MWG: Ch.00 Contents Preface

Mi cro eco no mi cTheory Andreu Mas-Colell Michae l D. WJ.inston and Jerry R. Green New York Oxford OXFORD UNIVERS ITY PRE>S 1995 by any form or by any mean~. electroni~·. cm. IU. Andreu. Microeconomics. Library of Congre:ss Cataloging-in-Publication Data Mas-Cole!!. or tr~nsmiucd.M6247 I '. withoul the prior permission of Oxford Unh'cr•il)' Press. Published by O~ ford University Press. New York 10016 Odotd is a rcgi~ttred trademark of QJ. and Jerry R. Green. I.l9S 3J8.01ocopying. Inc . No part of this publica1ion may he rcprudut>cd.330.S-dc20 9S-18128 f 98765~:\21 Prinred in rite Uniied Srare~ of America on add-fru paper . Ti!tc lIB I 72. lnclude.icl 0. 'Nh inston. s1orcd in a rctric\·al system.• 198 Madi•on A\'enue.s bibliographical references and indr. Mich.x. Green. mech::mical. Whinstun. p.ford Univo=rsity Press All righls reserved.f r-131 OXFORD UtHVERSITY PRESS Oxford New York A1hens Auckland Bangkok Bombay Calcutta Cape Town Dar es Salum Deli Aon:ncc Hong Kong Istanbul Karachi Kuala Lumpur PAadru Madrid Melbourne Mexico City ·Nairobi Paris Singapore Taipei Tokyo Toronto and associated co111p:1nies in Berlin Ibadan Copyright© 1995 by Oxford University Press. recording. ISBN 0-19-S0734-0-l (cloth) ISBN 0-19-~!10268-1 (paper) I. II. Micr~conomic th rory I Andreu Mas·Colcll. nr o!hcrwisc. Inc. Michael Dennis. New York. ph. Jerry R. character. for his sweetness and joy at the book's completion. for helping me get started M. for her kindness. D. and spirit 1. To Bonnie. strength.A Esther. for keeping me smiling throughout. w. M.-c. and to Nan. R. . to Noah. G. To Pamela. por todo A. C 2.A 67 80 91 Appendix A: Continuity and Differentiability Properties of Wa\rasian Demand 96 Exercises 4.H 3. Indirect Utility.E 2.F I7 17 Introduction 17 Commodities 18 The Consumption Set 20 Competitive Budgets 23 Demand Functions and Comparative Statics The Weak Axiom of Revealed Preference and the Law of Demand Exercises 3. Aggregate Demand 4. Preference and Choice 1. Consumer Choice 2. and Expenditure Functions 75 Integrability Welfare Evaluation of Economic Changes The Strong Axiom of Revealed Preference Chapter 4.D 5 Introduction 6 Preference Relations 9 Choice Rules The Relationship between Preference Relations and Choice Rules Exercises 2.B 11 15 Chapter 2. Classical Demand Theory 3.A 2. B I .B 3 92 105 105 Introduction Aggregate Demand and Aggregate Wealth 106 vii .D 3.C 3.C l .1 3.F 3.A I.B 28 36 Chapter 3.J 40 40 Introduction 41 Preference Relations: Basic Properties 46 Preference and Utility 50 The Utility Maximization Problem 57 The Expenditure Minimization Problem 63 Duality: A Mathematical Introduction Relationships between Demand.A 3.G 3.E 3.Contents xiii Preface PART ONE: INDIVIDUAL DECISION MAKING 5 Chapter I.D 2. A Introduction 127 Production Sets 128 5.B 8. Cfioicc Under Uncertainty 6.Viii C 0 NT ENT S 4.D Strategics and the Normal Form Representat ion of a Game 7.C Profit Maximizati on and Cost Minimizatio n 135 5. Production 116 127 5.B 6.Hand Perfection 258 Appendix A: Existence of Nash Equilibrium 260 Exercises 262 253 .sic Elements of Noncoopera tive Games 219 7.D The Geometry of Cost and Supply in the Single-Outp ut Case 5.F 143 167 Introduction 167 Expcc1cd Utility Theory 168 Mon€y Lotteries and Risk Aversion 183 ComJJarison of Payoff Distribution s in Terms of Return and Risk State-depen dent Utility 199 Subjective Probability Theory 205 Exercises 194 208 PART TWO: GAME THEORY 217 Chapter 7.F Efficient Production 149 5.E 6.E Games of Incomplete Information : Bayesian Nash Equilibrium 8.D Aggiegate Demand and the Weak Axiom 109 Aggregate Demand and the Existence of a Representat ive Consumer Appendix A: Regularizing Effects of Aggregation 122 Exercises 123 Chapter 5.C 4.A 6.A 7.0 Nash Equilibrium 246 8.C The Extensive Form Representat ion of a Game 221 7.E Rand()mizcd Choices 231 Exercises 233 Chapter 8.E Aggregation 147 5.C 6.C Introductio n 235 Dominant and Dominated Strategies 236 Ratio11alizable Strategies 242 8.A 8.F The Possibility of Mistakes: Trembling.G Rem 4rks on the Objectives of the Firm 152 Appendix A :The Linear Activity Model 154 5.B Exercises 160 Chapter 6. Simultaneo