so forth are held constant. The authors estimated that, for an averagequality horse in terms of observable attributes, the expected price would be $88,259. But the additional fact that the horse was sold on a noncertied basis reduced the expected price to $9,253 almost 90% less! Some breeders also enter their own horses in races. These owners have a very strong motivation to retain their best horses. Buyers, aware of this, are reluctant to pay high prices for the horses those breeders offer for sale. Consequently, noncertied horses sold by racing-intensive breeders received lower prices than noncertied horses offered by breeders who less commonly race their own horses. a Bradley S. Wimmer and Brian Chezum, An Empirical Examination of Quality Certication in a Lemons Market, Economic Inquiry, v. 41 (2003), pp. 279291. P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 11.3 ASYMMETRIC INFORMATION 321 Table 11.1 Price versus cost in each of two periods Case 1 Low quality Price 4 Cost of production 4 High quality 13 5 Case 2 Low quality 4 4 High quality 7 6 Conveying Quality through Reputation Any rm may claim to offer a high-quality product, so how can consumers know which ones are telling the truth? A reputation may make it protable to produce a high-quality product even in the face of initial consumer ignorance. Taking account of reputation requires thinking of the future as well as of the present. To keep things simple, assume that rms and consumers are concerned with only two periods. Assume also that the rm decides in the rst period what quality to produce and cannot protably modify its decision in the second period. Customers are willing to pay a premium price for superior quality, but can only determine quality after an initial purchase. So the rms reputation is established in the rst period. In Table 11.1, the numbers for price and for cost of production apply for each of the two periods. High quality is more highly valued by consumers, but also involves higher cost of production. To begin with, assume consumers have pessimistic expectations, and so are willing to pay in the rst period only the low-quality price ($4). Suppose the rm aims to maximize the sum of prots (Price minus Cost of Production) over the two periods.5 Then, in Case 1 it would do better producing the high-quality product. A low-quality rm just breaks even: its production cost of $4 in each period just equals the price in that period. A high-quality rm suffers a $1 loss in the rst period. But having earned a good reputation, its second-period prot of $13 $5 = $8 outweighs the rst-period loss. In Case 2 the numbers do not warrant production of the high-quality product. The rms cost in the rst period is higher by $2, but the second-period gain is only $1. EXERCISE 11.1 Instead of consumers holding pessimistic beliefs about the products offered in the rst period, suppose instead they are optimistic (they initially believe they are buying from a high-quality rm). (a) For Case 1 of the table, which type of rm does better? (b) Same question, for Case 2. A N S W E R : (a) In Case 1, a high-quality rm has total prot $8 + $8 = $16; a low- quality rm has total prot $9 + $0 = $9. As before, here the high-quality rm does better. (b) In Case 2, a high-quality rm has total prot $1 + $1 = $2; a low-quality rm has prot of $3 + $0 = $3. As before, here the low-quality rm does better. So, in this example, whether consumers are initially optimistic or pessimistic does not affect the relative protability of high-quality products versus low-quality products. 5 Chapter 15, which covers the economics of time, will show that future benets and costs are normally discounted relative to the present. For simplicity here, second-year benets and costs have not been discounted. P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 322 11. DEALING WITH UNCERTAINTY THE ECONOMICS OF RISK AND INFORMATION Returning to Case 1 in Table 11.1, assume now that, since producing the high-quality product is more protable regardless of consumer beliefs, consumers will plausibly expect the rm to produce a high-quality product. (This is an instance of the concept called rational expectations. The idea of rational expectations is that each individual and rm makes predictions about what others will do that are consistent with the incentives that these other rms and individuals face.) Specically, here, under rational expectations the consumers would be willing to pay $13 each period and the rms prots would be $16, just as under the optimistic assumption of Exercise 11.2. In Case 2, however, the optimistic assumption is shown to be mistaken, since under that assumption prots are greater for a rm supplying the low-quality product. So rational expectations dictate that, under the conditions of Case 2, the rm will indeed offer the low-quality product. CONCLUSION Even in the face of initial consumer ignorance, market forces can support production of high-quality products. Depending upon the specic demand and cost conditions, it may pay a high-quality rm to accept a temporary loss while building a reputation, thereby gaining future business. But in other circumstances it would be unprotable for a rm to incur the extra costs of establishing a reputation for high quality.6 EXAMPLE 11.4 RESTAURANT HYGIENE Restaurant patrons can observe cleanliness in the dining area, but might wonder about what goes on back in the kitchen. Since any restaurant could claim to have good kitchen hygiene, mere assertions to that effect have to be discounted. In Los Angeles County, eating establishments had been subject to inspection by the Department of Health Services for a number of years. As of December 1997 restaurants were required, in a number of cities within the county, to publicly display grade reports rating their hygiene as A, B, or C. A study by Ginger Zhe Jin and Phillip Leslie investigated whether the public displays tended to raise hygienic standards.a As shown in the table, there was indeed a noticeable rise in hygiene scores in the period surrounding the new requirement. In the rst half of the period, through the second quarter of 1997, the average scores were consistently between 75 and 76. In the second half of the period, starting with the third quarter of 1997, the scores were all above 80 ranging up to and even slightly beyond 90. The authors also investigated the effect of the A, B, or C grades upon restaurant prices and volume of business. Price and quantity data were not available separately, but taxation statistics provided useful information about revenue (price times quantity). Mandatory posting was associated with a 5.7% increase in revenue for an A-rated restaurant, a 0.7% revenue increase for a B-rated restaurant, and a 1% decrease for a C-rated restaurant. Thus consumers were evidently attending to the posted ratings. Another question was whether the better information made available by the ratings improved the overall market for restaurant services. This indeed appeared to be the case. Despite the higher average level of quality evidenced by the rise in the hygiene ratings, the price index for restaurant meals in Los Angeles actually 6 The more important the future relative to the present, the more attractive it is to produce a higher-quality product. If a reputation lasts for many years, even a small annual future advantage (prot improvement) could justify incurring a considerable rst-period loss. P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 11.3 ASYMMETRIC INFORMATION 323 fell relative to restaurant price indexes in other regions, and relative to price indexes for other retail goods in Los Angeles. Presumably, restaurant patrons, being better informed, were able to shift their patronage to restaurants representing better buys in terms of price as related to quality. The effects of grade cards on restaurant hygiene score in Los Angeles Quarter 1996 Q1 Q2 Q3 Q4 1997 Q1 Q2 Q3 Q4 1998 Q1 Q2 Q3 Q4 Hygiene score 75.62 75.37 75.03 75.27 75.81 75.31 83.99 81.82 86.69 90.26 89.85 90.30 Source: Adapted from Table 1 in Jin and Leslie (2003). a Ginger Zhe Jin and Phillip Leslie, The Effect of Information on Product Quality: Evidence from Restaurant Hygiene Grade Cards, Quarterly Journal of Economics, v. 118 (2003), pp. 409451. Do Prices Signal Quality? Information as a Public Good In the lemons situation consumers were assumed to be unable to distinguish qualities of used cars on the market. Now suppose instead that, for branded products, some consumers know the quality of each brand while others do not. Imagine that brands X and Y of a particular product such as cell phones may differ in quality. If none of the consumers knows which brand is better, prices PX and PY would have to be the same. But if some consumers know that X is better, their market choices would tend to raise PX over PY . Then an initially ignorant consumer, observing that X is now selling for a higher price, would rationally conclude that X must be the higher quality brand. Thus, market prices tend to reveal quality differentials. This process works out if informed consumers incur no extra costs in discovering which brand is better. But if the information can only be obtained at a cost, consumers who spend nothing on collecting information, merely observing the quality-revealing price differential, are better off than consumers who have incurred the costs of collecting the information. Since the information revealed by the price is visible to all, it is a public good in the sense of Chapter 10. As in all public goods, each individual is tempted to let others bear the cost of providing it. The paradox is that if all consumers reason in this way, no one would collect the needed data, and all the consumers would remain ignorant. P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 324 11. DEALING WITH UNCERTAINTY THE ECONOMICS OF RISK AND INFORMATION Table 11.2 Should you pay for information? Pay Pay Dont pay Pay Dont pay Value of paying or not paying 7, 7 10, 2 Dont pay 2, 10 0, 0 Rank-ordered payoffs for chicken 3, 3 2, 4 4, 2 1, 1 Using uses the game-theoretic concepts introduced in the preceding chapter, Table 11.2 is a payoff matrix for two consumers considering whether to pay for information about quality. Panel (a) shows the specic numbers used for this example, while Panel (b) shows the rank ordering of the payoffs. Comparison of the rank orderings with those in Table 10.3 reveal that this situation is not a Prisoners Dilemma. Instead it follows a different pattern called by game theorists the Chicken game. Whereas in Prisoners Dilemma the bottom row and the right-hand column are always the more desirable choices, in Chicken each partys preferred action depends upon the other players decision. Specically, if the other party is paying for information, you do best by not paying. Instead, you can observe the price without incurring any cost. But if the other party is not paying, then by assumption you would be better off buying the information yourself rather than remain ignorant. In contrast with Prisoners Dilemma, there is no dominance equilibrium in Chicken. Instead there are two Nash equilibria in pure strategies: (Pay, Dont Pay) with payoffs 3,5 and (Dont Pay, Pay) with payoffs 5,3. Both of these are asymmetrical; in Chicken-type games there is no symmetrical solution in pure strategies. However, Chapter 10 showed how to nd a mixed-strategy equilibrium. Using the formula of equation (10.1), here a = 7, b = 10, c = 2, and d = 0. Then Rows probability choice pR for his rst (top) strategy and Columns pC for her rst (left-hand) strategy are given by the symmetrical solution: p R = pC = 02 = 0.4 7 10 2 + 0 So each decision-maker would choose Pay with probability 40% and Dont Pay with probability 60%. But this symmetrical mixed-strategy solution is inefcient. With 16% probability both consumers pay for the information, the payoffs summing to 14. Or, with 36% probability, neither pays. Both are then ignorant about the product quality, and the summed payoffs are 0. Last, with probability 48% either of the two asymmetrical outcomes (in which only one of the consumers buys the information) occurs; the summed payoffs are 12. Calculation shows the overall expectation (probability-weighted average) of the summed payoffs for the mixed-strategy solution to be 8, or 4 per player. In contrast, as just seen, the asymmetrical solutions have summed payoffs of 12, or 6 per player. As always, it is possible to nd a contract that rescues the parties from social traps such as Prisoners Dilemma or Chicken. For example, the individuals could agree to divide the cost of acquiring the information, or to take turns in doing so. So if information about quality is inadequately available in markets, that failure must be due to the difculty of entering into a suitable contract. P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 11.4 HERD BEHAVIOR AND INFORMATIONAL CASCADES 325 Conveying Information Advertising Again assuming two brands X and Y, another quality-revealing force operates on the supply side of the market. The manufacturer of the superior brand, brand X, has a motive to publicize that information through advertising. But, although brand X can claim to be better, so can brand Y. How can the consumer know which one to believe? Brand X has one advantage: the truth is often more intrinsically credible than a lie. True facts and logically valid inferences are, to a degree, self-evident. If so, then brand X s ads will, other things equal, be more convincing. But suppose readers of ads simply cannot tell whether X or Y is lying. Even so, ads may have an effect. Suppose the prices PX and PY are initially the same. Imagine that consumers, observing the ads placed by brands X and Y, are still totally in doubt and so buy the two brands in equal quantities. But, on average, purchasers of brand X will have better experiences with the product. They are likely to recommend X to their friends, and to buy more X themselves in the future. The opposite will hold, of course, for brand Y. So, in the long run at least, this reputation effect means that advertising will pay off more for the higher-quality brand.7 Consequently, better brands are likely to advertise more heavily. Consumers can therefore, to a degree, expect that a heavily advertised product is likely to be of better quality. But this is only part of the story. An important force operates in the other direction. The low-quality manufacturer can likely produce at lower cost. The high unit returns associated with low production costs make it more protable to advertise heavily. In effect brand Y can try to look as much as possible like the high-quality brand X not only in what it says in its ads, but in the scale of its advertising. A rm producing an inferior brand has two main options. It can adopt a hit-and-run strategy, aiming at quick sales and then a quick exit. Alternatively, to nd a permanent niche in the market, it is likely to cut its price in order to offer consumers a low-price low-quality alternative to brand X. So, in the long run, we can indeed expect that prices tend to reveal quality. 