Chapter 1 - Mathematics

# Chapter 1 - Mathematics - Chapter 1 Introduction 1.1...

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Unformatted text preview: Chapter 1 Introduction 1.1 Microeconomic theory The point of departure for microeconomic theory is the assumption that decision makers act in pursuit of some well-defined objective. 1 As a practi- cal matter, this amounts to assuming that decision makers maximize some mathematical payoff function. For example, firms choose prices or output levels to maximize profits, consumers purchase goods to maximize satis- faction, or governments choose tax policies to maximize the welfare of the citizenry. The particular objectives do not matter. It might be the case that a firm maximizes sales, not profits - perhaps because the firm’s manager wishes to gain the prestige that goes along with running a large enterprize. A gov- ernment might make decisions that maximize its own consumption rather than the welfare of citizens. Whether or not one objective is posited in- stead of another depends largely on what best suits the situation. The only requirement is that decision makers have some well-specified objective. The requirement that decision makers - commonly referred to as “agents”- have a well-defined objective essentially means that one can graph, write 1 Many books start out with a definition of the subject, but I have deliberately avoided doing this. No two economists define “microeconomics,” or “economics,” for that matter, in the same way. See Backhouse and Medema (2008) for a discussion of the rather diverse definitions of economics. 1 2 CHAPTER 1. INTRODUCTION down, or otherwise describe some mathematical function describing how the actions the agent might take translate into returns or payoffs. While there is a tension between developing realistic payoff functions and formulating objectives that are easy to analyze using graphical or mathematical meth- ods, it is nonetheless useful to come up with clean mathematical ways of characterizing decisions and objectives using mathematics. 1.2 Mathematics While microeconomic theory is a mathematical subject, one can actually get quite far with a working knowledge of a few key ideas. Since the point of departure is that agents make decisions so as to maximize some payoff function, of importance is the method by which the values of a variable that maximize a function can be found. The usual situation is one in which x represents some potential action that an agent might take, and f ( x ) repre- sents the returns derived from taking different actions, commonly called a payoff function. If the agent is rational, he or she should choose the x that results in the largest possible value of f ( x ). A significant portion of this book will be devoted to deriving different sorts of expressions for f ( x ) that capture the payoffs of consumers, producers, etc., but before jumping into the material, it is useful to begin with a review of the basics of multivariate calculus, which allows one to find maxima and minima of functions....
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Chapter 1 - Mathematics - Chapter 1 Introduction 1.1...

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