us-Move Games 228 235 8.D 6. Ba.B lntrocluctio n 219 What Is a Game? 219 7. B 10.B I J.C 9.A 10.A 9.G 307 311 Introduction 311 Pareto Optimality and Competitive Equilibria 312 Partial Equilibrium Competitive Analysis 316 The Fundamental Welfare Theorems in a Partial Equilibrium Context Welfare Analysis in the Partial Equilibrium Model 328 Free-Entry and Long-Run Competitive Equilibria 334 Concluding Remarks on Partial Equilibrium Analysis 34 l Exercises 268 368 374 383 Introduction 383 Monopoly Pricing 384 Static Models of Oligopoly 387 Repeated Interaction 400 Entry 405 The Competitive Limit 41 l Strategic Precommitmcnts to Affect Future Competition Appendix A: Infinitely Repeated Games and the Folk Theorem Appendix B: Strategic Entry Deterrence and Accommodation Exercises 428 417 423 414 325 ix .D 11.E 10.C t l.C 0 NT ENT S Chapter 9. Dynamic Games 9.B 12.E 12.A 11. Competitive Markets 10.D 267 Introduction 267 Sequential Rationality. and Subgame Perfection Beliefs and Sequential Rationality 282 Reasonable Beliefs and Forward Induction 292 Appendix A: Finite and Infinite Horizon Bilaleral Bargaining 296 Appendix B: Exlensive Form Trembling-Hand Perfect Nash Equilibrium Exercises 299 30 I PART THREE: MARKET EQUILIBRIUM AND MARKET FAILURE Chapter 10.D 12.B 9.D 10.C 10. Externalities and Public Goods I I.G 344 Chapter 11.A 12.E 350 Introduction 350 A Simple Bilateral Externality 351 Public Goods 359 Multilateral Externalities 364 Private Information and Second-Best Solutions Appcndix A: Nonconvexitics and the Theory of Externalities Exercises 378 Chapter 12.C 12.F 12.F 10. Market Power 12. Backward Induction. The Positive Theory or Equilibrium 17. Equilibrium and Its Basic Welfare Properties 545 545 16.D Exercises 1 467 473 .C Allocations 578 578 Introduction Equilibrium: Definitions and Basic Equations 584 Existence of Walrasian Equilibrium 579 549 551 573 504 .A 15.C : 5.A 17.C 13. Adverse Selection.A Introduction 546 16. The Principal-Agent Problem 14. One-Produce r Economy 529 The 2 x 2 Production Model General Versus Partial Equilibrium Theory Exercises 525 538 540 ·:.A : 4.:1pter 16.: 'RT FOUR: GENERAL EQUILIBR IUM 511 515 11apter 15. and Screening 436 436 Introduction Informationa l Asymmetries and Adverse Selection 450 Signaling 460 Screening Appendix A: Reasonable-Beliefs Refinements in Signaling Games l .G Some Applications \ppendix A: Technical Properties 575 faercises or the Set or Feasible l1apter 17.B 17.D J S.C 14.1pter 14.D 437 477 477 Introduction 478 Hidden Actions (Moral Hazard) 488 Hidden Information (and Monopolistic Screening) Hidden Actions and Hidden Information: Hybrid Models 501 502 Appendix A: Multiple Effort Levels in the Hidden Action Model the Principal-Agen t Problem with Hidden Information ·\ppcndix B: A Formal Solution 507 1 ~xcrcises or . Signaling.E 515 Introduction 515 Pure Exchange: The Edgeworth Box The One-Consum er.E Pareto Optimality and Social Welfare Optima 561 l 6.B : 4.C The First Fundamental Theorem or Welfare Economics 16.B 5.B The Basic Model and Definitions 16. F First-Order Conditions for Pareto Optimality 566 16.B 13.I NT S ~·apter 13.lA l 3.D The Second Fundamental Theorem of Welfare Economics 558 16. General Equilibrium Theory: Some Examples 15. Equilibri um and Time 20. Interest Rates.D 18.A I 9.G 19.B 19.I 660 673 Chapter 19.B 20.B 18.D 20. General Equilibri um Under Uncertai nty 19.H 17.A 20. Some Foundati ons for Competit ive Equilibri a 18.F 17. and Golden Rules Dynamic s Equilibri um: Overlapp ing Remarks on Exercises 713 725 Chapter 20.E 20.E 19.E 670 687 687 Introduc tion A Market Economy with Continge nt Commod ities: Descripti on 691 Arrow-D ebreu Equilibri um 694 Sequentia l Trade 688 699 Asset Markets 709 Incomple te Markets ty Firm Behavior in General Equilibri um Models Under Uncertain 716 Imperfec t Informat ion Exercises 732 732 Introduc tion 733 lntertemp oral Utility 736 lntertcmp oral Producti on and Efficiency 743 Equilibri um: The One-Con sumer Case Stationar y Paths.H 20.G 20.C 0 NT ENT S 17.H 632 652 652 Introduc tion 652 Core and Equilibri a Noncoop crative Foundat ions of Walrasia n Equilibria 665 The Limits lo Redistrib ution Equilibri um and the Margina