11.4 HERD BEHAVIOR AND INFORMATIONAL CASCADES One can gain useful information by observing the actions of others. If your tastes resemble other peoples, a crowded restaurant is likely to be a good place to eat, and a popular movie is likely to be good entertainment. Suppose a number of individuals face the same choice problem, for example which movie to go to. But imagine that each person can observe the decisions of those preceding him or her. Let everyone be risk-neutral so that the calculation can run in terms of the mathematical expectation (the probability-weighted average) of monetary gains and losses. Imagine the choice concerns a fork in the road. Let action a be taking the left branch and action b taking the right branch. In state of the world A only the left branch leads to your desired destination; in state B the right branch does. Matching the action to the state of Nature yields a payoff of 1, whereas a mismatch has payoff 1. Before making a decision, suppose each person receives an imperfect private signal, either or . For example, a signal can be a hazy recollection of what an old tour book 7 Phillip Nelson, Advertising as Information, Journal of Political Economy, v. 82 (1974), pp. 729754. P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 326 11. DEALING WITH UNCERTAINTY THE ECONOMICS OF RISK AND INFORMATION said. Signal has some probability p >1/2 of being observed when the state is A; signal has the same probability p >1/2 when the state is B. So p is the probability that the observed signal, or , is correct. For a person with no other information, action a is evidently better if the person sees signal , and action b if the person sees signal . Imagine that Aaron, the rst individual in the sequence, follows this rule. By assumption, everyone after Aaron knows what Aaron did (which branch of the fork he chose). If they believe that Aaron acted rationally, these successors can all infer Aarons signal perfectly from his decision. If he chose action a, he must have seen signal ; if he chose b, he must have seen signal . Now consider the next individual in sequence, Barbara. If she observes that Aaron chose a, and if Barbaras own private signal is , then she should choose, a herself. As Barbara sees it, there have now been two signals, one inferred from Aarons actions and the other that she herself observed; both signals favor action a. If, however, Barbaras private signal is , then the signal inferred from Aarons action and her own private signal point in opposite directions. So she should be exactly indifferent between a and b. In that case, suppose Barbara tosses a fair coin. The third individual, Clarence, knows the actions of his predecessors. He faces one of three possible situations: both Aaron and Barbara chose a, both chose b, or their choices diverged. If Aaron chose a and Barbara chose b , then Aaron must have seen an signal and Barbara a signal. If so the two predecessor actions balance out, and no information is conveyed to Clarence. He therefore will decide on the basis of his own signal, choosing a if he observes and b if he observes . If both Aaron and Barbara chose a, Clarence should also choose action a regardless of his own personal signal. The reasoning is as follows. First, if Aaron rationally chose a, he must have seen signal . As for Barbara, she must have chosen action a either because she saw herself or because she saw and then tossed a coin which happened to come up in favor of action a. More likely than not she saw , since if she had seen her action would have depended on the coin ip, which could have led her to choose b instead of a . Even if Clarence observed , the fact that Aaron observed is enough to make Clarence indifferent between a and b . Since he infers that Barbara probably saw , Clarence unambiguously prefers a . Of course, if Clarence observes , he prefers a even more strongly. So Clarences action does not depend on his signal. A corresponding argument applies, in the other direction, if Aaron and Barbara had both chosen action b . So Clarences choice does not convey any information to later observers. If the fourth person, Donna, observes Clarence choosing a , she is in the same position informationally as Clarence. Donna also chooses a . But this means that her action is uninformative too. And Edward, Francine, and so forth all take the same action as well. This situation, in which individuals decide based upon observing others without regard to their own signals, is called an information cascade. No later series of signals can break the cascade. Ones own private signal, being imperfect, after a certain point, cannot outweigh the public information represented by the aggregate of all the prior actions. Once an informational cascade starts, information stops accumulating. Later private signals never join the public pool of knowledge. And, supposing that obtaining a private P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 11.4 HERD BEHAVIOR AND INFORMATIONAL CASCADES 327 signal involves some cost, people will rationally stop paying for them. So once the cascade begins not only public information but also private information will no longer accumulate. Nevertheless, cascades are fragile, as they rest upon only a small amount of public information the actions of a few decision-makers early in the sequence. Cascades may break because of leakage of private signals. To the extent that not just predecessors actions but also the signals they observed are known, a cascade is less likely to begin and more likely to end. Another factor is the weight of ones private information. An individual who receives a very powerful signal, which she knows to be more informative than the signals received by predecessors, may rationally deviate and possibly break the cascade. But most important is the arrival of information about whether action a or action b was more successful. Later decision-makers usually can observe, to a degree, not just the actions of their predecessors but the results of those actions. So information tends to accumulate, over time, about the true state of the world. That helps explain why cascades seldom go on forever. Not all commonality of behavior stems from herd effects. Producers or consumers may all choose to do the same thing simply because doing so is best for one and all. Or, it may make sense for everyone to buy the same good or service because of returns to scale in production or consumption. EXAMPLE 11.5 FADS AND CASCADES IN TELEVISION PROGRAMMING Television programming seems to run in cycles. In some years reality shows predominate, at other times comedies or dramas or westerns. One possible explanation is that the public taste itself runs in cycles. If viewers currently are in the mood to watch comedies, that is what the networks will show. But another possibility is a herd effect or cascade: executives in the various networks might be imitating one another. One or two networks having taken the lead by introducing reality shows, a cascade gets under way that other networks are inclined to follow. A study by Robert E. Kennedy of program introductions and cancellations by ABC, CBS, and NBC between September 1961 and October 1989 provides some support for the cascade interpretation.a During this period the selection process began 1218 months before each fall season. After looking at a great many program ideas, each network chose about 150 programs to be developed into scripts, and from these about 30 to develop into pilot episodes. The network then evaluated the pilots and chose seven to ten for inclusion in the fall schedule. All three networks announced their schedules in early May each year. Through word of mouth, each network knows early on what pilot programs the other networks are developing. Later in the process, information about each networks strengths, weaknesses, and portfolio of pilots gradually becomes accessible to rivals. And nally, once broadcasts actually begin, their relative success in attracting viewers is visible to all. After classifying all prime-time television program introductions into 15 categories, the author estimated whether a network was more likely to introduce programs in a particular category when rival networks were doing so, and to cancel programs in a particular category when other networks were cancelling theirs. Imitation turned out to be common. For example, if NBC increased its introductions of dramas by 10 percentage points, CBS increased its new hours of drama by 2.3 percentage points. Cancellations showed a similar pattern. P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 328 11. DEALING WITH UNCERTAINTY THE ECONOMICS OF RISK AND INFORMATION But was such imitation protable? For each category of television programs, the author measured trendiness as the percentage change in the hours of programming in that category from one year to the next. On average, nontrendy introductions outperformed trendy introductions. For example, programs in the top third on the trendiness scale lasted an average of 1.82 years; programs in the bottom third of trendiness lasted longer, an average of 2.29 years. Similarly, programs in a trendy category had, on average, lower ratings than nontrendy programs. So, it appears, in this period herding behavior had been carried beyond what could rationally be justied. a Robert E. Kennedy, Strategy Fads and Competitive Convergence: An Empirical Test for Herd Behav- ior in Prime Time Television Programming, Journal of Industrial Economics, v. 50 (2002), pp. 5784. 11.5 COPYRIGHT, PATENTS, AND INTELLECTUAL PROPERTY RIGHTS The laws of most nations recognize several types of private property rights in information, among them copyrights, patents, trademarks, and trade secrets. The central problem with intellectual property (IP) rights is the need to balance two conicting ends: inducing the creation of novel ideas and promoting their widespread use. By allowing creators to charge a price for their product, IP rights reward and therefore encourage creation of new ideas. But the prices charged discourage use of the same ideas. Patent royalties provide incentives to inventors but may freeze out some potential uses of the invention. The various forms of intellectual property rights represent different compromises between the ends of promoting the creation and the dissemination of valuable new ideas. A patent requires the public disclosure of the invention and grants to its owner the right for a period of years to exclude others from making, using, offering for sale, selling, or importing the invention. Trade secrets (such as the formula for Coca-Cola) are not disclosed to the general public, but are to some extent protected against theft. The disadvantage of trade secrets, as opposed to patents, is that the owner has no protection against anyone who comes up with the same idea independently. A copyright gives its owner the exclusive right, again for a limited period, to make and distribute copies of a literary, musical, or artistic work. There is an important procedural difference between patent and copyright. The U.S. Patent Ofce awards a patent only after careful investigation that the invention is novel (the invention is not the same as any previously described or known to the public), useful (the invention functions for its intended purpose), and nonobvious (the invention would not be self-evident to a person of ordinary skill in the art.). In contrast, copyrights are granted automatically simply by registration. A copyright does not protect ideas but only a particular expression of them. So though anyone can use the ideas in this book, another author cannot extensively copy the exact words in it. But it is difcult to maintain this distinction in any consistent way. Unauthorized translation of a work, though surely a different expression of its ideas, would almost always be considered an infringement of copyright. Expressions further removed from the original, for example summaries or parodies, may or may not be considered infringements. Three main policy issues are involved in the economics of copyright and patent. (1) Are IP rights given out too freely, or not freely enough? In the case of patents, should the P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 11.5 COPYRIGHT, PATENTS, AND INTELLECTUAL PROPERTY RIGHTS 329 Table 11.3 Creation without copyright a Prisoners Dilemma Author #2 Author #1 Create Dont create Create 2, 2 5, 3 Dont create 3, 5 0, 0 criteria of originality and utility be interpreted more or less stringently? (2) A related question concerns scope. Should the Wright Brothers have been granted a broad patent covering all powered ight, or only a narrow patent on powered ight using wings warped by wires for control purposes?8 (3) When granted, are the rights too strong, or too weak? For example, should fair use9 be permitted without charge? One confusion should be cleared away. A patent or a copyright is a property right, not a monopoly in the sense used in economic analysis. An intellectual property right, like any property right, must grant some special power to the owner. But that property right becomes a monopoly only if close competitors are absent. Consider a patent for a new rose variety. Thousands of rose varieties have been invented, and hundreds are in the market. So, although the patent protects against unauthorized use of that unique variety, there is no monopoly. (These cases, of unique yet closely competing products, fall under the heading of monopolistic competition as discussed in Chapter 9 above.) Or consider a patent for a new type of bottle-opener. Again, dozens of designs for bottle-openers are on the market, so there is no monopoly. On the other hand, a sufciently broad patent could have monopoly implications. If the Wright brothers had been granted a patent on all powered ight, they would have had a stranglehold over the aircraft industry. Thinking for concreteness of copyright, in the absence of legal protection authors would face a public good problem like that discussed in Chapter 10 and earlier in this chapter. The payoffs in Table 11.3 here are, by assumption, identical to the Prisoners Dilemma payoffs of Table 10.4 that dealt with draining marshy soil as a public good. Here, instead of two farmers there are two potential authors. Instead of Pump and Dont Pump, the strategy options are Create and Dont Create. If one author chooses Create, the other can free-ride by copying which, by assumption, yields the highest payoff (namely, 5). The creative author, having invested time and effort to little or no avail, gets the lowest payoff (3). If both choose Create the payoffs are 2,2; if both choose Dont Create, the payoffs are 0,0. Here Dont Create is better for a player regardless of what the other player does. As before the equilibrium is the inefcient (Dont Create, Dont Create) strategy-pair with payoffs 0,0. The authors might escape this trap by signing a binding contract not to copy. That could be feasible if there were only two potential authors, but not when there are many. As an alternative to such a contract, copyright law, by making unauthorized copying illegal, enables both authors to create and thus achieve the efcient (2,2) payoffs. But this analysis is too extreme. It implies there would be little or no creative activity in the absence of copyright. Yet books, symphonies, and other compositions were created 8 9 They were awarded only the narrow patent. Under the copyright law in the United States, anyone can copy copyrighted material without the permission of the original author, if the amount copied is limited and if the purpose falls into specied categories such as criticizing or parodying the copyrighted work. P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 330 11. DEALING WITH UNCERTAINTY THE ECONOMICS OF RISK AND INFORMATION before copyright laws existed and would undoubtedly be created today even if copyright were abolished. There are several possible reasons. (1) Some people are willing to create without material reward, simply for the pleasure and glory. (2) Original composition may yield indirect material gains. Wolfgang Amadeus Mozart (17561791) was paid a pittance for the operas, concertos, and symphonies he composed. He was hoping for an indirect reward, appointment as a salaried musician to a European court or church. (His predecessors Franz Joseph Haydn and Johann Sebastian Bach found such positions, but Mozart never realized his hopes). (3) The original creator can prot from a time advantage over imitations. Paris and Milan high-fashion designs are rapidly copied, yet command a steep premium while still new. Original digital recordings may reap substantial revenues before unauthorized digital copies become widely available. (This was one of the arguments used by the defense in the Napster litigation.) EXAMPLE 11.6 THE NAPSTER STORY a Digital technology has made it possible to produce essentially perfect copies of CD recordings at extremely low cost. As a result, it is technologically possible for consumers to copy recordings without compensating the original creators. In January 2000, MP3.com began making musical works available for copying via its Internet computer servers. (MP3 had purchased single copies, but had not purchased licenses to reproduce them, claiming an exemption for fair use.) Major record companies and artists then sued MP3 for copyright infringement. MP3 lost its case and went out of business. But then Napster was initiated as a peerto-peer network for transfer of downloaded recordings. The fair use defense was stronger for Napster than for MP3, since Napster was not directly selling services to anyone. But Napster also lost in court and was forced to go out of business as well. At the date of writing the recording industry has so far won the major legal battles, yet may still lose the war. The reason is that, in part with the help of successors to Napster such as Gnutella and Kazaa or even without any special help, it is becoming increasingly feasible to transfer recordings from computer to computer without payment to copyright holders. The copyrights, though upheld in court, may turn out to be impossible to enforce. The recording industry has tried a number of strategies in defense. One is encryption, which is subject to attack by hackers. Prices have also been reduced, and there have been experiments with new marketing techniques such as subscription services. Another device is to package additional features such as interviews and photos together with legitimate copies. Industry leaders have also, perhaps with some degree of success, appealed to customers sense of