ESSENTIAL MICROECONOMICS - Assetsassets.cambridge.org/97805218/27478/frontmatter/9780521827478... · ESSENTIAL MICROECONOMICS Essential Microeconomics is designed to help students

ESSENTIAL MICROECONOMICS

Essential Microeconomics is designed to help students deepen their under-standing of the core theory of microeconomics. Unlike other texts, this bookfocuses on the most important ideas and does not attempt to be encyclope-dic. Two-thirds of the textbook focuses on price theory. As well as taking anew look at standard equilibrium theory, there is extensive examination ofequilibrium under uncertainty, the capital asset pricing model, and arbitragepricing theory. Choice over time is given extensive coverage and includes abasic introduction to control theory. The final third of the book, on gametheory, provides a comprehensive introduction to models with asymmetricinformation. Topics such as auctions, signaling, and mechanism design aremade accessible to students who have a basic rather than a deep under-standing of mathematics. There is ample use of examples and diagrams toillustrate issues, as well as formal derivations.

John G. Riley is Distinguished Professor of Economics at the University ofCalifornia, Los Angeles. A Fellow of the Econometric Society, his researchhas appeared in eminent journals such as the American Economic Review,Econometrica, Journal of Political Economy, Quarterly Journal of Eco-nomics, Review of Economic Studies, Journal of Economic Theory, andthe RAND Journal of Economics. With the late Jack Hirshleifer, ProfessorRiley coauthored The Analytics of Uncertainty and Information (CambridgeUniversity Press, 1992), a new edition of which is forthcoming with SushilBikhchandani of UCLA.

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Cambridge University Press978-0-521-82747-8 - Essential MicroeconomicsJohn G. RileyFrontmatterMore information

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ESSENTIAL MICROECONOMICS

JOHN G. RILEYUniversity of California, Los Angeles






cambridge university pressCambridge, New York, Melbourne, Madrid, Cape Town,

Singapore, Sao Paulo, Delhi, Mexico City

Cambridge University Press32 Avenue of the Americas, New York, NY 10013-2473, USA

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C© John G. Riley 2012

This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place without the written

permission of Cambridge University Press.

First published 2012

Printed in the United States of America

A catalog record for this publication is available from the British Library.

Library of Congress Cataloging in Publication data

Riley, John G.Essential microeconomics / John G. Riley, University of California, Los Angeles.

pages cmIncludes index.

ISBN 978-0-521-82747-8 (hardback)1. Microeconomics. I. Title.

HB172.R55 2012338.5–dc23 2011052561

ISBN 978-0-521-82747-8 Hardback

Additional resources for this publication are available at www.essentialmicroeconomics.com.

Cambridge University Press has no responsibility for the persistence or accuracy of URLs for externalor third-party Internet Web sites referred to in this publication and does not guarantee that any content

on such Web sites is, or will remain, accurate or appropriate.






Brief Contents

1 Prices and Optimization page 1

2 Consumers 43

3 Equilibrium and Efficiency in an Exchange Economy 85

4 Firms 106

5 General Equilibrium 139

6 Dynamic Optimization 182

7 Uncertainty 218

8 Equilibrium in Financial Markets 259

9 Strategy: Games in Which Preferences and History AreCommon Knowledge 303

10 Games with Asymmetric Information 347

11 Incentive Compatibility and Mechanism Design 382

12 Auctions and Public Goods 436

Appendix A: Mathematical Foundations 491

Appendix B: Mappings of Vectors 521

Appendix C: Optimization 567

Answers to Odd-Numbered Exercises 593

Index 691

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Contents

Preface page xi

Synopsis of the Text xiii

Approach of the Text and Summary of Chapters and Appendixes xv

Web Site xxi

1 Prices and Optimization 11.1 Supporting Prices 11.2 Shadow Prices 141.3 The Envelope Theorem 231.4 Foundations of Constrained Optimization 301.5 Application – Monopoly Pricing with Joint Costs 37

2 Consumers 432.1 Theory of Choice 432.2 Budget-Constrained Choice with Two Commodities 512.3 Consumer Choice with n Commodities 652.4 Consumer Surplus and Willingness to Pay 732.5 Choice over Time 78

3 Equilibrium and Efficiency in an Exchange Economy 853.1 The 2 × 2 Exchange Economy 853.2 The Fundamental Welfare Theorems 101