l Productiv ity Principle Appendix A: Cooperati ve Game Theory 684 Exercises 598 782 754 759 765 Several Consume rs 769 Generati ons Nonequi librium Dynamic s: Tatonnem ent and Learning 778 Xi .E 17.A 18.F 20.J 589 Local Uniquene ss and the Index Theorem breu Theorem antel-De chein-M Sonnens The Goes: Anything 606 Uniquene ss of Equilibri a 616 Compara tive Statics Analysis 620 Tatonnem ent Stability 627 Large Economi es and Nonconv exities 630 Appendix A: Character izing Equilibriu m through Welfare Equations Equilibrium Appendix B: A General Approach to the Existence of Walrasian 641 Exercises Chapter 18.G 17.D 19.F 19.D 17.C 18.C 19.C 20. J 956 M.F M.xii C 0 NTEN T6 787 PART FIVE: WELFARE ECONOMICS AND INCENTIVES Chapter 21.G M.M Linear Programming 969 M.B 22. Elements of Welfare Economics and Axiomatic Bargaining 22.0 M.C 23.C 21.A 21.C M.F 850 Chapter 23.E 22.N Dynamic Programming M.H Index 817 817 lntroduction 818 Utility Possibility Sets 825 Social Welfare Functions and Social Optima 831 Invariance Properties of Social Welfare Functions 838 Tile Axiomatic Bargaining Approach 846 C<>alitional Bargaining: The Shapley Value Exercises 23.C 22.E 789 789 Introduction A Special Case: Social Preferences over Two Alternatives 792 The General Case: Arrow's Impossibility Theorem 799 Some Possibility Results: Restricted Domains 807 Social Choice Functions Exercises 812 Chapter 22.0 22. Incentives and Mechanism Design 857 857 Introduction 858 Tile Mechanism Design Problem 869 Dominant Strategy Implementation 883 Bayesian Implementation 891 Participation Constraints 897 Optimal Bayesian Mechanisms 910 Appendix A: Implementation and Multiple Equilibria Appendix B: Implementation in Environments with Complete Information 918 Eitercises MATHEMATICAL APPENDIX 971 912 926 926 Matrix Notation for Derivatives 928 Homogeneous Functions and Euler's Formula 930 Concave and Quasiconcave Functions Matrices: Negative (Semi)Definiteness and Other Properties 940 The Implicit Function Theorem 943 Continuous Functions and Compact Sets 946 Convex Sets and Separating Hyperplanes 949 Correspondences 952 Fixed Point Theorems M.I 954 Unconstrained Maximization M.B M.B 23.A 23.F 790 935 .K Constrained Maximization 964 M.E 23.B 21.A M.A 22.D 23. Social Choice Theory 21.E M.0 21.L The Envelope Theorem 966 M. Andreu Mas-Colell and M ichacl Whinston assumed full responsibility for the project. as well as the implementati on of social choices in the presence of incomplete information about agents' preferences. the extension of the theory of individual decision making to situations in which several decision makers interact. Part 111 initiates the investigation of market equilibria. It also provides an introduction to the theory of individual choice under uncertainty. The project was first planned and begun by the three of us in the spring of 1990. Starting rrom these notes. in February 1992. Microeconom ic Tlreory (the book) follows exactly this outline. and asymmetric information. The original sources for much of the book's material arc the lecture notes that we have provided over the years to students in the first-year microeconom ic theory cou~se at Harvard. It discusses the possibilities for aggregation of individual preferences into social preferences both with and without interpersonal utility comparisons. The nonlcxicograp hic ordering of our names deserves some explanation. Pan I covers individual decision making. It opens with a general treatment of individual choice and proceeds to develop the classical theories of consumer and producer behavior. It is divided into five parls. From this point in time until the manuscript's completion in June 1994. The Organization of the Book Microeconom ic theory as a discipline begins by considering the behavior of individual agents and huilds from this foundation to a theory of aggregate economic outcomes. Part V studies welfare economics. a position that forced him to suspend his involvement in the project. With the conclusion of Jerry Green's service as Provost. arter early versions of most of the book's chapters had been drafted. Part II covers game theory. A Mathematica l Appendix provides an introduction to