ethics. For all these reasons the recording industry will not be totally going out of business. However, the number of recorded new compositions and new performances or their quality may well fall off. As an impending development, rising hard-drive capacities of personal computers and continuing improvements in transmission speeds and bandwidth seem bound to threaten the business of selling recorded motion pictures. a For a description of the legal history, see Peter K. Yu, The Escalating Copyright Wars, Hofstra Law Review, v. 32 (2004). P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 11.5 COPYRIGHT, PATENTS, AND INTELLECTUAL PROPERTY RIGHTS 331 Table 11.4 Creation without copyright a chicken game Create Create Imitate 7, 7 10, 2 Imitate 2, 10 0, 0 Last, a fourth explanation for the continued creation of original compositions even in the absence of copyright protection is that the situation may not really be a Prisoners Dilemma. Though freely copyable compositions are public goods, the choice situation facing potential creators may be better reected by the payoff environment of Chicken. Just as Table 11.3 repeated the Prisoners Dilemma payoffs of Table 10.5, Table 11.4 here repeats the Chicken payoffs of Table 11.2. But instead of paying to acquire information as a public good, here the issue is whether to create information as a public good or to imitate an existing creation. The logic is essentially the same. The idea is that, although copying is preferred when there is something to copy (Imitate is a players best choice if the other player chooses Create), if the other player produces nothing you would rather choose Create. Imagine a theatrical entrepreneur who wants to produce live musicals. If he can put on a revival of Oklahoma or Guys and Dolls without paying royalties, that would be ideal. But if no musicals are available for reviving, to present something to the public he would have to commission one himself. Or imagine that Paris and Milan stop creating original dress designs. Then a dress manufacturing rm previously specializing in knockoffs might nd it protable to begin creating its own designs. Since Table 11.4 is numerically equivalent to Table 11.2, the solutions are the same. In particular, the symmetrical mixed-strategy equilibrium is p R = p C = 0.4. It is possible also to interpret this mixed-strategy solution nonprobabilistically. Instead of saying the game has only two players, each choosing a 40:60 strategy mix, we can say there are many players of whom 40% choose Create and the other 60% choose Imitate. So in the absence of rights in intellectual property we would expect to see a decrease in intellectual creative activity, but not its complete elimination. The preceding discussion emphasized the role of legal protection for encouraging intellectual creation. But what of the other side of the picture, the spread and use of such ideas as are created? Without copyright fewer musical recordings may be produced, but those that are produced will be more accessible. When it comes to life-saving or life-enhancing pharmaceutical drugs, striking a proper balance between having new medications and allowing for their widest possible use is a highly important issue. EXAMPLE 11.7 PHARMACEUTICALS CREATION VERSUS UTILIZATION If patents on pharmaceutical drugs were eliminated, generic competitors for alreadydeveloped medications (see Example 5.4) would rapidly enter. To meet the competition the branded products would have to come down in price, and consumers would benet. On the other hand, manufacturers incentives to undertake the costly research needed to develop new drugs according to some estimates, as high as $800,000,000 per genuinely new drug (new chemical entity or NCE) would fall off correspondingly. So consumers, though beneting in the short run, would very likely suffer later on from a deciency of new drugs. P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 332 11. DEALING WITH UNCERTAINTY THE ECONOMICS OF RISK AND INFORMATION James W. Hughes, Michael J. Moore, and Edward A. Snyder attempted to quantify these conicting considerations. They estimated the aggregate Consumer Surplus under the two alternative policies having drug patents or not.a In their calculations the authors took into consideration a great many factors including the years of useful life per new drug, the period of exclusivity if patented (the number of years before generic competitors could enter), the market share retained by branded products after generic entry, and the fraction of drug prots allocated to research. In allowing for all of these, the authors balanced the benet to consumers of lower current prices (the static gains) against the loss to consumers of reduced future availability of new drugs (the dynamic losses). Balancing the present against the future is a topic that will be taken up in Chapter 15 that deals with the economics of time. For a variety of reasons among them the brevity of human life, the fact that resources grow over time, and the presence of risk markets discount the future relative to the present, and the far future relative to the near future. The authors calculated the Present Values of current and future benets from abolition of patents, using a range of discount rates ranging from 1% to 5% per annum. The table here shows that at the extremely low 1% discount rate, which weights the future relatively heavily, the benet from abolishing drug patenting is far less than the loss. The benet/cost ratio is only 0.15. As the discount rate rises the balance swings in the other direction. But only at the extremely high 5% discount rate, associated with very heavy discount of future benets, does the gain/loss ratio for abolition of patents rise above unity, to 1.11. What the authors regard as the most accurate assumption, a discount rate of 2%, is associated with a cost/benet ratio of 0.33. So, they conclude, although the short-run gain in Consumer Surplus due to lower prices for drugs would be quite substantial, the long-run loss from abolition of patents and consequent reduced future availability of drugs would be even greater around three times as great. Benets and costs of abolishing pharmaceutical patents (present values of consumer surplus, 2001 dollars, billions) Discount rates Static (current) gains Dynamic (future) losses Gain/loss ratio 1% 882 5760 0.15 2% 840 2501 0.33 3% 800 1454 0.56 5% 727 673 1.11 Source: Adapted from Hughes, Moore, and Snyder, Table 6. a James W. Hughes, Michael J. Moore, and Edward A. Snyder, Napsterizing Pharmaceuticals: Ac- cess, Innovation, and Consumer Welfare, National Bureau of Economic Research Working Paper No. 0229 (October 2002). For frequently repeated and independent decisions, the Law of Large Numbers in effect cancels out risk. Then it is possible to choose the best action on the basis of maximizing ones average (expected) dollar gain. But for nonrepeatable choices involving large fractions of the decision-makers resources, individuals averse to risk are willing to sacrice expected gain to in order to avoid very bad outcomes. Analytically, the individual is then maximizing expected utility rather than expected dollar gain. Risk aversion is equivalent to diminishing marginal utility of income. SUMMARY P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 SUMMARY 333 A fair gamble or insurance contract is one for which the mathematical expectation of net gain is zero. If already in a riskless position, a risk-averse decision-maker would always reject such a gamble or contract. On the other hand, if initially in a risky income situation for example, facing a risk of theft such a decision-maker will accept gambles or contracts that offset his or her initial risk. Indeed, a risk-averse decision-maker would be willing to accept even some unfair gambles or insurance contracts, provided they tended to offset the riskiness of his or her endowed income combination. This is typically the case when insurance is purchased. It sometimes pays to delay taking action until further information becomes available. But for the information to be of value, it must be that different messages or signals might lead to different optimal actions. As one example, a consumer may delay deciding whether to buy a good, even if the expected price is expected to rise. The delay reects the option value of being able to buy the good only if its price turns out to be low. When sellers know more than do potential buyers about the characteristics of a good, a lemons problem may emerge. Owners of low-quality items are more eager to sell than are owners of high-quality items, and that makes potential demanders less eager to buy. As a result only low-end items may appear on the market, ranging up to some critical level of quality. Above that quality level the peaches (better-quality items) may never be available for purchase. People can sometimes infer quality from the price of the good itself. An ignorant but rational consumer who knows that informed consumers are willing to pay more for a better product may conclude that higher-priced goods are of higher quality. But these informed consumers, if they have incurred cost in evaluating product quality, are providing a kind of public good. If the payoff situation is a Prisoners Dilemma, no one will be willing to incur the cost. But if the payoffs correspond to the pattern of Chicken, there will be a mixed-strategy equilibrium in which with some positive probability each decision-maker makes the investment in information. Owing to anticipation of repeated sales, other things equal, producers of high-quality goods can expect to prot more from advertising than producers of low-quality goods. If so, the fact that a product is advertised may signal quality (regardless of what the ads actually say). But such an inference is not entirely reliable, since a bad product is likely to be cheaper to produce. Then the seller, even with little hope of repeated sales, may nd it pays to advertise. People who know they are imperfectly informed can try to gain information by observing others actions. When others in aggregate are likely to have better information than one single person can advantageously acquire, the result may be an informational cascade. If a crowded restaurant is likely to be a good place to eat, and a popular movie to be good entertainment, then any one person has an incentive to follow the choices of others rather than to rely on his private information. Once an informational cascade starts, information stops accumulating. But informational cascades are fragile, leading sometimes to short-lived fads. Intellectual property (IP) rights encourage the creation of inventions and novel ideas by permitting creators to reap some return from their efforts. But holders of IP rights are likely to make the new ideas available only for a price, which discourages their use and dissemination. The laws covering various forms of intellectual property patent, copyright, trademarks and so on balance these factors in different ways. In the absence of IP rights the creation of new ideas would be a public good. The payoff pattern is likely to fall into the Chicken category, so that a certain amount of creative activity would P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 334 11. DEALING WITH UNCERTAINTY THE ECONOMICS OF RISK AND INFORMATION continue to take place, though less than would occur under strong intellectual property rights. QUESTIONS The answers to daggered questions appear at the end of the book. 1. Explain graphically why a convex utility function implies a preference for greater risk. 2. Why do insurance companies require medical tests before agreeing to sell an individual a life insurance policy? 3. a. b. For Review Describe a benet and a cost to consumers of drug patents. Are patents more likely to be desirable if consumers place high value on long-term costs and benets? 4. Do the following increase or decrease the certainty-equivalent associated with a gamble? The risk premium? a. High risk (variability). b. High risk aversion. c. High expected value. 5. Would a risk-averse individual who is endowed with riskless wealth ever accept a fair gamble? 6. What is another word for the acquisition of a gamble that offsets endowed risk? 7. Why might an individual underinsure? 8. Theorists who study nancial economics have developed models that have been very successful in determining the value of nancial options. For example, a call option gives the holder the right (but not the obligation) to purchase a stock at a prespecied price during a prespecied time period. Why is a call option valuable? Discuss in relation to the value of information. 9. What is adverse selection? How does it affect the price that consumers are willing to pay for a product whose quality is not observable at the time of purchase? 10. Suppose that the quality of a product is not observable to consumers at the time of purchase. How can reputation encourage a rm to produce a high-quality product? 11. What can impair the credibility of price as a signal product quality? Despite this problem, can high product price work as a signal? 12. Why would a high-quality brand have a higher marginal benet from advertising than a low-quality brand? 13. Employers are often skeptical of job applicants who have gaps in their resumes periods of time during which the individual had no employment. Explain why based on informational cascades. For Further Thought and Discussion 1. You want to nd out whether there is a lemons problem in the market for houses. How, if at all, could you use the following information to answer the question? a. Repair rates for homes owned by the original buyer compared to houses which have been resold. b. The fraction of houses resold in each year after purchase. 2. A rm spends money on advertising attempting to persuade consumers of the brand name of its grapes. Should consumers conclude that its grapes have better quality than grapes sold by other rms? P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 QUESTIONS 335 3. Suppose that consumers are willing to pay as much as $8,000 for a good used car but only $2,000 for a lemon. Each owner of a good used car will sell only if the price exceeds $4,000; each owner of a lemon will sell only if the price exceeds $600. Buyers cannot tell if a used car is a lemon or not, and 20% of all used cars are lemons. In equilibrium, which cars are sold, and at what prices? 4. Some mortgage companies offer mortgages without asking the borrower anything about her income or nonhouse assets. Why do such loans have higher interest rates? 5. Medford University offers each new faculty hired a choice: he or she can get a tenured job, or else choose a series of shorter-term (e.g., 3 or 5 years) contracts at a higher salary level designed to compensate for the decreased job security. What is likely to be the outcome of this menu plan if faculty members differ in quality, that is, in ability to nd a job elsewhere? 6. Why is it usually incorrect to call a patent award a monopoly? 7. John argues, Sure, I dont like risk. But if I always choose the option with higher expected value, over the long run the wins and losses will more or less cancel out, except that Ill end up getting a higher payoff on average. So it is irrational to be averse to risk. Do you agree? 8. Investment advisors typically recommend that individuals diversify, by placing portions of ones invested wealth into different asset classes (such as bonds, domestic stocks, and foreign stocks). Suppose that there are two asset classes A and B, which are similar in variability and expected payoff; sometimes A does better and sometimes B. Which investment strategy do you think is riskier, placing all your invested wealth in asset A, or dividing it equally between assets A and B ? 9. Many employees invest for retirement by using their retirement plans to buy stocks in their own companies. Is this likely to be a good decision if the employee is risk-averse? 10. You are trying to decide how much to offer for a television set being sold at a garage sale. One of the other shoppers mentions to you that the reason for the sale is that owner is planning on moving to another country and cannot bring anything with him. How does this news affect the amount you should be willing to offer? How is this related to the problem of adverse selection? 