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**Unformatted text preview: **DAVIDM.KREPS V(~ -\ \~ -·v Jr \, A course in· microeconomic theory A course in microeconomic theory David M. Kreps PRINCETON UNIVERSITY PRESS Copyright © 1990 by David M. Kreps
Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 All rights reserved Library of Congress Cataloging-in-Publication Data
Kreps, David M.
A course in rnicroeconornic theory I David M. Kreps.
P·
em.
Includes bibliographical references.
ISBN 0-691-04264-0 (alk. paper)
1. Microeconomics. ·r. Title.
HB172.K74 1990
338.5-dc20 89-27619 This book has been composed in Palatino and Computer Modern typefaces. Princeton University Press books are printed on acid-free paper, and meet tlie guidelines for
permanence and durability of the Committee on Publication Guidelines for Book Longevity
of the Council on Library Resources
Printed in the United States of America by Princeton University Press, Princeton, New Jersey 10 9 8 7 6 54 3 2
Figures from Gt;lpter 20 have been adapted with pemuss10n of The Free Press, a
C INSTITUTIONS OF CAPITALISM by
Division of Macmillan, Inc. fro
Oliver E. Williamson. Cop ( for Anat :•.'-'·.· . I "!·. contents
preface
chapter one: An overview XV 3 1.1. The basic categories: Actors, behavior,
institutions, and equilibrium 3
1.2. The purpose of microeconomic theory 7
1.3. Scope, detail, emphasis, and complexity 10
1.4. A precis of the plot 12 part I: Individual and social choice
chapter two: The theory of consumer choice
and demand 17 Prologue to part I 17
2.1. Preferences and choices 18_ 21
2.2. Marshallian demand without derivatives 37
2.3. Marshallian demand with derivatives 51
2.4. Aggregate demand 62
2.5. Bibliographic notes 63
2.6. Problems 65 chapter three: Choice under uncertainty
3.1.
3.2.
3.3.
3.4.
3.5.
3.6.
3.7.
3.8. Von Neumann-Morgenstem expected utility 72
On utility for money 81
Applications to market demand 87
States of nature and subjective probability 98
Problems with these models 112
Normative applications of the theory 120
Bibliographic notes 122
Problems 124 71 Contents viii chapter four: Dynamic choice
4.1.
4.2.
4.3.
4.4. Optimal dynamic strategies 133
Menus and meals 139
Bibliographic notes and discussion
Problems 146 133 143 chapter five: Social choice and efficiency
5.1.
5.2.
5.3.
5.4.
5.5.
5.6.
5.7. 149 The problem 149
Pareto efficiency and optimality: Definitions 153
Benevolent social dictators and social welfare functionals 156
Characterizing efficient social outcomes 164
Social Ch9ice rules and Arrow's possibility theorem 174
Bibliographic notes 181
Problems 182 part II: T}le price mechanism
chapter six: Pure exchange and
general equilibrium 187 Prologue to part IT 187
6.1. Pure exchange and price equilibrium 187
6.2. Why (not) believe in Walrasian equilibrium? 193
6.3. The efficiency of a general equilibrium 199
6.4. Exis~ce and the number of equilibria 205
6.5. Time, uncertainty, and general equilibrium 216
6.6. Bibliographic notes 223
6.7. Problems 225 chapter seven: The neoclassical firm
7.1.
7.2.
7.3.
7.4.
7.5. Models of the firm's technological capabilities 234
The profit function 239
Conditional factor demands and cost functions 250
From profit or cost functions to technology sets 253
Cost functions and -runs 255 233 Contents
7.6. Bibliographic notes
7.7. Problems 259 ix
259 chapter eight: The competitive firm and
perfect competition
8.1.
8.2.
8.3.
8.4.
8.5.
8.6. A perfectly competitive market 264
Perfect competition and -runs 267
What's wrong with partial equilibrium analysis?
General equilibrium with firms 283
Bibliographic notes 292
Problems 292 263 279 chapter nine: Monopoly
9.1.
9.2.
9.3.
9.4.
9.5.
9.6.
9.7. 299 The standard theory 299
Maintaining monopoly 302
Multigood monopoly 304
Nonlinear pricing 306
Monopoly power? 314
Bibliographic notes 317
Problems 318 chapter ten: Imperfect competition 325 10.1. The classic models of duopoly 325
10.2. Bibliographic notes and discussion 340
10.3. Problems 347 part III: Noncooperative game theory
chapter eleven: Modeling competitive
situations
Prologue to part ill 355
11.1. Games in extensive form: An example 356
11.2. Games in extensive form: Formalities 363
11.3. Games in normal or stategic form 376 355 x Contents
11.4. Mixed strategies and Kuhn's theorem
11.5. Bibliographic notes 384
11.6. Problems 385 380 chapter twelve: Solution concepts
for noncooperative games 387 12.1. Opening remarks 387
12.2. Dominance and iterated dominance for normal form games
12.3. Backwards induction in games of complete
and perfect information · 399
12.4. Nash equilibrium 402
12.5. Equilibria in mixed strategies 407
12.6. Why might there be an obvious way to play a given game?
12.7. Refinements of Nash equilibrium 417 393 410 12.7.1. Weak dominance 418 • 12.7.2. Subgame perfection (and iterated
weak dominance) 421 • 12.7.3. Sequential equilibrium 425 • 12.7.4.