most of the more advanced mathematics used in the book (e.Preface Microeconomic Theory is intended to serve as the text for a first-year graduate course in microeconom ic theory. as are extensions or the theory to equilibrium under uncertainty and over time. we have tried to produce a text that covers in an accessible yet rigorous way the full range of topics taught in a typical first-year course. The positive and normative aspects of the theory are examined in detail. It then explores the possibilities for market failures in the presence of externalities. It begins with an introduction to competitive equilibrium and the fundamental theorems of welfare economics in the context of the Marshallian partial equilibrium model. Part IV substantially extends our previous study of compelitive markets to the general equilibrium context. Jerry Green was selected to serve as Provost of Harvard University. concave/conv ex xiii . the original three-person team was reunited for the review of galley and page proofs during the winter of 1994/1995. However.g. market power.. (We certainly have never taught all of it in any one year. they can be shifted easily among the parts to accommodate many other course sequences. is that this makes for a more abstract first semester. An inevitable consequence of this choice is that the book covers more topics than any single first-year course can discuss adequately. Ob\'iously. Wherever possible we give precise definitions and formal proofs of propositions. constrained optimization techniques. We have sought a style of presentation that is accessible. Our aim has been to assure coverage of most topics that instructors in a first-year graduate microeconomic theory course might want to teach. As a result. Some of these exercises also appear within the text of the chapters so that students can check their understanding along the way (almost all of these are level A exercises). some topics in each case). Each chapter offers many exercises. 1 The advantage of this alternative sequence is that the study of general equilibrium analysis more closely follows the study of individual behavior in competitive markets that is developed in Part I. fixed point theorems. etc. For example. oligopoly. some familiarity with linear algebra (although the use of vectors and matrices is introduced gradually in Part I). At the same time. and V in the Spring. A very natural alternative to this sequence (one used in a number of departments that we know of) might instead teach Parts I and IV in the Fall. and Parts II. Students also will find helpful some familiarity with microeconomics at the level of an intermediate undergraduate course. Teachin{J the Book The material in this book may be taught in many different sequences.) as well as references for further reading. yet also rigorous. some adjustment needs to be made by programs that opera1e on a quarter system. The disadvantage. .) Our hope is that the range of topics presented will allow instructors the freedom to emphasize those they find most important.PREFACE functions. I. ranging from easy to hard [graded from A {easiest) to C (hardest)] to help students master the material. The Style of the Book In choosing the content of Microeconomic Tl1eory we have tried to err on the side of inclusion. The mathematical prerequisites for use of the book are a basic knowledge of calculus. Typically we have taught Parts I-III in the Fall semester and Parts IV and V in the Spring (omitting. and the reason we have not used this sequence in our own course. Ill. Where we have considered a proof or topic either too difficult or too peripheral we have put it into smaller type to allow students to skip over it easily in a first reading. and asymmetric information after studying Part L The chapters have been written to be relatively self-contained. we have often opted to teach game theory on an "as needed" basis. and a grasp of the elementary aspects of probability. we accompany this analysis with extensive verbal discussion as well as with numerous examples to illustrate key concepts. our students have seemed happy to have the change of pace offered by game theory. A-B before studying oligopoly.A-D and 3.. 