11. The evidence on restaurant hygiene in Los Angeles (Example 11.4) suggests that regulation forcing conspicuous public display of hygiene scores caused restaurants to improve their hygiene. Even without such regulation, a private ratings agency could have gone into the business of inspecting restaurants and offering grades. If customers valued hygiene, hygienic restaurants might have been willing to pay the ratings agency to provide evaluations, in order to win more business. Does the absence of conspicuous private hygiene ratings prior to the regulation indicate that customers did not value hygiene very much? 12. Consider a setting like that in Section 11.4 in which individuals with private information make decisions in sequence. Suppose, however, that Aaron possesses a signal that is slightly more accurate than Barbaras. In other words, his signal probability is q > p, where p is Barbaras signal probability. Suppose that Aaron chooses action a. What will Barbara do? How many individuals must make decisions before a cascade forms? 13. During the rise of the personal computer industry, IBM allowed competitors to produce compatible PCs whereas Apple maintained a proprietary design. What are some possible advantages of permitting imitation by competitors? P1: JPJ/KIC 0521818648c11.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:37 336 P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 IV FACTOR MARKETS AND INCOME DISTRIBUTION 337 P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 338 P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12 12.1 The Demand for Factor Services Production and Factor Employment with a Single Variable Input 340 The Production Function 340 Diminishing Returns 340 From Production Function to Cost Function 343 The Firms Demand for a Single Variable Input 345 12.2 Production and Factor Employment with Several Variable Inputs 349 The Production Function 350 Factor Balance and Factor Employment 355 The Firms Demand for Inputs 358 12.3 12.4 12.5 The Industrys Demand for Inputs 362 Monopsony in the Factor Market 364 An Application: Minimum-Wage Laws 366 SUMMARY 371 QUESTIONS 373 EXAMPLES 12.1 12.2 12.3 12.4 12.5 12.6 12.7 New Mexico Onions 342 The Price of Rice and the Price of Slaves 346 Missouri Corn 353 Agricultural Production in Canada 354 The Black Death 359 Monopsony in Professional Baseball 365 Do Minimum-Wage Laws Reduce Employment? 369 339 P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 340 12. THE DEMAND FOR FACTOR SERVICES The text so far has concentrated on markets for nal products: cars, cameras, haircuts, and so forth. Here in Part Four the emphasis shifts to the markets for productive inputs such as land, labor, and machines. The demand side of the markets for these factors of production is the topic of this chapter: rms decide upon the amounts of land, labor, and other productive services to hire. On the supply side, the topic of the following chapter, owners of land or machines decide where to put their assets to use, and workers (owners of their labor power) decide where and how much to work. 12.1 PRODUCTION AND FACTOR EMPLOYMENT WITH A SINGLE VARIABLE INPUT The Production Function A mining rm, in order to extract ore, has to employ land (the mine itself) together with labor, buildings, electric power, gasoline, and machines. The technological relation between such inputs and the rms output is called the production function. It can be expressed: q (a , b , c , . . .) (12.1) This equation says that the output quantity q depends in some specied way upon the amounts a , b , c , . . . of the resource inputs A, B , C , . . . .1 Suppose all inputs are held xed except for the amount of a single variable factor A. Then the production function can be written in the simpler form: q q (a ) (12.2) This equation says that q depends algebraically only upon the single variable a. The amounts b, c, . . . of the xed inputs B, C, . . . no longer directly appear but the levels at which these inputs are held xed do affect the shape of the q (a ) function. EXERCISE 12.1 Suppose the underlying production function makes use of two inputs A and B. Specically, let equation (12.1) take the form q = 6a 1/2 b1/4 . What would be the form of equation (12.2) if the quantity of input B were held xed at b = 1? At b = 16? For b = 16, equation (12.2) becomes q = 12a 1/2 . A N S W E R : Substituting b = 1 in equation (12.1), equation (12.2) becomes q = 6a 1/2 . Diminishing Returns The Law (or Laws) of Diminishing Returns explain why costs of production rise as output grows, that is, why the Total Cost, Average Cost, and Marginal Cost functions as shown in Chapter 6 must, at least eventually, all rise as the rm increases output. 1 In the notation here A, B, C are the names of factors of production; the lower-case symbols a, b, c signify specic amounts of those factors. P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12.1 FACTOR EMPLOYMENT WITH A SINGLE VARIABLE INPUT 341 q q Pointofdiminishing totalretur ns tpa Output Figure 12.1. The Laws of Diminishing Returns 0 Pointof diminishing marginal returns a q/ a OutputperUnitInput The upper panel shows the Total Product function for factor A, tpa . The lower panel shows the corresponding Average Product function apa and Marginal Product function mpa . Diminishing marginal returns set in rst (the mpa curve reaches its peak), then diminishing average returns set in (the apa curve reaches its peak), and nally diminishing total returns set in (the tpa curve reaches its peak, at output q ). apa Pointof diminishing average returns 0 a QuantityofInput mpa Let the only variable factor be A. As a (the amount used of factor A) increases, the Total Product tpa (which is the quantity produced, so that tpa q ), the Average Product apa (which is quantity per unit of input, so that apa q /a ), and the Marginal Product mpa (which is the change in quantity per unit change of input, so that mpa q / a ) all eventually rise: THE LAWS OF DIMINISHING RETURNS: If the amount a of input A increases, with other inputs held xed, the rate of increase of Total Product q that is, the Marginal Product mpa eventually begins to fall. This is the point of diminishing marginal returns. As the input amount increases further, Average Product apa also begins to fall. This is the point of diminishing average returns. And as use of input A rises further, even Total Product may fall. (An extreme overabundance of input A could be counterproductive.) This would be the point of diminishing total returns. Figure 12.1 illustrates the Laws of Diminishing Returns. The upper panel shows the Total Product curve tpa . The lower diagram shows the corresponding curves for Marginal Product mpa and Average Product apa . The diagram conrms that diminishing P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 342 12. THE DEMAND FOR FACTOR SERVICES marginal returns set in rst, then diminishing average returns, and then (possibly) diminishing total returns. EXERCISE 12.2 A rms Total Product function is tpa q = 100a 2 a 3 . The Average Product function is then apa q/a = 100a a 2 . It can be shown algebraically2 that the Marginal Product function is mpa q/ a = 200a 3a 2 . (Or the same result can be obtained by calculus.) (a) When do diminishing marginal returns set in? (b) Diminishing average returns? (c) Diminishing total returns? A N S W E R : (a) Diminishing marginal returns set in where the mpa function reaches a maximum. It can be determined by plotting the function (or by calculus) that Marginal Product reaches its maximum at a = 33 1/3 . (b) Average Product reaches a maximum (diminishing average returns set in) at a = 50. (c) Total Product reaches a maximum (diminishing total returns set in) at a = 66 2/3 . EXAMPLE 12.1 NEW MEXICO ONIONS In dry climates such as New Mexico, onions, a water-intensive crop, need irrigation. M. S. Al-Jamal, T. W. Sammis, S. Ball, and D. Smeal studied the relation between inputs of water and crop yield (the water production function) in an experiment at the Fabian Garcia Research Center in Las Cruces, NM.a One of their studies estimated the relationship as: Yield = 7809.28 + 693 Water 1.164 Water2 The negative squared term implies that, as more water is increasingly applied, Marginal Product and Average Product and even Total Product must eventually fall. The table shows a selection of their data for the year 1995. Total Product is measured in kilograms per hectare, and water in centimeters (cm) applied (including natural rainfall). The last two columns on the right calculate the Average Product and Marginal Product for various amounts of water applied. (Following the recommended approximation method of Chapter 2, Section 2.2, the marginal estimates are placed at the midpoints of the intervals.) The table indicates that, consistent with the discussion in the text, diminishing marginal returns set in before diminishing average returns. (As can be seen, diminishing marginal returns hold here from the beginning the Marginal Product of water is declining throughout.) 2 Mathematical Footnote : Algebraically, q is the difference between q (a + a ) (a + 2 3 2 a ) and q(a), so that: q = [100(a + a ) ] [100a a 3 ] a leads to: a) a can be Carrying out the algebraic expansion, simplifying, and dividing through by q = 200a 3 a 2 + (several terms involving a Since marginal calculations deal with small changes, to a good approximation the terms involving neglected, leading to the expression in the text. P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12.1 FACTOR EMPLOYMENT WITH A SINGLE VARIABLE INPUT 343 Water input and onion crop, New Mexico 1995 Water (cm) 86.8 109.1 131.3 153.5 175.7 Total product (kg/ha) 39,665 50,267 57,888 62,162 64,906 Average product (per cm of water) 457.0 475.4 460.7 343.3 440.9 192.5 405.0 123.6 369.4 Source: Adapted from Table 2 of Al-Jamal et al. (2000). a M. S. Al-Jamal, T. W. Sammis, S. Ball, and D. Smeal, Computing the Crop Water Production Function Marginal product (at mid-interval) for Onion, Agricultural Water Management, v. 46 (2000), pp. 2941. From Production Function to Cost Function The cost functions described in Chapter 6 reect the underlying production function together with the prices of inputs. There are two ways the rm might pay to use a resource: by purchasing it or hiring it. A business rm can own its trucks or lease them as needed; a farmer might either buy or rent the land he cultivates. (Labor, of course, cannot be purchased but only hired.) In this chapter it will be more convenient to think of the rm as always hiring inputs.3 The rental rates or hire-prices of inputs A, B , C , . . . will be denoted h a , h b , h c , . . . . To begin with, suppose the rm is a price-taker (has no monopsony power) in its input markets. This means that the hire-prices of factors of production can be taken as constants in calculating costs of production. For any given combination of inputs, the rms Total Cost is: C ha a + hb b + hc c + (12.3) When some factors are held xed say, all but input A Total Cost can be divided into a xed component F and a variable component V: C F + V F + ha a (12.3 ) The Variable Cost, the spending on input A, is V h a a . Fixed Cost F corresponds to spending on the nonvarying inputs B, C, and so forth. Suppose the production function (12.2) is q = a , all other factors being xed. Since then a = q 2 , in equation (12.3 ) the rms cost of producing any output q becomes C = F + ha q 2. 3 A rm that decides to purchase rather than hire a needed input is making an investment decision. Investment decisions involve choices between present and future, a topic taken up in Chapter 15. P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 344 12. THE DEMAND FOR FACTOR SERVICES $ Cost C V F 0 $/q MC CostperUnitOutput AC Output q q Figure 12.2. From Production Function to Cost Function Multiplying the horizontal axis of the previous diagram by the constant hire-price h a shifts the dimension from units of input (a) to units of Variable Cost (h a a ). Rotated 180 and ipped over, the tpa curve of the previous diagram becomes the Total Variable Cost V curve in the upper diagram. The mpa curve of the previous diagram becomes the Marginal Cost curve MC in the lower diagram; the apa curve becomes the Average Variable Cost curve AVC. AVC 0 Output q q More generally, if q q (a ) is the production function, the inverted function is a a (q ).4 So the cost function can be written: C F + h a a (q ) (12.4) Thus Total Cost depends upon the xed cost F, the hire-price ha , and (after inversion) the production function q = q (a ). In Figure 12.2, the shape of the Total Variable Cost curve V in the upper panel reects the shape of the tpa curve of Figure 12.1 rotated 180 and ipped over. The dashed vertical bound on the right of Figure 12.2 represents the same maximum output q as the dashed horizontal bound q in Figure 12.1. Note also that the Total Cost curve C lies above the Variable Cost curve V by the amount of the Fixed Cost F.5 The Marginal Cost (MC) and Average Cost (AC) curves of Figure 12.2 look like upside-down versions of the mpa and apa curves of Figure 12.1. For the marginal curves the reason is evident from the relation between Marginal Cost MC and Marginal 4 5 Mathematical Footnote : As a technical qualication, it is sometimes impossible to uniquely invert q q (a ) so as to write a a (q ). This complication will be ignored here. The rm would always ignore the dotted upper branches of the C and V curves. These correspond to the range in Figure 12.1 where tp is a declining function of input amount a. It would never pay the rm to produce any given output at greater cost if it can do the same at lower cost. P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12.1 FACTOR EMPLOYMENT WITH A SINGLE VARIABLE INPUT 345 Product mpa : MC C ha a q q ha ha q/ a mp a (12.5) So Marginal Cost MC necessarily increases as Marginal Product mp a decreases. (Recall that since the rm is a price-taker in the factor market, hire-price ha is assumed constant.) Thus, the Law of Diminishing Marginal Returns (which states that as use of an input rises, Marginal Product eventually declines) explains why the MC curve must eventually rise. A corresponding inverse relationship holds between Average Product apa and Average Variable Cost AVC V /q . As apa falls, AVC rises: AVC V ha a ha ha q q q /a ap a (12.6) Taking into account xed costs as well, for Average Cost the relationship is: AC F + ha a F C ha + q q q ap a (12.7) Since F /q on the right-hand side (Average Fixed Cost) shrinks towards zero as q rises, the AC curve converges toward the AVC curve. So both curves must eventually rise as a continues to increase. EXERCISE 12.3 Suppose the rms short-run production function, corresponding to equation (12.2), is tpa q 2 a . Let the hire-price be ha = 4, and the xed cost F = 50. (a) Find the Total Variable Cost function V and the Total Cost function C. (b) Relate Marginal Cost MC to Marginal Product mpa . (c) Relate Average Variable Cost AVC and Average Cost AC to Average Product apa . A N S W E R : (a) Inverting the production function, a = q2 /4. So Total Variable Cost is V ha a = 4a = q2 and Total Cost is C F + V = 50 + q2 . (b) Since C = 50 + q2 , direct tabulation (or calculus) shows that Marginal Cost is MC C/ q = 2q. And since Total Product is q = 2 a , it follows that mpa q/ a = 1/ a . From equation (12.5), MC ha / mpa = 4/ mpa , which can be directly conrmed: ha / mpa = 4 a = 2q = MC . (c) Using equation (12.6), AVC ha /apa = 4/apa . And equation (12.7) becomes AC = 50/q + 4/apa = 25/ a + 4/apa . The Firms Demand for a Single Variable Input The production function is a technological relation between inputs and outputs. But in deciding upon the amounts of factors to employ, the rm must go beyond technology and consider nancial variables as well in particular, the factor hire-prices ha , hb , hc , . . . . Dealing with a single variable input A, the assumption that the rm is a price-taker in the factor market means that the horizontal line in Figure 12.3 at hire-price ha can be regarded as the supply curve sa of the resource to the rm. Just as the price-taking (nonmonopolist) rm in the product market faces a horizontal product demand curve d P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 346 $/a 12. THE DEMAND FOR FACTOR SERVICES Figure 12.3. Optimal Factor Employment: Price-Taking Firm in Both Factor Market and Product Market sa ha afca mfca da vmpa mrpa a A The horizontal line, showing the supply curve s a to the price-taking rm at hire-price h a , is the curve of Average Factor Cost (afc a ) and also of Marginal Factor Cost (mfca ). If the rm is a price-taker in the product market as well, the Value of the Marginal Product (vmpa ) curve coincides with the Marginal Revenue Product (mrpa ) curve. The rms demand curve da for input A is then the downward-sloping branch of the vmpa mrpa curve. DollarsperUnitof 0 a a QuantityofInput A (as shown in the lower panel of Figure 6.1 in Chapter 6), here sa is the horizontal input supply curve facing a price-taking (nonmonopsonist) rm in the factor market. In deciding whether to employ an additional unit of input A, the rm must balance the hire-price ha to be paid against the benet to be gained. This benet has two elements: the additional physical output, and what that added output generates in the way of revenue. Assume to begin with that the rm is also a price-taker