Restrictions on out-of-equilibrium beliefs 432 • 12.7.5. 'frembling-hand
perfectio"~ 437 • 12.7.6. Proper equilibria and stable sets of equilibria 442 12.8. Reprise: Classic duopoly .443
12.9. Bibliographic ~otes 449
12.10. Problems 451 chapter thirteen: Incomplete information
and irr~tionality
13.1.
13.2.
13.3.
13.4.
13.5.
13.6. Games of incomplete information 463
An application: Entry deterrence 468
Modeling irrationality 480
More on refinements: Complete theories
Bibliographic notes 496
Problems 498 463 489 chapter fourteen: Repeated play:
Cooperation and reputation
14.1. The prisoners' dilemma 503
14.2. Repeating games can yield cooperation: The folk theorem
14.3. Noisy observables 515 503
505 Contents
14.4.
14.5.
14.6.
14.7.
14.8. xi
Implicit collusion in oligopoly 524
Reputation 531
Reputation redux: Incomplete information
Bibliographic notes 543
Problems 546 536 chapter fifteen: Bilateral bargaining
15.1.
15.2.
15.3.
15.4.
15.5.
15.6.
15.7. 551 Simultaneous offers and indetermi:O.ancy 552
Focal equilibria 554
Rubinstein's model 556
The experimental evidence about alternating offers
Models with incomplete information 568
Bibliographic notes 570
Problems 571 565 part W: Topics in information economics
chapter sixteen: Moral hazard and incentives
Prologue to part N
577
16.1. Introduction 578
16.2. Effort incentives: A simple example 579
16.3. Finitely many actions and outcomes 586
16.4. Continuous actions: The first-order approach
16.5. Bibliographic notes and variations 608
16.6. Problems 616 chapter seventeen: Adverse selection
and market signaling
17.1.
17.2.
17.3.
17.4.
17.5. Akerlof's model of lemons 625
Signaling quality 629
Signaling and game theory 645
Bibliographic notes and discussion
Problems 654 650 577 604 625 Contents xii chapter eighteen: The revelation principle
and mechanism design
18.1.
18.2.
18.3.
18.4.
18.5.
18.6. 661 Optimal contracts designed for a single party 661
Optimal contracts for interacting parties 680
The pivot mechanism 704
The Gibbard-Satterthwaite theorem 712
Bibliographic notes 713
Problems 715 part V: Firms and transactions
chapter nineteen: Theories of the firm
19.1.
19.2.
19.3.
19.4.
19.5.
19.6. The firm as a profit-maximizing entity
The firm as a maximizing entity 729
The firm as a behavioral entity 731
Firms in t;he category of markets 739
Bibliographic notes 740
Problems 740 723 724 chapter twenty: Transaction cost economics
and the firm
20.1. Transaction cost economics and firms 743
20.2. Mathematical models of transaction cost economics
20.3. Bibliog:-aphic notes 769 743
756 postscript 771 appendix one: Constrained optimization 775 Al.l.
A1.2.
A1.3.
A1.4.
A1.5. A recipe for solving problems 775
The recipe at work: An example 778
Intuition 782
Bibliographic notes 788
Problems 789 xiii Contents appendix two: Dynamic programming
A2.1.
A2.2.
A2.3.
A2.4.
A2.5.
A2.6. 791 An example with a finite horizon 791
Finite horizon dynamic progranurung 796
An example with an infinite horizon 801
Stationary Markov decision problems 806
Bibliographic notes and discussion 813
Problems 814 addendum to the second and
subsequent printings 817 index 819 preface
This book provides an illtroduction to the content and methods of microeconomic theory. The primary target for this book is a -~~ru:_ gi_aduate student who is lookllg for an illtroduction to microeconomic theory
that goes beyond the traditional models of the consumer, the firm, and
the market. It could also be used by undergraduate majors who seek an
."advanced theory" course followmg traditional illtermediate micro. And,
for relatively mathematically sophisticated students, it could be used as a
nontraditional illtermediate micro course. The book presumes, however,
that the reader has survived the standard illtermediate microeconomics
course, and the student who has not gone through such a course may find
it helpful on occasion to consult a traditional illtermediate text. There are
many excellent books around; four that I have recommended to students
are Friedman, Price Theory (South-Western Publishllg, 1986), Hirshleifer,
Price Theory and Applications (4th edition, Prentice Hall, 1988), Nicholson,
Microeconomic Theory - Basic Principles and Extensions (3d edition, Dryden Press, 1985), and Pilldyck and Rubinfeld, Microeconomics (Macmillan,
1989).