3. In particular. our use of mathematical notation is standard. Sections 9.E. the indirccl u1ili1y runction. and mechanism design (Chapter 23) together in a section of the course focusing on information economics. 2.. it has the same meaning as x Ty. A similar point applies to the product symbol n. For example. vectors are always treated mathematically as column vectors.A··D. One perhaps unfortunate consequence of this choice is that mathematical symbols sometimes appear slightly differently there than in the rest of the text.g. This and other aspects of matrix notation are reviewed in greater detail in Section M. Although we think there are good reasons to reverse this sequence as we have done in Part I.. we hope that no confusion will result. Chapter 7.A of the Mathematical Appendix. Some other possibilities include teaching the aggregation of preferences (Chapter 21) immediately after individual decision making and covering the principal-agent problem (Chapter 14). it has been common in many programs to teach the preferencebased theory of consumer demand before teaching the revealed preference.F and 3. signaling. 2 we have made sure that the material on demand can be covered in this more traditional way as well. and the choice·based theory gives you almost all the properties of demand that follow from assuming the existence of rational preferences. and Sections 9. discusses the properties of uncompensated and compensated demand functions.. even within each part. it is lllllc/1 easier LO introduce and derive many properties or demand in the choice-based theory than it is using the preference-based approach.. When taking the inner product of two (column) vectors x and y. The transpose of the (column) vector x is denoted by x T. Summation symbols {2_) are displayed in various ways throughout the text. Sometimes they arc written as n=l (usually only in displayed equations). or . Chapter 8.C-D before covering signaling). the sequence of topics can often be altered easily. 3 011 Mathemacica/ Notation For the most part. In addition. and the expenditure function u&ing Seclions 3. we typically write just I:.PREFACE breaking it up into segments that are discussed right before they are used (e. XV . we write x · y. but often to conserve space they appear as :[~'. and in the many cases in which no confusion exists about the upper and lower limit of the index in the summation. Perhaps the most important mathematical rule to keep straight regards matrix notation. 1 .D-l and 2. choice-based. To help highlight definitions and propositions we have chosen to display them in a different typeface than is used elsewhere in the text. one introduces the basics of the consumer's problem using Sections 2.. and screening (Chapter 13). and then studies revealed preference theory using Sections 2. even though they are often displayed within the wrilten text as rows to conserve space." theory. Put simply. To do this. adverse selection. With this warning.J (and Chapter I for a more general overview of the two approaches). Prajit Dutta. (When the expectation is over all of the arguments of the function we simply write E[J(x. finding errors in our proofs. while X and Y are sets]: Symbol Meaning x~y x. . and providing their support in hundreds of other ways. N. Chiaki Hara and Steve Tadelis have also given us extensive comments and corrections on the text itself. comments. Ariel Rubinstein. > y. Herb Addison.xvi p A£ FA c E Also described below are the meanings we attach to a few mathematical symbols whose use is somewhat less uniform in the literature [in this list. a number of current and former students have played a more formal role in the book's development.. Leslie Phillips or Oxford took our expression of appreciation for the look or the Feynman Lectures. and Billy Pizer were members of a team of first-year students that read our early drafts in the summer of 1992 and offered very helpful suggestions on how we could convey the material better. In addition. Martin Osborne. Our editor at Oxford. YN) are (column) vectors. y)]. and turned it into a book design that exceeded our highest expectations. and offered his support throughout the book's development. suggesting improvements in exposition. ••• . Gloria Ger rig kept careful track of our ever-increasing expenditures. Drew Fudenberg.