in the product market. Then each additional unit of output can be sold at the given product price P. Combining product price and Marginal Product leads to the concept called Value of the Marginal Product. DEFINITION: The Value of the Marginal Product for input A, vmpa , is the product price P times the physical Marginal Product mpa : vmpa P mpa Denition of vmpa (12.8) The Example that follows illustrates how changes in the price of the product can affect the demand for an input used in production. EXAMPLE 12.2 THE PRICE OF RICE AND THE PRICE OF SLAVES Peter C. Mancall, Joshua L. Rosenbloom, and Thomas Weiss studied South Carolina probate records to estimate the prices of slaves in the period 17221809.a During this period the major agricultural activity in South Carolina was rice cultivation using slave labor an inhumane system, but nevertheless subject to the laws of economic logic. The text indicates that product prices (P) affect the Value of the Marginal Product (vmp) of a factor. The table shows that upward movements in the price of rice were indeed associated with upturns in slave prices, reecting increased planter demand for slave labor and conversely for downward movements in the price of rice. (For other historical reasons, during this period slave prices were tending to rise.) As would be expected, high prices for rice were also associated with increased imports of slaves. P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12.1 FACTOR EMPLOYMENT WITH A SINGLE VARIABLE INPUT 347 Slaves and the price of rice in South Carolina Rice price (cents/lb) 1.40 1.64 1.18 1.56 1.58 1.87 3.15 2.73 3.81 Slave price (real $/adult male) 164.16 175.43 149.17 167.74 154.30 245.70 343.50 197.20 393.20 Period 17221729 17301739 17401749 17501759 17601769 17701779 17801789 17901799 18001809 Slaves imported 11,600 21,150 1,950 16,497 21,840 18,866 19,200 19,991 30,195 Source: Adapted from Mancall et al., Tables 2 and 5. a Peter C. Mancall, Joshua L. Rosenbloom, and Thomas Weiss, South Carolina Slave Prices, 1722 1809, National Bureau of Economic Research Historical Paper 123 (March 2000). The vmpa curve in Figure 12.3 has the same general shape as the mpa curve in the lower panel of Figure 12.1, since the only change is multiplication by a constant product price P. The vertical axis, however, differs. In Figure 12.1 the vertical axis is scaled in output per unit of input (q/a); in Figure 12.3 it is scaled in dollars per unit of input ($/a). Turning to the employment decision, whenever vmpa exceeds hire-price h a the rm can protably employ an additional unit of A. And if vmpa < h a , the rm would do better hiring fewer units. So for a rm that is a price-taker in both its product market and the factor market, the optimal employment of input A is given by the equality: vmpa = h a Factor Employment Condition for a Price-Taking Firm6 (12.9) It can happen, however, that this equality is satised at two or more input levels, for example a and a in Figure 12.3. So something more is needed. A secondary condition for an optimum is that the vmpa curve must be falling relative to the horizontal line associated with the current hire-price ha ;7 this occurs only at a in the diagram.8 A rm that used only a units of input would be missing out on the protable range in the diagram where the revenue increment vmpa exceeds the cost ha . 6 7 8 Equation (12.8) is a denitional identity, whereas equation (12.9) is an equality that holds only when the rm has chosen the prot-maximizing employment of the factor. Recall from Chapter 6 that the output optimum for the price-taking rm occurs at MC = P, provided that the MC curve cuts the horizontal line at price P from below. Here the input optimum occurs where vmpa = h a , provided that the vmpa curve cuts the horizontal line at hire-price ha from above. Mathematical Footnote : The conditions above correspond to the rst-order and second-order conditions for a prot maximum. The rm chooses the amount of A to maximize prot R C Pq h a a F (where F stands for xed costs representing expenditures on inputs other than A). Differentiating with respect to a and setting the derivative equal to zero leads to the rst-order condition: dq = h a or P mp a = h a da This corresponds to equation (12.9). Taking the second derivative of , the second-order condition for a maximum is: P P d 2q <0 da 2 or (since P is a positive constant) d 2q <0 da 2 This means that to have a prot maximum, the Value of the Marginal Product vmp a P mp a must be falling. P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 348 12. THE DEMAND FOR FACTOR SERVICES Constructing the rms demand curve for input A requires that the rm satisfy the Factor Employment Condition for all possible levels of the hire-price ha . CONCLUSION For a rm that is a price-taker in both factor and product markets, the demand curve for a single variable input A is the downward-sloping range along the vmpa curve. EXERCISE 12.4 Suppose the rms Total Product function is q = 2 a as in Exercise 12.3. Let the product price be P = 60 and let the input hire-price be ha = 4. (a) Find the equation for the vmpa curve. (b) Find the optimal input amount a . (c) What is the associated output q ? (d) What is the rms demand curve equation for the input? A N S W E R : (a) Exercise 12.3 showed that if q = 2 a then mpa = 1/ a . Thus, vmpa ( P )(mpa ) = 60/ a . (b) The optimal input amount a satises the condition vmpa = ha , or 60/ a = 4, which implies a = 225. (Here no other value of the input satises the condition.) (c) The associated output is q = 2 a = 2 225 = 30. (d) Since vmpa here slopes down throughout, the demand curve is identical with the vmpa curve. The equation is ha = 60/ a . What if the employing rm were instead a monopolist in its product market? A copper-mining enterprise, for example, might face a downward-sloping demand curve for copper ore. Then its additional revenue from an additional unit of input would no longer be the value of the physical Marginal Product (the price P of copper ore). Instead the additional revenue would be the Marginal Revenue MR where MR < P (as illustrated in Figure 8.1). The revenue gain from an additional unit of input A is dened as the Marginal Revenue Product mrpa : DEFINITION: Marginal Revenue Product mrpa equals Marginal Revenue MR times physical Marginal Product mpa : mrpa MR mpa Denition of mrpa (12.10) Since Marginal Revenue is less than price P for a monopoly rm, its mrpa curve always lies below the vmpa curve, as shown in Figure 12.4. For a monopolist, the protmaximizing input employment occurs where the mrpa curve not the vmpa curve intersects the horizontal input supply curve sa .9 It follows that the monopoly rms demand curve da for input A is given by the Marginal Revenue Product curve mrpa rather than by the Value of Marginal Product curve vmpa . For a price-taking rm in the product market, Chapter 6 showed that Marginal Revenue is simply the product price P. It follows that for such a rm vmpa and mrpa are 9 Mathematical Footnote : The rm maximizes R C Pq h a a F as before, but now recognizes that P decreases with output q and so, indirectly, decreases with the input a. Differentiating and setting equal to zero, the rst-order condition is: P dq dP dq +q = ha da dq da or P +q dP dq dq = ha da The element in parentheses is Marginal Revenue. So the condition can be expressed: MR mpa mrpa = h a P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12.2 FACTOR EMPLOYMENT WITH SEVERAL VARIABLE INPUTS 349 $/a Figure 12.4. Optimal Factor Employment: Monopolist in Product Market The rm is a price taker in the input market, as indicated by the horizontal supply curve s a at the level of the going hire-price h a . However, here the rm has monopoly power in the product market. Since at any output the product price exceeds Marginal Revenue, the Value of the Marginal Product (vmpa P mpa ) lies above the Marginal Revenue Product (mrpa MR mpa ). The rms optimum is at the intersection of s a and mrpa , leading to employment a of input A. The downwardsloping branch of the mrpa curve is also the rms demand curve for input A. A DollarsperUnitof sa ha da vmpa P mpa mrpa MR mpa a 0 a QuantityofInput A identical: vmpa mrpa . So the Factor Employment Condition, expressed in terms of mrpa , is a general condition that holds both for monopolists and for price-taking rms: mrpa = h a General Factor Employment Condition (12.11) Again, as a technical qualication, the mrpa curve must cut the horizontal input supply curve sa from above. CONCLUSION For a rm that faces a given hire-price h a , the optimal use of input A occurs where mrpa = h a . And since the rms demand curve for input A must satisfy the Factor Employment Condition for every possible hire-price h a , its demand curve for a single variable input A is the mrpa curve. (Except that if the mrpa curve has an upwardsloping branch, the demand curve consists only of the downward-sloping branch.) The rms output decision studied in Chapters 6 and 8, and its input (resource employment) decision studied in this chapter, are logically connected. To see how this works out with a single variable factor, start with equation (12.5) MC h a /mpa . Now divide both sides by Marginal Revenue MR to obtain: MC ha ha MR (MR)(mp a ) mrpa (12.12) So MC = MR the Maximum-Prot Condition of Chapter 8 implies the Factor Employment Condition of this chapter: mrpa = h a . 12.2 PRODUCTION AND FACTOR EMPLOYMENT WITH SEVERAL VARIABLE INPUTS In some ways, a rm hiring multiple inputs resembles a consumer choosing an assortment of goods and services. Consumers purchase goods to obtain utility; rms employ resources to generate output and revenue. P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 350 12. THE DEMAND FOR FACTOR SERVICES q E Outputcontours D E D C b C Qu E E D D ant ityo C a C fInp ut A Qu 0 tyo anti fInp ut B Figure 12.5. Output as a Function of Two Inputs Output q, measured vertically, is shown as a function of input quantities a and b. Curves CC, DD, and EE are contours of equal height (output) along the three-dimensional surface. The curves C C , D D , and E E are the projections of these contours in the base plane. The Production Function With two variable inputs, say labor and machines, the production function of equation (12.1) reduces to: q= (a , b ) (12.13) The three-dimensional output hill of Figure 12.5 (compare the utility hill in Figure 3.3) illustrates such a production function. Product quantity q is on the vertical axis and the input amounts a and b appear on the two horizontal axes. The curves CC, DD, EE , etc. are equal-output contours known as isoquants. Each isoquant represents all the combinations of input amounts a and b that generate a given output q. Figure 12.6 shows these isoquants in a two-dimensional diagram. b C QuantityofInput B D E Isoquants Figure 12.6. Isoquants of Output H q = q2 G q = q1 q = q0 D C a QuantityofInput A E The projections C C , D D , and E E in the base plane of the previous diagram are shown here as isoquants (curves of equal output) in a contour map, without the overlying vertical dimension. Each isoquant is associated with a denite quantity of output (q 0 , q 1 , or q 2 ). 0 P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12.2 FACTOR EMPLOYMENT WITH SEVERAL VARIABLE INPUTS 351 q tpa(b = b1) tpb(a = a1) tpb(a = a0) tpa(b = b 0) a b b1 Qu an tity ofI a1 a0 b0 np ut B a Qu nti ty n ofI pu t A 0 Figure 12.7. Total Product Functions Total Product curves are drawn along an output hill. The Total Product curves for input A, designated tpa , hold constant the amount of the other input, B. However, the heights of the tpa curves depend upon the specic constant values assumed for b in each case; similarly the tpb curves depend on the values assumed for a. In Figure 12.7 the Total Product curves along the surface of the output hill indicate how output q changes as one input increases, with the other input held constant. Figure 12.1 showed only one Total Product curve tpa , corresponding to the single variable factor A. But now there are two whole families of Total Product curves tpa and tpb . Along each of the tpa curves, output q is a function of the input amount a. Similarly, along each tpb curve output q is a function of b. In the diagram the labelling tpa (b = b0 ), for example, identies the Total Product curve for input A when input B is held xed at the specic level b = b 0 . Notice that the entire tpa curve shifts upward as the amount of B increases. Similarly the entire tpb curve shifts upward as the amount of A increases. (More acreage enables a given number of farm workers to produce more, and vice versa.) In Figure 12.8, the two families of Total Product curves are displayed again, but now as a pair of two-dimensional diagrams. Here each separate curve resembles the tpa curve of Figure 12.1, with the general shape dictated by the Laws of Diminishing Returns. As is consistent with the three-dimensional picture of Figure 12.7, the highest tpa curve in Panel (a) of Figure 12.8 corresponds to the largest amount of input B (b = b 2 ) and the lowest curve corresponds to the smallest amount of B (b = b 0 ). The same considerations apply also for the other input, as shown in Panel (b). Associated with these families of Total Product curves are corresponding families of Marginal Product curves,10 as pictured in Figure 12.9. Now consider what happens when the factors are all changed together in the same proportion (this is called a change of scale). In the three-dimensional diagram of 10 Mathematical Footnote : With two or more variable inputs, the Marginal Product of any single input such as A becomes a partial derivative: mp a lim F (a + 0 q a , b ) F (a , b ) a a P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 352 12. THE DEMAND FOR FACTOR SERVICES q tpa(b = b2) tpa(b = b1) Output Output tpa(b = b0) q tpb(a = a2) tpb(a = a1) tpb(a = a0) 0 QuantityofInput A Panel(a) a 0 QuantityofInput B Panel(b) b Figure 12.8. Families of Total Product Curves Panel (a) shows tpa curves like those drawn along the output hill of Figure 12.7, but on q,a axes; the tpb curves are similarly shown on q,b axes in Panel (b). Figure 12.5, that would correspond to moving upward in some particular direction out of the origin along the surface of the output hill. If in that direction the surface at rst grows steeper, then in that range there would be increasing returns to scale. The Laws of Diminishing Returns, however, eventually apply even when all controllable factors increase together. So ultimately there will be decreasing returns to scale. The output hill must eventually atten out. q/a q/b A B OutputperUnitof OutputperUnitof mpb(a = a 2) mpb(a = a 1) mpb(a = a 0) mpa(b = b2) mpa(b = b1) mpa(b = b0) 0 b 0 QuantityofF actor B Panel(b) QuantityofF actor A Panel(a) Figure 12.9. Families of Marginal Product Curves The Marginal Product curves mpa and mpb are derived from the corresponding Total Product curves of Figure 12.8. Only the ranges where the curves have negative slope (where the Marginal Product of each factor is a decreasing function of its own quantity) are illustrated here. P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12.2 FACTOR EMPLOYMENT WITH SEVERAL VARIABLE INPUTS 353 EXAMPLE 12.3 MISSOURI CORN An agricultural experiment in Missouri, reported by John Ambrosius, studied how corn yield (bushels per acre) changed as two inputs (number of plants per acre and pounds of nitrogen per acre) were varied.a Reading across any single row, the table shows selected points on the Total Product curve tpa for plants per acre with nitrogen input per acre held constant along the row. Reading down any column, points are shown on the tpb curve for nitrogen input holding xed the number of plants per acre. If these points were plotted in a diagram like Figure 12.8, the entire tpa curve would shift upward as b increased, and the tpb curve would shift upward as a increased. Bushels of corn per acre (Q) Number of plants per acre (a) Nitrogen per acre (b) 0 50 100 150 9,000 50.6 78.7 94.4 88.9 12,000 54.2 85.9 105.3 107.1 15,000 53.5 88.8 111.9 121.0 18,000 48.5 87.5 114.2 130.6 21,000 39.2 81.9 112.2 135.9 Source: Adapted from Ambrosius, as cited in Doll et al., p. 89. Diminishing returns apply here even to proportionate variation in both inputs together. For example, doubling both inputs from the combination (9,000, 50) to the combination (18,000, 100) does not double corn output, which rises from 78.7 to only 114.2. a John Ambrosius, The Effects of Experimental Size upon Optimum Rates of Nitrogen and Stand for Corn in Missouri (1964), cited in J. P. Doll, V. J. Rhodes, and J. G. West, Economics of Agricultural Production, Markets and Policy (Homewood, IL: Richard D. Irwin, 1968). The Missouri corn Example suggests why decreasing returns to scale must always eventually hold. In that experiment, nitrogen and number of plants per acre were the