4 Firms 1064.1 What Is a Firm? 1064.2 Decision Making by Price-Taking Firms 1084.3 Returns to Scale 1174.4 Firm and Industry Analysis 1234.5 Monopoly Pricing 130

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viii Contents

5 General Equilibrium 1395.1 The Robinson Crusoe Economy 1395.2 Equilibrium and Efficiency with Production 1455.3 Existence of Equilibrium 1535.4 Public Goods 1635.5 Equilibrium Futures Prices 1675.6 Equilibrium with Constant Returns to Scale 173

6 Dynamic Optimization 1826.1 Life-Cycle Consumption and Wealth 1826.2 A Family of Dynamic Optimization Problems 1916.3 The Ramsey Problem 1966.4 Dynamic Programming Reformulation 2016.5 Optimal Control 206

7 Uncertainty 2187.1 Risky Choices 2187.2 Attitudes toward Risk 2297.3 Comparing Risky Alternatives 2407.4 Principal-Agent Problem 250

8 Equilibrium in Financial Markets 2598.1 Arrow-Debreu Equilibrium 2598.2 Security Market Equilibrium 2698.3 Capital Asset Pricing Model 2848.4 Arbitrage Pricing Theory 292

9 Strategy: Games in Which Preferences and History AreCommon Knowledge 3039.1 Strategic Equilibrium 3039.2 Games with a History 3199.3 Duopoly Games 3289.4 Infinitely Repeated Games 338

10 Games with Asymmetric Information 34710.1 Games of Incomplete Information 34710.2 Refinements of Bayesian Nash Equilibrium 36010.3 Games with Unobservable Strategies and Public Signals 373

11 Incentive Compatibility and Mechanism Design 38211.1 Incentive Compatibility 38211.2 Information Revelation, Adverse Selection, and Signaling 39611.3 Mechanism Design 411

12 Auctions and Public Goods 43612.1 Auctions 43612.2 Revenue Equivalence Theorem 451






Contents ix

12.3 Optimal Auctions 45612.4 Designing an Efficient Mechanism 46212.5 Trade-Off between Efficiency and Designer Profit 47412.6 Efficient Production and Exchange with Private Values

and Costs 480

Appendix A: Mathematical Foundations 491A.1 Is It Really True? 491A.2 Mappings of a Single Variable 495A.3 Derivatives and Integrals 500A.4 Optimization 507A.5 Sufficient Conditions for a Maximum 513

Appendix B: Mappings of Vectors 521B.1 Vectors and Sets 521B.2 Functions of Vectors 526B.3 Transformations of Vectors 544B.4 Systems of Linear Difference Equations 555

Appendix C: Optimization 567C.1 Maximization with Two Variables 567C.2 Unconstrained Optimization 570C.3 Implicit Function Theorem 573C.4 Constrained Maximization 578C.5 Supporting Hyperplanes 584C.6 Taylor Expansion 586

Answers to Odd-Numbered Exercises 593

Index 691











Preface

Although proving a theorem is always a special joy, finding a convincing wayto understand why theorems are true has always been a major fascination. Ioften learn much more from an informal graphical argument or from a well-thought-out example than from the formal analysis. Perhaps that is why Ihave always enjoyed teaching so much. It is very satisfying to take a majoridea in economic theory and explain it in a way that gives students a new anddeeper understanding.

I have written this text with the core goal of answering the question“Why?” in a clear and convincing manner. Some texts try to be encyclope-dic. This one does not. Instead it explores the most important contributionsof both price theory and game theory with the objective of developing stronginsights as to why the results are true.

People learn in different ways. I remember once excitedly showing RoyRadner a diagrammatic explanation of a paper he had written with JoeStiglitz. Roy listened patiently, then smiled and said, “Very good, John, butI never did understand a graphical argument!” Despite this disappointment,most people do find a clear diagram very helpful. There are a lot of themin this text. Yet looking at a graph only takes learning so far. There is nosubstitute for learning by doing. For this reason there is a strong focus onexercises. Many of the exercises are illustrative examples, but many oth-ers provide opportunities for a student to prove something related to thetheorems presented in the text. Answers to all of the questions are pro-vided. Half are in the text, and the rest can be found on the Web site,http://www.essentialmicroeconomics.com.