[J(x... Phil Panet. Steve Goldman. with the assistance or Marc Nachman. The expected value of the function f( ·) over realizations of the random variable x. and led to many other substantive improvements in the text. and corrections. John Nachbar. Chiaki Hara. Ilya Segal.. Shira Lewin read the entire manuscript. y)] ~ y. and have suggested how they might be formulated properly when our first attempt to do so failed. for all n = 1. N.. . . Sergiu Hart. Emily Mechner.) Acknowledgments Many people have contributed to the development of this book. David Card. have checked that the book's many exercises could be solved. Betsy Carpenter and Claudia Napolilli provided expert secretarial support throughout the project. The book would undoubtedly have been better still had we managed to incorporate all of their ideas. Their comments at that early stage were instrumental in the refinement of the book into its current style. xN) and y = (y 1 . Eric Maskin.. . for all n = I. and Martin Weitzman offered numercus helpful suggestions. x = (x 1. Bengt Holmstrom. Dilip Abreu. The set {x:xeX but x¢ Y}. Doug Bernheim. Chiaki Hara. Ben Polak.. and Steve Tadelis. and even (indeed. serving as research assistants in various capacities. Many generations of first-year Harvard graduate students have helped us with their questions. copying material on very tight deadlines. helping to type some chapter drafts.. ••• . John Panzar.. weak set inclusion (x e X implies x E Y). Simon Grant.. and David Pearce all (bravely} test-taught a very early version of the manuscript during the 1991-92 academic year. often) correcting our grammar. Nick Palmer. was instrumental in developing the test teaching program that so helped us in the book's early stages. x. Alan Chesterton and the rest of the . x)) y XcY X\Y E. Our colleagues (and in some cases former students) Luis Corchon. Leo Hurwicz. These usually can be found in the references of the works we do list. The influence of many other individuals on the book. Dale Jorgenson. Good exercises are an enormously valuable resource. although more indirect.. we want to offer a special thanks to those who first excited us about the subject matter that appears here: Gerard Debreu.). Franklin Fisher.D. Steve Marglin.). Many interesting and important contributions have not been included. Many of the exercises that appear in the book have been conceived over the years by others.G.).W.D. We also thank the NSF and Sloan Foundation for their support of our research over the years. from whom we learned a great deal about microeconomics and its teaching. The Universitat Pompeu Fabra also offered its hospitality to Andreu Mas-Colell at numerous points during the book's development.p R £FA staff at Keyword Publishing Services did an absolutely superb job editing and producing the book on a very tight schedule. David Cass. A.-C. indeed. J. In addition. We have also had the good fortune lo teach the first-year graduate microeconomic theory course at Harvard in the years prior to writing this book with Ken Arrow.R. Of necessity we have been able to provide references in each chapter to only a limited number of sources.M. and Mike Spence. and Hugo Sonnenschein (A. Sanford Grossman. We have indicated our source for an exercise whenever we were aware of it. Their complete professionalism has been deeply appreciated. Ron Jones. Finally.M. most chapters include at least one reference to a general survey of their topic. Lionel McKenzie.R. MA March 1995 c E xvii . M..W. Marcel Richter. Emmanuel Drandakis. Peter Diamond. Cambridge. We thank the anonymous authors of many of the exercises that appear here. Roy Radner. the Center for Advanced Study in the Behavioral Sciences provided an ideal environment to Michael Whinston for completing the manuscript during the 1993/1994 academic year. Eric Maskin.G. has been no less important. both at Harvard and elsewhere. and Eric Maskin (M. The work of numerous scholars has contributed to our knowledge of the topics discussed in this book. and Edward Zabel (J.-C.