two controlled inputs. The amounts of other potentially controllable inputs, among them labor input, were held constant. But even if labor and other controllable inputs were also increased in proportion, other aspects of the environment that affect plant growth such as the Earths gravity, or the oxygen content of the atmosphere cannot be experimentally manipulated. Thus it is impossible to vary literally all inputs. This means that the essential condition underlying the Laws of Diminishing Returns, the xity of one or more inputs, is inescapable. So even when all controllable variables are increased in proportion, there must eventually be diminishing returns to scale. The Example that follows employs the CobbDouglas production function, an algebraic form that has proved useful in economic analysis. For two inputs A and B the function is: q a b CobbDouglas production function (12.14) (The Greek letters (kappa), (alpha), and (beta) here are given constants.) P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 354 12. THE DEMAND FOR FACTOR SERVICES In the CobbDouglas equation, it can be shown that if the sum of the exponents, + , exceeds one, there will be increasing returns to scale. Then a doubling of both inputs will more than double output.11 If the sum of the exponents exactly equals 1 there will be constant returns to scale. Decreasing returns to scale hold if the sum is less than 1. Under constant returns to scale, if a factors hire-price equals its Marginal Product then each exponent also equals the fractional share of total output going to that factor.12 EXAMPLE 12.4 AGRICULTURAL PRODUCTION IN CANADA Christina Echevarria estimated agricultural production functions for provinces of Canada in the period 19711991.a A CobbDouglas function was used, under the assumption of constant returns to scale. The independent variables were the traditional three basic factors of production: land, labor, and capital: Yt = At K t L t Nt Here Yt is the value added each year in the provinces agricultural sector. Kt , Lt , and Nt are estimates of the amounts of capital, land, and labor inputs employed in agriculture each year. Annual changes in At , total factor productivity, represent the output growth not accounted for by changes in the amounts of the inputs. Presumably, At reects general technological progress. Over the period studied total factor productivity grew about 0.35% per year. The table shows a selection of the results for Canada as a whole and for several provinces. Notice that in British Columbia labors share is high, consistent with the fact that agriculture in that province concentrates on labor-intensive commodities such as dairy products and fruit. By contrast, in the prairie state of Saskatchewan, large-scale grain production is land-intensive and labors share is relatively small. Agricultural production in Canada CobbDouglas shares Province Saskatchewan Quebec British Columbia Canada (Average) Share of land ( ) 0.2217 0.1240 0.0956 0.1597 Share of labor ( ) 0.2954 0.4308 0.6530 0.4138 Share of capital () 0.4830 0.4452 0.2514 0.4265 Source: Echevarria, selected from Table 3. a Christina Echevarria, A Three-Factor Agricultural Production Function: The Case of Canada, International Economic Journal, v. 12 (Autumn 1998). 11 12 Let = = = 1. Since + > 1, there should be increasing returns to scale. To verify this, suppose the initial (a,b) input combination is (10,20). Now imagine that the inputs double to (20,40). Then output increases from q = 200 to q = 800 not a doubling but a quadrupling! Mathematical Footnote : From equation (12.14), the Marginal Product for factor A is the partial derivative: q q = a 1 b = a a So if each unit of factor A receives its Marginal Product mpa , then h a a = mpa a = q . The owners of factor A in aggregate receive the fractional share of the total output q. P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12.2 FACTOR EMPLOYMENT WITH SEVERAL VARIABLE INPUTS 355 b C /hb QuantityofInput B Figure 12.10. Scale Expansion Path Along any isocost line, the tangency with an output isoquant represents the largest output attainable at that cost. Each such tangency shows the best factor proportions for that level of cost and output. The Scale Expansion Path (SEP) connects all these tangency positions. C /hb SEP C /hb F q b E q 0 a C /ha C /ha C /ha a QuantityofInput A G q Factor Balance and Factor Employment The question of factor balance asks what are the best input proportions at any given level of cost or output. This is a preliminary to asking about factor employment the actual amounts of inputs to hire at any given set of factor hire-prices. Consider a specic level of Total Cost, say $100. Suppose the hire-price of labor A is h a = $1 per man-hour and the hire-price of a machine is h b = $2 per machine-hour. If the rm used only one or the other, for $100 it could hire either 100 units of labor or 50 machines. More generally, the rm could employ any combination of inputs A and B whose cost comes to $100. For two variable factors, A and B, Figure 12.10 pictures isocost lines C o , C , C , . . . At a specied level of cost, say C o , equation (12.3) takes the form C o h a a + h b b . The intercepts are C o/h a on the horizontal axis and C o/h b on the vertical axis. Since C o cancels out in taking the ratio of rise over run, all the isocost lines have the same slope ha /hb . The diagram also shows output isoquants q o , q , q , . . . . Along isocost C o the highest attainable isoquant q o is found at the tangency point E with coordinates a o , b o . At cost level C o , therefore, the rm maximizes output by using the input combination a o , b o . Equivalently, the input combination a o , b o is the cheapest way of producing output q o . Figure 12.10 resembles Figure 4.1 in Chapter 4, which illustrated the optimum of the consumer. Instead of indifference curves now there are isoquants, and the isocost lines look like the budget line of the earlier diagram. But there is an important difference. The consumer, constrained by a given level of spendable income, had a single budget line. But a rm is not restricted to a single isocost line. A rm decides how much cost to incur. It may be protable to incur higher costs to produce more output. Consequently, the analysis must consider the tangencies E, F, G, . . . associated with all possible cost levels C o , C , C , . . . . The curve passing through all these tangencies is called the Scale Expansion Path SEP. The Scale Expansion Path shows the best combination of inputs at each level of cost. The optimum of the rm must lie somewhere along the Scale Expansion Path. P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 356 12. THE DEMAND FOR FACTOR SERVICES In Chapter 4 the consumers optimum condition was expressed in equation 4.5 as an equality between the product price ratio Px / P y (the absolute slope of the consumers budget line) and the Marginal Rate of Substitution in Consumption MRSC (the absolute slope of the indifference curve). MRSC was dened as the ratio at which a person was just willing to substitute a small amount of Y for a small amount of X in the consumption basket. In other words, MRSC is the ratio leaving the consumer indifferent (at the same level of utility). Correspondingly here, the Marginal Rate of Substitution in Production MRS Q is dened as the amount of input B that can be substituted for a small change in input A while leaving the rm indifferent in the sense of generating the same output q. Also, just as MRSC was shown in Section 4.1 of Chapter 4 to equal the ratio of the Marginal Utilities, here MRS Q is equivalent to the ratio of the Marginal Products.13 Thus: MRS Q b a q mpa 14 mpb (12.15) Since the slope of the isocost line is ha /hb , the tangency condition is: ha mpa = mpb hb (12.16) This leads immediately to the rms Factor Balance Equation, the analog of the Consumption Balance Equation 4.3 in Chapter 4: mpb mpa = ha hb Factor Balance Equation 15 (12.17) Inputs are in balance when the Marginal Products per dollar are equal for all resources employed. If this condition were violated, the rm could increase output at the same level of overall cost by substituting toward the more economical input the one with higher Marginal Product per dollar. When the Factor Balance Equation is satised, the rms input combinations at each level of output are shown by the Scale Expansion Path of Figure 12.10. But beyond the question of factor balance, answered by the Scale Expansion Path, the rm has to 13 14 15 Imagine that at an assumed initial output level q = 20 the Marginal Products are mpa = 2 and mpb = 1/2. A unit reduction of A( a = 1) would reduce output by 2 units, which could be recouped if input B were increased by 4 units ( b = +4). So the slope of the isoquant is b / a = +4/ 1 = 4, and MRS Q equals the absolute value 4. (This argument holds if a and b represent small changes, so that mpa and mpb can be regarded as remaining approximately constant.) The notation of the middle expression indicates that a small change in a is substituted for a small change in b in such as way as to hold q constant. Mathematical Footnote : The Factor Balance Equation generalizes in a direct way for any number of inputs A, B, C, . . . employed in positive amounts. So, with a third input C: mpa (a > 0) mpb (b > 0) mpc (c > 0) = = ha hb hc If, however, the current hire-prices are such that some input (say D) is not employed at all, its ratio of Marginal Product per dollar is related to the others by an inequality : mpb (b > 0) mpd (d = 0) mpa (a > 0) = > ha hb hd That is, for the optimal employment of D to be zero, its Marginal Product per dollar must be less than that of other inputs, even for the very rst unit of D. (Note the parallel with the Consumption Balance Inequality of Chapter 4.) P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12.2 FACTOR EMPLOYMENT WITH SEVERAL VARIABLE INPUTS 357 $ TotalCost C Figure 12.11. Total Revenue and Total Cost Functions Each point on the Scale Expansion Path of the previous diagram is associated with a particular level of cost and output. This information permits plotting the Total Cost curve C. Also, each level of output is associated with a level of revenue R = P Q . This information permits plotting the Total Revenue curve R. The prot-maximizing output q determines the rms optimal factor employments as shown in the preceding diagram. Dollars R TotalRe venue 0 q Output q determine the actual amounts not just the ratios of the factors to be used. That requires some additional information. Figure 12.10 indicated that output q o can be produced at a cost of C o , output q can be produced at cost C , and so on. This information leads directly to the Total Cost curve C shown in Figure 12.11. To construct the curve of Total Revenue R P q , the needed information as to how P varies with q is provided by the rms demand function. In Figure 12.11 prot is maximized at output q , where the difference between Total Revenue and Total Cost is greatest as shown by the maximized prot . (The R curve pictured in Figure 12.11 applies to a rm with monopoly power. For a price-taking rm, P would be a constant and R would be a straight line out of the origin.) Last, the optimal output q tells on which isoquant in Figure 12.10 (or equivalently, on which isocost line) the rm should operate to determine the best combination of inputs. The exercise that follows illustrates the solution process. EXERCISE 12.6 A rms production function has the CobbDouglas form q = a 0.5 b0.5 . Using calculus, it can be shown that the Marginal Product functions are mpa = 0.5q/a and mpb = 0.5q/b. Suppose the demand function for the rms product is P = 100 q. (This rm has monopoly power in its product market.) The input prices are ha = 4 and hb = 1. (a) Find the equation of the Scale Expansion Path (SEP). (b) Derive the Total Cost and Total Revenue equations. (c) Find the prot-maximizing output. (d) Find the optimal input employments a and b . (e) What is the maximized prot? A N S W E R : (a) The Factor Balance Equation can be written: 0.5q/a 0.5q/b = 4 1 From this it follows that b = 4a . This is the equation of the Scale Expansion Path. (b) Substituting b = 4a into the production function equation leads to q = (a 0.5 )(4a )0.5 = 2a . Total Cost is C ha a + hbb = 4a + b. Since q = 2a and b = 4a , it follows that Total Cost is C = 4q. This is the Total Cost function. Using the given P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 358 12. THE DEMAND FOR FACTOR SERVICES demand function, Total Revenue is R P q = 100q q2 . (c) For the cost function C = 4q, Marginal Cost is MC = 4. Since the demand curve P = 100 q is linear, Marginal Revenue is MR = 100 2q. Equating Marginal Revenue to Marginal Cost, the prot-maximizing output is q = 48. (d) Since q = 2a , it follows that a = 24. And since b = 4a it follows that b = 96. (e) Total Cost is C = 4q = 4(48) = 192. Total Revenue is (100)(48) 482 = 2,496. So prot is = 2,304. The Firms Demand for Inputs Since inputs are used jointly, the rms demands for them will be interrelated. How much labor the rm will want to hire depends upon the amount of machinery used, and vice versa. First, making use of the Factor Balance Equation, equation (12.5) MC h a / mpa can be extended to obtain: ha hb = = MC mpa mpb (12.18) This is a valid generalization because, when the rm uses the optimal input proportions as dictated by the Factor Balance Equation, it is equally costly to expand output by hiring a small extra amount of A, or by hiring a small extra amount of B, or by any mixture of the two. Dividing through by MR: hb ha MC = = MR mrpa mrpb (12.19) So when a rm maximizes prot by equating Marginal Cost to Marginal Revenue, it automatically satises the Factor Employment Conditions: mrpa = h a mrpb = h b Factor Employment Conditions (12.20) These equations parallel equation (12.11), which applied for a single variable input. But in the multi-input case, Marginal Product mpa and therefore also Marginal Revenue Product mrpa will generally also depend upon the amount of the other input B employed. Similarly, of course, mpb and mrpb will vary with the amount of input A.16 Two inputs are said to be complementary if increased use of one raises the Marginal Product of the other. Examples of complementary input pairs are ships and sailors, computers and programmers, bosses and secretaries. If instead one input has no effect at all upon the Marginal Product of the other input, the two are said to be independent. Handcraftsmen and mass-production machines may be such a pair. (A rm might offer customers both a machine-produced line of goods and also a premium handmade line, the two produced entirely separately.) It is even possible that increased use of one input would reduce the Marginal Product of the other. If so, the two inputs 16 Mathematical Footnote : If q = (a , b ), the Marginal Products or partial derivatives q/ a and q/ b will in general both be functions of a and b. Geometrically, in Figure 12.7 the slope along the Total Product curves tpa in the a-direction ( q/ a) varies both as a increases and also from one curve to the next as b increases. And similarly for the slope along the tpb curves ( q/ b). P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12.2 FACTOR EMPLOYMENT WITH SEVERAL VARIABLE INPUTS 359 are anticomplementary.17 Inputs that closely substitute for one another tend to be anticomplementary. Employing more male waiters, for example, might reduce the need for (that is, lower the marginal productivity of) female waitresses and vice versa.18 Normally, however, factors are complementary in production, especially when large categories such as land and labor are considered. EXAMPLE 12.5 THE BLACK DEATH In the years 13481350 between a fourth and a third of the population of Western Europe died of the Black Death (bubonic plague). The reduced labor supply led to sharp wage increases. The increase [in English farm wages] due to the plague is 32 percent for the threshing of wheat, 38 percent for barley, 111 percent for oats in the eastern counties. In the middle counties the percentages of rise are 40, 69, 111; in the south, 33, 38, 75; in the west, 26, 41, 44; in the north, 32, 43, and 100.a The consequent shift in the wage/rent ratio led to shifts in the relative employments of labor and land and consequently to changed patterns of land uses. For England, the table shows some results reported by David D. Haddock and Lynne Kiesling.b Land use in essex before and after the Black Death (mean acreage) Date 12721307 13771399 14611485 Arable 243 164 143 Meadow 8 10 16 Pasture 11 28 30 Wood 7 14 20 Total acreage 269 216 209 % arable 90.2% 76.1 68.4 Source: Adapted from Haddock and Kiesling, Table 1. Of the land uses tabulated, arable (land devoted to crops) is the most laborintensive, so would be hit the hardest by the reduced labor supply. The table shows that the