I have learned from many remarkable economists. My earliest inspirationand mentor was Bert Brownlie at the University of Canterbury. In addition,two very early and profoundly different teachers were Joe Stiglitz, who pre-sented a freshly written paper in every class, and Gerard Debreu, whoseteaching discipline and clarity were stunning. At MIT my approach to bothteaching and research was deeply influenced by Bob Solow. Then, as a junior

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xii Preface

colleague at UCLA, I taught my first classes on the economics of uncertaintywith my most important mentor, Jack Hirshleifer. Our teaching styles werevery different but complementary. Among my recent colleagues at UCLA,Christian Hellwig and William Zame have been especially influential. Ofcourse I have learned much from coauthors, in particular from Eric Maskin.






Synopsis of the Text

Essential Microeconomics is designed to help students deepen their under-standing of the core theory of microeconomics. Unlike other texts, this bookfocuses on the most important ideas and does not attempt to be encyclo-pedic.

Two-thirds of the book focuses on price theory. As well as taking a newlook at standard equilibrium theory, there is an extensive examination ofequilibrium under uncertainty, the capital asset pricing model, and arbi-trage pricing theory. Choice over time is also given extensive coverage andincludes a basic introduction to continuous time models (control theory).

The final third of the book, on game theory, has an extensive introductionto models with asymmetric information. Topics such as auctions, signaling,and mechanism design are made very accessible to students who have a basicrather than a deep understanding of mathematics.

There is extensive use of examples and diagrams to illustrate the essenceof an issue, as well as formal derivations. Readers have a choice of whetherto go beyond the core ideas to the underlying mathematics of the model.

Problem solving is crucial to developing a deep understanding of a topic.Therefore the book contains a large number of exercises (all with answersavailable). Most provide the reader with opportunities to apply economicprinciples. Other questions ask the reader to extend the formal theory.

There is also a Web-based self-learning course to help students review themathematics that is used in the text.

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Approach of the Text and Summary of Chaptersand Appendixes

In contrast to most economics textbooks, which typically hide all the“required mathematics” in an appendix, this book opens with a discussion ofthe theory of maximization. To be an effective economic theorist it is essen-tial to develop the ability to look at a problem from both a mathematicaland an economics perspective. To use a language metaphor, a student needsto be able to think not only in the language of mathematics but also like aneconomist. Developing that bilingual skill is the goal of the first chapter.

It is very important to read Chapter 1 carefully and thoroughly. Then, inworking through the next four chapters, the reader will develop both a highcomfort level with the principles of maximization and an appreciation of therole that prices play in allocating resources.

Although a large part of modern research is game theoretic, the coreof economic theory is price theoretic. Therefore anyone who wants to bean effective economics practitioner needs to understand both the power ofprice theory and its limitations. Chapter 2 examines price-taking behaviorby a consumer. In contrast with traditional texts, it focuses on extractinginsights about the elasticity of demand with respect to prices and income.The timeless model is then generalized to incorporate choice over time. In aformal sense this is a direct reinterpretation of the timeless model. However,this mathematical viewpoint glosses over the role of futures markets, futurespot markets, and market intermediaries like banks.

In Chapter 3 the two great welfare theorems are examined in a simpleeconomy in which consumers exchange their endowments of commodities.In such an economy the theorems are quite easily proved. However, todevelop a real appreciation of the theorems it is extremely helpful to con-sider them in the context of examples with two commodities and two con-sumers. These “Edgeworth box” economies are examined in detail.

Chapter 4 on firms begins by examining cost minimization by a singlefirm that is a price taker in input markets and then studies the relationshipbetween local returns to scale and minimized average cost. The chapter then

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xvi Approach of the Text and Summary of Chapters and Appendixes

focuses on how costs influence the equilibrium price of output if there aremany competing firms. Introductory textbooks study market equilibrium iffirms are price takers in the output market as well as input markets. Giventhe deeper analysis of the relationship between input prices and cost, thefocus here is on how changes in input prices affect each firm’s cost and hencethe equilibrium output price.