The distinguishllg feature of this book is that although it treats the
traditional models (ill parts I and mit emphasizes more recent variations,
with special emphases on the use of noncooEerative game theory to mod~l
__sQmpetitive ~teracti~ns_ (part_.!!P.L transact!_o.!:IS in_which private informa:tion plays a role (part N), and the theory of :firn:l$__giJ.!=l_o_tb.e:cnoruncu:}sgt_
institu!lons (part V).
For the most part, the formal mathematical requirements of this book
are mild. The reader will have to be able to do constramed optimization
problems with inequality constramts, using Lagrange multipliers and the
complementary slackness conditions. A cookbook recipe for this technique
and an example are presented ill an appendix. The reader can trust that
for any problem ill this book, with exceptions as noted, any solution to
the first-order conditions and the complementary slackness conditions is a
global optimum. That is, with a few exceptions, only "convex" problems
are considered. The reader is expected to know basic probability theory.
For the sake of completeness, I sometimes delve illto "optional" topics
that either require a significant amount of mathematics or deal with somewhat advanced and/ or esoteric topics. This material is presented both ill
footnotes and ill slightly smaller typesize ill the text. For the most part, it XVl Preface is up to the reader to supply the necessary mathematical background. The
one exception concerns dynamic programming; a second appendix gives
just enough background :in the techniques of d.p. to get through its uses :in
this book I apologize for any frustration the more technical material may
cause. I have tried to make the book comprehensible even if the reader
skips all this material
The level of mathematical sophistication required (as opposed to the
number of mathematical tools) rises as the book progresses. I have written
this book with a first-year graduate student :in mind, and I expect that the
tolerence of such students for abstract arguments will rise as their first
year of study unfolds.
The general style of the book is informal, and the number of theorems
and proofs is relatively low. This book is meant to be a skeleton survey
of microeconorl:tic theory or, more precisely, of some of the topics and
techniques of microeconomic theory; students and instructors will wish to
supplement what is here accord:ing to their own tastes and :interests. I try
at the end of each chapter to :indicate where the reader should go for more
advanced and complete coverage of the topics under discussion. 1 The
text is relatively more complete and formal :in part ill, the :introduction
to noncooperative game theory, because there are fewer good advanced
treatments of that material other than the original papers. Two caveats are called for by ·the style I employ. Despite the very
impressive number of pages in this book, the number of ideas per page
is low relative to a standard text. I prefer, and I think students prefer,
books that are relatively chatty. Be that as it may, this book is relatively
chatty. (This is my excuse for calling this A Course in . . . . Perhaps it would
have been better to have called this Lectures in .... ) I hope that readers
who know some of the material aren't put off by this but can get to what
they don't know without much delay. Second, fve tried to write a good
textbook, which is not to my mind the same thing as a good reference book
The reader who goes back to this book to find something specific may find
the exercise somewhat trying. In particular, many important concepts are
discussed only in the context of specific problems, with the reader left to
think through the general structure. I think this makes for a good textbook;
but it doesn't make for a good reference book Besides not always giv:ing
general formulations of concepts, I never give exhaustive surveys of the
1
These reading lists are products of convenience, which means that they emphasize my
own work and the work of close colleagues; there is certainly a Stanford and then American
bias to these lists. They are not intended to be exhaustive; they certainly are not intended
to establish precedence. It is inevitable that I have omitted many excellent and important
citations, and apologies are hereby tendered to anyone offended. Preface xvii range of applications that can be found in the literature; I hope that the
reader, having digested my one example in one context, will be prepared
to study other examples and contexts encountered outside this book. And
I have not tried to diversify among topics. Some economy is achieved
by using related examples (many of which I draw from the literature on
industrial organization), and a book this long should economize whenever
and wherever possible.
Owing to the limitations of time (and, less importantly, space), I didn't
get to a few topics that I would have liked to have included. These fall
primarily in the areas of parts IV and V and include: rational expectations
with differential information; search; coordination failures; micromodels
of market institutions, including auctions; models of political institutions.
If ever there is a second edition, perhaps it will be longer still!
Insofar as a textbook can have a plot or a story or a message, I believe
that this book does; this is not simply a compendium of many interesting
and somewhat connected models. It is traditional, I believe, to give a
precis of the "message" in the preface. But I have instead moved this to
the end of chapter 1 in the hope that more readers will see it there than
would see it here.