percentage of land used for arable did drop sharply between the preepidemic years (12721307) and the postepidemic years (13771399). The decline continued into the period 14611485, owing in part to recurrences of plague throughout these centuries. The total amount of land employed fell as well. Evidently, land and labor were complements in production. With less labor available, and its hire-price very high, the Marginal Product of land fell so drastically that large areas were simply abandoned. COMMENT The feudal system is far removed from the economists model of a competitive labor market. Feudal economic relationships are, in principle, dictated solely by custom 17 18 Mathematical Footnote : Whether factors are complements or anticomplements is indicated by the sign of the second cross-derivative of the production function. In the normal complementary case, ( q/ a)/ b 2 q/ a b is positive. Independence corresponds to a zero cross-derivative, and anticomplementarity to a negative crossderivative. Anticomplementary inputs should not be confused with interfering inputs. With anticomplementary factors, hiring more of input A reduces mpb , and vice versa, but does not reduce the Total Product of either factor. But for interfering factors, Total Product actually declines. (Such a situation might arise if a mining rm in an undeveloped country attempted to employ members of two hostile tribal groups.) A rm would never rationally employ two interfering inputs in the same productive process. It should use only one of them, to the exclusion of the other. P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 360 12. THE DEMAND FOR FACTOR SERVICES and status. Nevertheless, the forces of supply and demand did operate. Wages rose relative to land rents, to the disadvantage of the high-status land-owning classes. An attempt in the reign of Richard II to return to the old feudal status relationships led to the Peasants Revolt of 1381, which almost overthrew the monarchy. The agricultural laborers demanded the end of serfdom, of feudal dues and services, of governmental monopolies, and of restrictions on what they could buy or sell. In short, the peasants wanted laissez faire so that marketplace revisions of economic status could proceed in their favor without government interference. a H. Robbins, A Comparison of the Effects of the Black Death on the Economic Organization of France and England, Journal of Political Economy, v. 36 (August 1928), p. 463. b David D. Haddock and Lynne Kiesling, The Black Death and Property Rights, Journal of Legal Studies, v. 31 (June 2002). Figure 12.9 pictured two complementary inputs A and B. Notice that as the amount of input B increases from b0 to b1 to b2 , the mpa curves shift up. Similarly, as input A rises from a0 to a1 to a2 , the mpb curves shift up. This stacking would be reversed if the two inputs were anticomplements. The rms demand curve for a single variable input A is, as noted above, the downward-sloping range along the Marginal Revenue Product curve mrpa . But with more than one input, matters are more complicated. To derive the rms demand curve for one of the two inputs, say input A, suppose that at point G in Figure 12.12 the Factor Employment Conditions in Equations (12.20) o are met. At the initial hire-prices h a and h o the rm employs a o units of A and b o b o units of B. Now let the hire-price of A fall from h a to h a . If the quantity of the other input B were unchanged, the diagram indicates that the rm would want to employ a units of input A since that is where mrpa (b = b o ) equals h a . But suppose inputs A and B are complementary. If so, the increase from a o to a is not the full adjustment. Greater use of input A increases the Marginal Product of input B, so all the mrpb curves will shift up. This leads to increased use of input B, which makes input A more productive (now the mrpa curves shift up), making the rm desire to hire still more of A. Such a reverberation process must, however, reach a limit. There is some increased employment of both inputs that restores the equalities of equation (12.20). The restored equalities can be expressed more explicitly as: mrpa (b = b ) = h a mrpb (a = a ) = h o b (12.20 ) The upshot, in Figure 12.12, is that the demand curve da goes not through points G and L, but through points G and K. So the rms demand curve for input A, when A and B are complementary, is atter (more elastic) than the mrpa curves. If the inputs are independent in production rather than complementary, the interaction effect disappears. A change in the hired amount of one input does not change the Marginal Product of the other. The initial adjustment to a change in the hire-price is the full adjustment. What about anticomplementary inputs? One might think that since da is atter than the mrpa curves in the complementary case and since da is the same as the unique mrpa P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12.2 FACTOR EMPLOYMENT WITH SEVERAL VARIABLE INPUTS 361 $/a mrpa (b = b ) A DollarsperUnitof ha ha G mrpa(b = b ) L K da 0 a a a a QuantityofInput A Figure 12.12. Firms Demand Curve for an Input o At the initial hire-price h a the Factor Employment Conditions are met by employments a = a o and o b = b o . Thus, mrpa (b = b o ) equals h a at point G; this is one point along the rms demand curve for input A. If the hire-price of A falls to h a , increased employment of A to the amount a will be indicated by a movement along mrpa (b = b o ) to point L. But this movement throws the employment condition for input B out of equality, if there is any complementarity (or anticomplementarity) between A and B. Restoring the equality for input B raises the Marginal Product of input A. The Factor Employment Condition can only be reestablished at a point such as K, where h a equals mrpa (b = b ) with b representing the optimal increased amount of input B. The rms demand curve da is therefore atter than the slope of the mrpa curves for input A. curve when the inputs are independent, then da would be steeper than the mrpa curves in the anticomplementary case. Not so. In the anticomplementary as in the normal complementary case, the rms demand curve for a factor is atter than the mrp curves, as illustrated in Figure 12.12. CONCLUSION Given either complementarity or anticomplementarity between inputs, the demand curve for any input is atter (more elastic) than the Marginal Revenue Product curves. One important implication: the employment of a variable input is more sensitive to hire-price changes in the long run, when the amounts of the xed factors can be varied. Another result follows directly from this analysis: factor demand curves always slope downward. That is, there can be no such thing as a Giffen factor (see Chapter 4, Section 4.4). A reduced hire-price ha can never lead to smaller employment of A. For a single variable input, since the input demand curve da is the negatively sloped portion of the vmpa curve, a fall in ha must increase the rms use of input A. Allowing for possible interactions with some other input B either leaves da unchanged (the independent case), or otherwise makes the rms demand curve for the factor atter. This attening means that a fall in ha causes the rm to use even more of input A. So a positively sloped factor demand curve, implying a decrease in desired use of A after a fall in the hire-price ha , is impossible. P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 362 12. THE DEMAND FOR FACTOR SERVICES $/a $/a A DollarsperUnitof ha ha k n da(P = P ) da(P = P ) a DollarsperUnitof A ha ha K N L da(P = P ) da(P = P ) Da A a 0 aa a QuantityofInput A (Firm) Panel(a) FirmDemand 0 AA A QuantityofInput A (Industry) Panel(b) IndustryDemand Figure 12.13. Demand for an Input: The Product-Price Effect Panel (a) pictures a rms demand for input A; Panel (b) pictures industry demand. At an initial o hire-price h a and product price P o , point k in Panel (a) lies on the rms demand curve for input A. In Panel (b) the solid curve da ( P = P o ) is the horizontal sum of these rm demand curves. When factor price falls to h a , each rm aims to expand use of A from a o to a the corresponding industrywide summations in Panel (b) are Ao and A, But as rms use more of input A, industrywide output also rises, reducing product price to P . Thus, each rms demand curve will fall to a position such as the (dashed) curve da ( P = P ) in Panel (a); the dashed summation curve in Panel (b) will move similarly. The new point on the industry factor demand curve in Panel (b) will be L. Thus, the product-price effect tends to make the industry demand curve for a factor steeper (less elastic). 12.3 THE INDUSTRYS DEMAND FOR INPUTS The question here is how to combine the individual rms demands into the overall demand for an input by a competitive industry.19 The short answer is that the industrys demand will be the horizontal sum of the rms separate demands for that input. This is basically correct, but there are complications to take into account. Consider rst the short run, with a single variable input. In Figure 12.13, Panel (a) pictures a typical rm and Panel (b) pictures the industry as a whole. Suppose that, at o some given initial hire-price h a for an input like labor, the equilibrium product price o was P = P . In Panel (a), the curve labelled da ( P = P o ) is the rms demand curve for labor when P = P o . (This curve corresponds to the curve da derived in the previous o diagram.) Given this product price and a hire-price of h a for labor, the rm would employ a o workers (point k). If the hire-price falls to h a , the rm would employ a workers (point n). The rst complication is the product-price effect. Although product price P is unchanged when a single competitive rm adjusts its output, for the industry as a whole price P will decline when output Q increases and will rise if Q decreases. 19 If the industry is monopolized, the industry demand for an input is of course identical with the single rms demand. (The analysis here will not cover intermediate cases such as oligopoly and monopolistic competition.) P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12.3 THE INDUSTRYS DEMAND FOR INPUTS 363 As a rst step, the rms separate da ( P = P o ) curves can be summed horizontally to obtain the industry curve labelled da ( P = P o ) in Panel (b). At the initial input o price h a , the industry uses Ao units of input (point K). What happens if the hire-price falls to h a ? Looking only at the curve da ( P = P o ), it appears that the industry would want to use A units of labor (point N). But as the rms use more labor, industry output necessarily rises. This means, given a normally- sloping demand curve, that the equilibrium product price must fall, say to P = P . And since the Value of Marginal Product for input a, vmpa , is P mpa , for each and every rm vmpa ends up lower than before. So in Panel (a) the rms demand curve for labor shifts down from the original da ( P = P o ) curve to the new dashed curve da ( P = P ). It follows that the horizontal sum of the rm demand curves also shifts down as indicated by the dashed curve da ( P = P ) in Panel (b). The upshot is that at the lower hire-price h a , a typical rm uses not a units of labor but only a units (point ). The industry as a whole uses not A units but only A units (point L). So the true demand Da is o drawn through point K (for h a = h a ) and point L (for h a = h a ): the industry demand curve is steeper (less elastic) than the simple horizontal sum of the rms demand curves. EXERCISE 12.7 Suppose all rms have the same production function q = 2 a ; let the initial product price be P = 60. The price-taking rms demand for input A was found in Exer cise 12.4 to be ha = 60/ a . Suppose that the industry consists of 1,000 identical such rms, and that the market demand curve for the product is given by the equation P = 90 Q/1,000. (a) What is the equation corresponding to the curve labelled da ( P = P o ) in Figure 12.13? (b) What is the industry demand equation for input A? (c) Compare the effect on the rm and on the industry of a fall in the hire-price o of A from ha = 4 to ha = 3. A N S W E R : (a) The rms demand equation ha = 60/ a implies a = 3,600/ha2 . Summing horizontally for 1,000 identical rms, A 1,000a = 3,600,000/ha2 . (b) The industry demand equation corresponds to the curve Da in Panel (b) that allows for the interaction between input price ha and product price P. Since Q 1,000q, the product demand curve P = 90 Q/1,000 can be written as P = 90 q. Exercise 12.3 showed that mpa = 1/ a . Since each price-taking rm sets vmpa P mpa = ha , it follows that (90 q) (1/ a ) = (90 2 a ) (1/ a ) = ha , or a = 8,100/(ha + 2)2 . So, since A 1,000a , the industrys demand equation for labor is A = 8,100,000/ (ha + 2)2 . (c) Using the rms demand function a = 3,600/ha2 , when the hire-price falls from ha = 4 to ha = 3, employment rises from a o = 225 to a = 400. But as indus try hiring expands beyond the initial Ao = 225,000, the product price P falls. At the new equilibrium, using the industrys input demand function A = 8,100/(ha + 2)2 , employment rises only to A = 324,000 for the industry as a whole, or to a = 324 for the typical rm. At the new equilibrium, product price has fallen from P o = 60 to P = 54. There is also an entry-exit effect. A fall in the hire-price of any input tends in the short run to increase prots in the industry, so new rms are likely to enter. With more rms in the industry, in Panel (b) the dashed summation curve da for factor A would shift to the right. (Correspondingly, after an increase in any hire-price, exit of rms P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 364 $/a 12. THE DEMAND FOR FACTOR SERVICES mfca A M sa afca Figure 12.14. Monopsony in the Factor Market The rising supply curve of A to the rm, s a , is also a curve of Average Factor Cost afca . The curve of Marginal Factor Cost mfca will then lie above afca , as shown here. The optimum factor employment for the rm is a , where the mfca and mrpa curves intersect (point M). The associated hire price h a is the price along the s a curve at this level of employment. a DollarsperUnitof h a N mrpa 0 a QuantityofF actor A would shift the summation curve to the left.) The overall consequence is to make the industry demand curve Da atter (more elastic) than would otherwise be the case. CONCLUSION After a fall in hire-price h a , industry-wide output increases and so product price falls thus lessening the rms incentive to hire more of the cheapened input A. This product-price effect makes the industry demand curve steeper than the simple aggregate of the individual rm demand curves for the factor. On the other hand, the entry-exit effect cuts in the opposite direction. A fall in h a increases rms prots, inducing new rms to enter and thereby attening the industry demand curve for input A. 12.4 MONOPSONY IN THE FACTOR MARKET Just as a monopolist is a sole seller in a market, a monopsonist is a sole buyer. If everyone in a small town works for a single enterprise, that rm has monopsony power in its local labor market. Just as a product-market monopolist faces a downward-sloping demand curve, a factor-market monopsonist faces an input supply curve that is upward-sloping. The curve labeled s a afca in Figure 12.14 shows the supply of factor A to a monopsonist. At any employment level the wage h a , or equivalently the Average Factor Cost afc h a a /a , is the height of the supply curve. As the diagram shows, the corresponding Marginal Factor Cost curve mfca ( h a a )/ a rises faster than afca . The reason is that Marginal Factor Cost consists of two elements: the hire-price paid to the extra unit plus the additional payments to the previous units: mfca Ca ha + a a ha a (12.21) Turn now to the monopsonists employment decision. The optimal quantity to hire, a , is found where Marginal Factor Cost mfc equals Marginal Revenue Product mrp (point M in the diagram). At that point the marginal expense of hiring one more unit P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12.4 MONOPSONY IN THE FACTOR MARKET 365 equals the rms marginal benet from the extra revenue: mfca = mrpa Factor Employment Condition for a Monopsonist (12.22) Note that the hire-price is not the height of point M, but the height of point N in the diagram. EXERCISE 12.8 Suppose the rm of Exercise 12.5, with production function q = 2 a , has monopoly power in its product market (faces demand curve P = 90 q) and also has monopsony power in the factor market. Specically, let the supply curve of factor A to the rm be ha = 1 + a /75. What is the rms prot-maximizing use of input a, and its prot-maximizing output? A N S W E R : Using the Factor Employment Condition for a monopsonist, the rm sets mrpa MR mpa = mfca . Marginal Revenue is MR = 90 2q. Marginal Prod uct here is mpa = 1/ a . With a linear factor supply curve