Under the assumption of increasing returns to scale it is efficient for indus-try output to be produced by a single firm. The final topic of the chapter ismonopoly pricing. A monopoly firm profits from raising output price abovemarginal cost. If resale is costly, a monopoly also has an incentive to pricea commodity differently for different groups of buyers. In addition, it hasan incentive to vary the price per unit with the number of units purchased.One simple way to do so is to introduce two-part pricing. Each buyer ischarged a monthly fee for access to the product or service and also pays aprice for each unit purchased. Legal restrictions typically prohibit firms fromexcluding classes of consumers. However a monopoly still has an incentive tooffer a menu of different two-part pricing schemes. The chapter concludeswith a discussion of how to choose the profit-maximizing two-part pricingscheme.1

Chapter 5 adds firms to the simple exchange economy of Chapter 3, andalso examines the conditions under which there exist prices at which all mar-kets clear. The market equilibrium model is then generalized to incorporatepublic goods and choice over time. Finally the chapter considers equilibriumin an economy that exhibits constant returns to scale at the market level. Insuch an environment the price of outputs is determined by costs and henceby technology. This makes it possible to draw strong conclusions about theway technology affects equilibrium prices.

Most texts give short shrift to choice over time. Chapter 6 redresses thebalance. With a finite number of periods a model with time is mathemat-ically indistinguishable from a timeless model. However, to derive usefuleconomic insights it is necessary to make strong assumptions about the link-ages between periods, for both preferences and technology. As a modelingsimplification it is often easier to assume that there is no last period. Insteadthe number of periods is infinite. The goal of this chapter is to provide anunderstanding both of why simplifying assumptions are made and of thetight connection between models with a large but finite number of periodsand infinite horizon models. Another modeling choice is between models inwhich there are discrete time periods and those where time is a continuousvariable. A further goal is to introduce the reader to the continuous model.

1 The goal is to give the reader insights into “mechanism design” without having to worry about thesubtleties.






Approach of the Text and Summary of Chapters and Appendixes xvii

First it is examined as the limit of the discrete time model. Then Pontryagin’sMaximum Principle for continuous time models is derived.

Chapter 7 introduces uncertainty. A commodity is no longer defined onlyby its characteristics and time of delivery but also by the state of the world(or more simply “state”). For example, an insurance company contracts tosupply funds for surgery if the state of the world is “malfunctioning heart.”Aversion to risk is central to decision making under uncertainty. This chap-ter examines how to model differences in risk aversion. It also studies theconditions under which different risky prospects can be ranked regardless ofa consumer’s aversion to risk.

Chapter 8 extends the basic equilibrium model to financial markets. Typ-ically texts focus on the Arrow-Debreu “complete market” equilibrium inwhich every commodity can be traded in every contingency. Such equi-librium is a direct extension of the standard timeless model. This chaptertakes the complete market equilibrium as a starting point and then examinesequilibrium when there are more limited trading opportunities. The chap-ter first provides conditions under which trading only in securities marketsachieves complete market equilibrium outcomes. It then examines modelswhen trading in financial markets offers more limited risk-spreading oppor-tunities. Both the capital asset pricing model and arbitrage pricing model areexamined.

Chapter 9 introduces the reader to the basic concepts in game theory. Thestrategies of the players in a game are Nash equilibrium strategies if they aremutual best responses. To play such a strategy requires that players sharea deep understanding of the game being played. The chapter discusses indetail this critical but controversial assumption (the “common knowledge”assumption).

Chapter 10 takes up the subtleties of game theory when players haveprivate information. Typically such games have multiple Nash equilibriaor even a continuum of equilibria. The assumption that all players knowwhich equilibrium is being played stretches the common knowledge assump-tion even further. As an alternative, game theorists have sought ways torefine the definition of equilibrium to yield a unique refined equilibrium.Commonly used refinements are examined. The final section examines aninfinitely repeated game in which strategies are private but all playersobserve a public signal that is correlated with the actions taken.

Chapter 11 further develops the theory of games with private informa-tion. Different types of player typically take different actions. If each playeris taking his or her equilibrium action there can be no advantage in switch-ing to the strategy of some other type. Strategies for which this is true aresaid to be incentive compatible. At the core of successful modeling of pri-vate information is an assumption about preferences (the “single crossing






xviii Approach of the Text and Summary of Chapters and Appendixes

property”) that greatly simplifies the constraints imposed by incentive com-patibility. The implications of single crossing are examined and then appliedto the theory of signaling. The chapter next introduces mechanism designunder the single crossing property. To develop insights into solution meth-ods, the chapter then examines the design of selling schemes by a monopolistfacing buyers with different demand functions.