Concerning the ordering of topics, I am greatly undecided on one
point (and instructors using this book may wish to undo the decision I
settled on). To show applications of game theory as the techniques are
developed, it may be sensible to interleave parts m and rv. After finishing chapter 12, go on to the earlier sections of chapter 16. Then take up
chapter 17 and, when the game theoretic treatment of signaling is encountered, return to chapter 13. The disadvantage is that this breaks up the
"oligopoly story" that runs through part ill; my own experience is that
the oligopoly story generates sufficient interest for a first pass through
the techniques, and then parts IV and V provide good opport:unities to
review the techniques of part ill. More generally, the book is filled with
material that various instructors may find peripheral or too detailed for
a first course; the course that I have taught, which formed the basis for
this book, went from the first page to the last in ten weeks, but covered
perhaps a third to a half of what fits between.
Most of the chapters come with a set of problems at the end. The
serious student should do as many as possible. There are fewer problems
per topic than one normally finds in textbooks, and the problems tend to be
longer than most textbook problems because they often develop variations
on the basic themes that the text doesn't cover. Variations are left to the
problems on the principle that "doing" a model is a much better way
to learn than reading about the model. A few of these problems require xviii Preface mathematical skills substantially beyond those needed to read the text
of the book; the student who completes all the problems will have done
extraordinarily well.
In teaching a course based on this book, I've supplemented the material here with reading in other, more traditional, texts, and (as importantly)
with discussion of a few case studies from the Harvard Business School.
I have found particularly valuable: The Oil Tanker Shipping Industry in
1983 (Case #9-384-034) for discussion of perfect competition; GE vs. Westinghouse in Large Thrbine Generators (A), (B), and (C) (#9-380-128,129,130)
for discussion of implicit collusion in a noisy environment; The Lincoln
Electric Company (#376-028) for discussion of incentives, screening, and
nonneoclassical models of the firm; and The Washington Post (A) and (B)
(#667-076,077) for discussion of internal organization, implicit contracts,
transaction cost economics, and so forth.
I am gratefUl to a number of colleagues (some of whom were anonymous reviewers) and students who made helpful comments and suggestions on drafts of this book. 2 It would be impossible to give a comprehensive list, but Dilip Abreu, Anat Admati, David Baron, Elchanan Ben
Porath, Ken Binmore, Don Brown, Drew Fudenberg, Oliver Hart, Bengt
Holmstrom, David Levine, Nachum Melumad, Andrew McLennan, Paul
Milgrom, Barry Nalebuff, John Pencavel, Stefan Reichelstein, Peter Reiss,
John Roberts, Ariel Rubinstein, Jos·e Scheinkman, Jean Trrole, Guy Weyns,
Jin Whang, Bob Wilson, Mark Wolfson, and especially Alex Benos, Marco
Li Calzi, and Janet Spitz deserve special mention. I am also grateful to
Vrrginia Barker, who copy-edited the book with skill and grace, and to
Jack Repcheck of the Princeton University Press for his unflagging efforts
in the preparation of this book and for his confidence in it, even when
confronted with the possibility of yet another unexpected hundred pages.
It goes without saying that most of what is contained here I learned
from and with many teachers, colleagues, and students. The list of such
individuals is much too long to give here, so I will refrain except to note
my obvious debt to Robert Wilson and to thank him and all of the rest of
you.
Note: For the addendum to the second and subsequent printings, see
pages 817-18. 2
Many of the reviewers will be unhappy that I didn't more directly address their criticisms. But let me take this opportunity to assure them that I took those criticisms to heart,
and I think they all helped make this a far better book. A course in microeconomic theory chapter one An overview
This opening chapter sets out some basic concepts and philosophy for
the rest of the book. In particular, we address four questions: What are
the basic categories :in microeconomic theory? What are the purposes of microeconomic theory? How does one's purpose influence the levels of
scope, detail, and emphasis :in one's model? How will the development
of the theory proceed :in this book? 1.1. The basic categories: Actors, behavior, institutions, and equilibrium
Microeconomic theory: concerns t:l:!_eQ;>ehavior of~dividual economic\ I.(act9rs_and the·~gregati~__9f ~eh.:_~ction5 ~ diff~r_~i}ns_t!futional fraffiE;. works. This one-sentence description :introduces four categories: The :in-·
, dividual(qctor~ traditionally either a_£~~1Eller_CQP_~~~ theCJ!!Jz_apjor 9j_
1 the actor, traditionally(1J.tilitv(:naximization by consum~rs and_~rofit(m'!X-.
i ~ation by firms; a!! in~Jj~JjE_nal fiame'U!_~rk, which describes what( options
t!"te_!n<:!J.Y!dl.lal act()~_~ye and -~hat<putC_()_!!l~? they(receiv~ as i\..~!!on \
1
·of the actions of others, traditionall...

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