or Average Factor Cost curve, the curve of Marginal Factor Cost is also linear and rises twice as fast. Thus, mfca = 1 + 2a /75. The condition mrpa = mfca can be expressed either in terms of the variable q or the variable a. Working for convenience in terms of q, the equation becomes (90 2q) (2/q) = 1 + (q 2 /2)/75, which simplies to q 3 + 750q = 27,000. The rms optimal output is q = 21.9 and the optimal level of input is a = 120.2. EXAMPLE 12.6 MONOPSONY IN PROFESSIONAL BASEBALL Before some recent reforms, labor-market monopsony was an important feature of several professional sports. A legal quirk, perhaps based upon the idea that sports are a pastime rather than a business, permitted employers to form buyers cartels. In baseball the most important cartel instrument was the reserve clause, which effectively made the player the exclusive property of the team that rst signs him up, or to which he is traded. A player refusing to accept the wage offer of his assigned employer was forbidden to play for any other team in the cartel. Gerald W. Scully investigated the effect of the reserve clause in major-league baseball.a He anticipated that if the buyers cartel was an effective monopsony, the wage rates for players, ha , would be less than their Marginal Revenue Products, mrpa (compare Figure 12.14). But rst, differences in player quality must be considered. Using 1968 and 1969 data, Scully estimated gross mrpa by calculating the players contribution to gate receipts and broadcast revenues. In this period, however, employers were incurring large costs for player development (on the order of $300,000) before knowing how successful the athlete would become. Allowing for this and certain other expenses led to net mrpa estimates for players of different qualities. Under competition, average wage rates at any quality level should tend to equal this net mrpa . If on the other hand the situation is one of monopsony, average wages should fall short of net mrpa . The table here indicates that, for mediocre players, during this period salary exceeded net mrpa and indeed, net mrpa was negative. But for average and especially for star players, net mrpa was far higher than the salary received. So this evidence suggests considerable monopsony power. P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 366 12. THE DEMAND FOR FACTOR SERVICES Quality versus pay of baseball players Quality group Hitters Mediocre Average Star Pitchers Mediocre Average Star Net mrp ($) 30,000 128,300 319,000 10,600 159,600 405,300 Salary ($) 17,200 29,100 52,100 15,700 33,000 66,800 Source: Scully, p. 928. Thus, contrary to common opinion among fans and sports writers, in the period studied it appears that star players were not overpaid. They received far less than their economic worth to employers. Since the time of Scullys analysis, legislation and judicial decisions have weakened the reserve clause in professional sports. In consequence, stars salaries have risen. In a later study Paul M. Sommers and Noel Quintonb examined the earnings of free agents players who are free to play for whichever club offers the best salary. For free-agent hitters the average mrpa was estimated at $521,923 while teams incurred an average of $827,393 in salaries, benets, and development costs. Free-agent pitchers had an average mrpa of $259,658, while teams paid an average of $257,600. So though the data suggest hitters were overpaid, the gures for pitchers approximated what would be expected under competitive conditions. a Gerald W. Scully, Pay and Performance in Major League Baseball, American Economic Review, v. 64 (December 1974). b Paul M. Sommers and Noel Quinton, Pay and Performance in Major League Baseball: The Case of the First Family of Free Agents, Journal of Human Resources, v. 17 (Summer 1982). 12.5 AN APPLICATION: MINIMUM-WAGE LAWS When it comes to analyzing the economic impact of minimum-wage laws, there are two conicting approaches. The rst approach assumes that low-wage labor markets are mainly competitive. Large numbers of demanders and suppliers interact to determine the levels of employment and wages. The second approach is based on the premise that employers typically have monopsony power. The competitive model is illustrated in Figure 12.15. Let the commodity be a certain grade or class of labor L, whose hire-price is the wage rate w. At the intersection of the supply and demand curves, the equilibrium wage is wc and employment is Lc . Now suppose a legal minimum wage w o is imposed, at a level higher than w c . At the higher wage w o the labor offered on the market is now the amount L s , larger than L e , but the labor demanded is only L d . So there will be an unemployment gap, the difference between the quantity offered and the quantity demanded at the legal wage, shown as BC = L s L d . The disemployment effect of the minimum wage, the number of workers who lose jobs, is the smaller amount FE = L c L d . When a minimum P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12.5 AN APPLICATION: MINIMUM-WAGE LAWS 367 w Figure 12.15. Minimum Wage: Competitive Model The competitive equilibrium point E is associated with wage w c and employment L c . A wage oor (minimum wage) at the level w o reduces employment to L d . The quantity FE is the reduction in employment. At the higher wage, L s units of labor are seeking employment, so the perceived unemployment gap is the larger quantity BC. WageRate w wc Disemployment effect F Unemployment S gap B C E D L 0 Ld Lc Ls Labor wage is set higher than the market equilibrium wage, therefore, the competitive-market model would clearly predict some disemployment of those previously working and an even larger amount of unemployment since at the higher wage more workers will be seeking employment. EXERCISE 12.9 Suppose the demand function for labor is D = 240 20w, and let the supply function be S = 60 + 80w. (a) What is the competitive equilibrium wage? The level of employment? (b) If a minimum wage w o = 5 is imposed, determine the amount of disemployment and compare it with the level of unemployment. A N S W E R : Solving the equation 240 20w = 60 + 80w, the market equilibrium wage rate is wc = 3. The associated level of employment is found by substituting w = 3 in either the demand or supply equation. The answer is D = S = 180. (b) If a minimum wage w o = 5 is imposed, the quantity demanded is 240 20(5) = 140; the quantity supplied is 60 + 80(5) = 320. Since employers want to hire only 140 workers, as compared with the unregulated solution the amount of disemployment is 180 140 = 40. But because so many more workers seek employment at the higher wage w o , the unemployment gap is much larger, namely, 340 140 = 200. The monopsony model has rather different implications, as shown in Figure 12.16. According to this model, a single employer is typically dealing with many individual workers. Employment is initially L m ; at this employment level the Marginal Revenue Product (mrp) curve intersects the Marginal Factor Cost (mfc) curves. The wage w m < mrp is determined along the labor supply curve S. An effective minimum-wage law replaces the market supply curve by a horizontal line at the level of the minimum wage (in the range where the market supply curve S lies below the level of the minimum wage). The monopsonist employer is forced to become a price-taker at the minimum wage, P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 368 12. THE DEMAND FOR FACTOR SERVICES $/L mfc S R U T M H w DollarsperUnitofLabor K w N w wm G mrp 0 L Lm L L d Labor Ls L Figure 12.16. Minimum Wage: Monopsony Model Under monopsony, the optimality condition mfc = mrp determines the wage w m at employment L m . If a minimum wage were imposed at the relatively low wage w , the optimality condition is satised at employment L both wage and employment would rise slightly. At an intermediate minimum wage w , employment would be L d . Here there is a considerable increase in both wage and employment; nevertheless, a perceived unemployment gap HK arises, because at wage w the offered labor supply is L s . At a sufciently high minimum wage such as w , employment falls to L as in the competitive model. wherever the market supply conditions would otherwise have permitted establishing a monopsony hire-price lower than the legally imposed oor. Three classes of possibilities are illustrated in Figure 12.16. First, suppose the minimum wage is only a little higher than w m , for example w in the diagram. Then the effective supply curve to the rm is horizontal at the level w until the S curve is reached at point N. In this range the Marginal Factor Cost (mfc) also equals w . If the monopsonist rm could hire as many units as desired at wage w , it would employ the quantity associated with point G, where w = mrp. But this is impossible. Beyond point N the effective supply curve of labor to the rm rejoins the original S curve, because at wage w the laborers are unwilling to supply more than L units. It follows also that, beyond employment L , the effective Marginal Factor Cost leaps upward discontinuously to rejoin the original mfc curve (at point U). Since the mrp curve in the diagram passes through this vertical discontinuity of the mfc curve, the rm will nd it optimal to employ L workers at wage w . Note that, relative to the unregulated outcome L m , the minimumwage law here has increased employment! Nor is there any perceived unemployment at the legally imposed wage. Second, consider a somewhat higher, intermediate level of minimum wage, w . As before the monopsonist rm is forced to become a price-taker until the supply curve S is reached (at point K). But then the condition w = mrp implies that the rm would want to employ no more than L d units (at point H). This employment is also greater than the Lm of the unregulated monopsony solution; no disemployment takes place. P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 12.5 AN APPLICATION: MINIMUM-WAGE LAWS 369 At wage w , however, the offered labor supply is L s , more than the rm wants to hire. The resulting unemployment gap is indicated by the distance NK in the diagram. So there is no disemployment indeed, employment actually increases yet there is unemployment! Last, w represents a high minimum wage, higher than the level at which the mrp and mfc curves intersect. Here employment would be reduced to L . Thus, a minimum wage as high as w would lead to the same qualitative implications as in the competitivemarket model. Such a high minimum would generate some disemployment, as compared with Lm , and generate a larger unemployment gap represented by the distance RT in the diagram. In applying this analysis it is important to appreciate that labor skill and quality vary across a spectrum. Although many unskilled workers might previously have been earning less than the imposed minimum wage, highly skilled workers were likely earning well above it. So minimum-wage laws would affect high-wage and low-wage workers differently. Using the competitive model, low-skilled (low-wage) workers would be affected as in Figure 12.15. Their wage rates would rise, but some will lose their jobs. In contrast, for the higher-skilled workers, the market equilibrium wage w c is likely to be already above the new minimum wage w o there will be no direct effect. What if instead the monopsony model of Figure 12.16 applies? Then: (1) For very low-skilled workers the imposed minimum wage would be effectively at a high level, like w in Figure 12.16, so their wage rates would rise but their employment would fall. (2) For medium-skilled workers, the minimum wage might be more like w or w , in which case both the wage rate and employment could increase. (3) For very high-skilled workers, the imposed minimum wage would be relatively low, even lower than w m in Figure 12.16. For such workers there would be no direct effect on wages or employment. Which of these models is the more correct picture is still debated by economists. The federal minimum-wage laws in the United States are uniform over the entire country, making no distinctions for age, experience, or geography. In contrast, most European countries have at least youth differentials. In Great Britain, for example, the youth minimum is only about 30% of the adult minimum. In Canada, minimum-wage schedules are set by the provinces rather than by the central government, a procedure that automatically allows for variations in cost-of-living and other differences across geographical regions. The absence of differentials in the United States leads us to expect that the brunt of the disemployment effects, if any, will be suffered by low-wage areas such as Appalachia and by low-wage demographic groups such as minorities and youthful workers. EXAMPLE 12.7 DO MINIMUM-WAGE LAWS REDUCE EMPLOYMENT? Economists, at least up to recently, have believed that in most labor markets the evidence supports the competitive model. A minimum wage, set higher than the previous equilibrium level, would be expected to reduce employment among the affected low-wage groups. The table here indicates some of the results of a study by Donald Deere, Kevin M. Murphy, and Finis Welch dealing with minimum wage increases legislated in 1990 and 1991.a P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 370 12. THE DEMAND FOR FACTOR SERVICES Percent employment reduction after 19901 minimum wage Increases Age group Men 1519 2024 2564 6569 Women 1519 2024 2564 6569 1 % low wage1 44.5 14.2 3.3 14.0 51.8 19.0 8.8 21.0 % employment change2 15.6 5.7 2.4 4.2 13.0 4.2 0.3 +3.1 Percentage of those employed in age group paid less than $4.25 between April 1, 1989 and March 31, 1990. 2 Calculated as percent change in employment between year ending March 31, 1992 and year ending March 31, 1990, divided by percent employed in earlier period. Source: Extracted from Deere, Murphy, and Welch, p. 48. The table shows that age-sex groups with the highest proportions of low-wage workers most notably the 1519 age groups generally suffered the largest proportionate reductions in employment. This is exactly what the competitive model would predict. (A possible exception was women 6569, but only a small percentage of this group was employed to begin with.) The investigators also found large employment drops across other demographic groups with high proportions of lowwage workers, among them African-Americans and persons of Mexican descent. Furthermore, the U.S. results conrming the competitive model have generally been supported by experiences with minimum wages in countries as different as Great Britain, Singapore, and Kenya.b As an interesting exception, however, a study by David Card and Alan Krueger obtained results in conict with the competitive model.c The competitive theory predicts that an increase in the New Jersey minimum wage would reduce employment of low-wage workers in New Jersey relative to the neighboring state of Pennsylvania, but if anything the opposite was found.d COMMENT As emphasized in Chapter 1, ongoing scientic debate in economics is healthy. Even seemingly well-established results, such as those concerning employment effects of minimum wage legislation, should be repeatedly tested. But these critiques must themselves be held to high scientic standards if they are to overcome a strong previous consensus of belief. a Donald Deere, Kevin M. Murphy, and Finis Welch, Sense and Nonsense on the Minimum Wage, Regulation (1995), No. 1. b Deepak Lal, The Minimum Wage: No Way to Help the Poor, The Institute of Economic Affairs, Occasional Paper 95 (1995). c David Card and Alan Krueger, Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania, American Economic Review, v. 84 (September 1994). d But see David Neumark and William Wascher, The Effects of New Jerseys Minimum-Wage Increase on Fast-Food Employment: A Re-evaluation Using Payroll Records, National Bureau of Economic Research Working Paper 5224 (August 1995). P1: JZP 0521818648c12agg.xml CB902/Hirshleifer 0 521 81864 8 July 2, 2005 15:40 SUMMARY 371 Regardless of their arguably adverse economic effects, minimum-wage laws have been politically popular. They appeal to humanitarian sentiments. In both the competitive and monopsonist models, low-skilled and high-skilled workers are affected differently. If the competitive model is valid, the supposed beneciaries, very low-wage workers (largely teenagers and minorities) previously earning less than the minimum wage, may end up worse off. True, many will receive the benet of an increased wage but others are likely to lose their jobs entirely. So for this main target group the good and bad effects are mixed. If the monopsonist model is valid, the only group who denitely gain both in employment and in wages are the mid-skilled workers, as analyzed in the discussion of Figure 12.16. In actuality the most powerful political pressure in the United States for higher mi