Chapter 12 applies the principles of mechanism design to the theory ofauctions and public good provision. It explores major results in rankingdifferent types of auctions. The method of analysis is then used to exam-ine efficient public good provision. In contrast with the auction environ-ment in which the efficient mechanism generates revenue to the mecha-nism designer, the efficient provision of public goods generates a loss to thedesigner. The reasons for the different results are examined, and it is shownthat an auction is only efficient and profitable if the reservation price of theseller is public information.

The three appendixes cover the mathematics that is essential to any gradu-ate course in microeconomics. Appendix A examines the foundations of cal-culus with a single variable and also introduces concave and quasi-concavefunctions. Appendix B focuses on mappings of vectors and includes an intro-duction to difference equations. Appendix C provides the foundations ofmultivariable constrained optimization.

Thoughts on Teaching Microeconomic Theory

Economics is built on two fundamental ideas: each agent in a populationmakes choices based on the agent’s underlying preferences, and the outcomefor the population is an equilibrium outcome. So a student who really under-stands individual optimizing behavior and notions of price and game theo-retic equilibria is ready to do research in any field of economics. Thereforethe key to successful teaching is to give each student a deep understandingof these two ideas.

Doing so means presenting the big theorems and proving a version of thetheorems that is appropriate to the mathematical preparation of the class.Yet this is only the beginning. It is even more important to breathe life intothe theorems by showing how they can be applied to generate useful insights.Thus I believe that a significant fraction of class time should be spent onapplications and examples.

Consider, for example, the Walrasian equilibrium. Understanding the twogreat welfare theorems and how to prove existence using a fixed point the-orem is important. Yet it is only through the study of the special casesof Edgeworth box and representative agent models that a student gets asense of how general equilibrium influences economic outcomes. One great






Approach of the Text and Summary of Chapters and Appendixes xix

example is the constant returns to scale model of international trade theorywith two inputs and two outputs. There is so much to learn from this model.A second example is equilibrium risk sharing through trading in contingentand security markets. At a formal level it is simply a matter of showingthat the new model is mathematically equivalent. Therefore all the theo-rems without uncertainty generalize. The important step is helping studentsdevelop an understanding of how risk is shared in a Walrasian equilibriumusing simpler models such as the capital asset pricing model.

To further develop the ability to draw insights from and apply theory,homework should be devoted almost entirely to examples and applications.Of course, the teaching assistant must first offer help where the instructorhas left students mystified, but after this is done, the focus should be onexamples and applications.

The text offers many practice exercises, and there are more on the Website. If you are willing to share exercises that you have found helpful, sendthem to me, and I will add a selection to the site and acknowledge yourhelp. The Web site also contains a set of slides for each chapter and theappendixes. I am never satisfied with my presentations so I cannot say thatthe slides represent the way I would next teach the material. However, toa first approximation, they represent the way I recently thought the topicsshould be presented.











Web Site

The Web site www.essentialmicroeconomics.com complements the text.One critical challenge for a teacher of a first-year graduate class is the widevariation in students’ mathematical backgrounds. To ameliorate these prob-lems the Web site offers a two-part approach. First, there is a Web page con-taining a set of calculus and linear algebra review modules that students canwork through to check their level of preparedness. Each module providesproblem sets (primarily on optimization) and lots of hints to help a studentwork through each problem. Second, there is a Web page containing a set ofslides on “Mathematical Foundations.” These cover most of the topics in thethree appendices. At UCLA these lectures are offered to entering graduatestudents in a two-week intensive “Summer Math Camp.” Any student whohas successfully worked through both the modules and the topics covered inthe slides will be fully prepared.

The Web site also provides a set of slides for each chapter. These aredesigned to help an instructor or teaching assistant prepare lectures and alsoto provide students with a summary of material covered. Although half ofthe answers to the problems sets are in the textbook, the other half areaccessible only from the Web site. Especially for the later chapters thereare also notes on topics not covered in the text, additional exercises, andlinks to other Web-based material. Suggestions as to additional helpful linksare welcome.

Finally the student has access to the UCLA Auction House. This Web siteis designed to introduce the reader to competitive bidding. For a series ofdifferent auction environments, students have the opportunity to bid againstone or more “robot” bidders who follow theoretical equilibrium strategies.Instructors are welcome to suggest additional auctions.

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ESSENTIAL MICROECONOMICS - Assetsassets.cambridge.org/97805218/27478/frontmatter/9780521827478... · ESSENTIAL MICROECONOMICS Essential Microeconomics is designed to help students