Table Of Content.,
Advanced
Microeconomic
Theory
I SECOND EDITION'
~:~ .: .'
..
Advanced Microeconomic Theory
Geoffrey A. Jehle and Philip J. Reoy
Executive Editor: Denise Clinton
Acquisitions Editor: Victoria Wameck
Managing Editor: James Rigney
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Library of Congress Caialoging-in-Publication Data
Jehle, Geoffrey Alexander.
Adva.nced microeconomic theory I Geoffrey A. Jehle, Philip I . Reny. .,
p. em. - (Tile Addison-Wesley series in economics)
Includes bibliographical references and index.
ISBN 0-321-07916-7
1. Microeconomics. 2. Economics, Mathematical. I. Reny, Philip J. II. 1itle.
m. Series.
HBI72. J44 2000
338.5-dc21 00-029988
Copyright 0 2001 Geoffrey A. Jehle and Philip J. Reny
All rights reserved. No past of this publication may be reproduced, stored in a retrieval
system, or transmitted, in any fonn or by any means, electronic, mechanical, photocopying,
recording. or otherwise, without the prior written permission of the publisher. Printed in the
United States of America.
910. ll 12~0607<X!
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To Rana and Kamran
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To Dianne, lisa, and Elizabeth
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CONTENTS
PR£fAa xi
PART I
ECONOMIC AGENTS
CHAPTER 1 CONSUMO tHEORY 3
1.1 Primiti¥e Notions 3
1.2 PI efetec ICft and Utility 5
1.2.1 Preference Relations s
1.2.2 The Utility Function 13
1.3 The Consumeio's Problem 19
1.4 Indirect Utility and Expenditure 27
1.4.1 The lndired Utility Function 27
1.4.2 The Expenditure Function 33
1.4.3 Relations Between the Two 40
1.5 Properties of Consumer Demond 46
l.S.t Relative Prices and Real Income 47
1.5.2 Income and Substitution Effects 48
1.5.3 Some Elasticity Relations 57
1.6 Exercises 60
CONTENTS
CHAPTER 2 TOPICS IN CONSUMER THEORY 69
2.1 Duality: A Closer l..ooll 69
2.1.1 Expenditure and Consumer Preferences 69
2
2.1.32 CInodnirveecxti tUy tailnitdy Manodn Cotoonnsiucimtye r Preferences 746 .•~.
.
2.2 Integrability 80 '!
2.3 Revealed Preference 86
2.4 Uncertainty 92
2.4.1 Preferences 93
2.4.2 Von Neumann-Morgenstern Utility 96
2.4.3 Risk Aversion 104
2.5 Exercises 112 .
•
CHAPTER 3 THEORY OF THE FIRM 117
3.1 Primitive Notions 117
3.2 Production 118
3.2. \ Returm to Scale and Varying Proportions 124
3.3 Cost 126
3• . ( Duality in Produdion 134
3.5 The Competitive Firm 135
3.5.1 Profit Maximization 136
3.5.2 The Profit Function 138
3.6 Exercises 145
PART II
MARKETS AND WElfARE 151
CHAmR4 PARTIAL EQUIUBRIUM 153
4.1 Perfect Competition 153
.4? lm~ Comoetition 158
~.-Vi-iTENTS IX
..
4.2.2 Demand Oligopoly 163
4.2.3 Monopolistic ~~J:e:i:i :>n 164
4.3 Eq«.~ilibrium ~nd Welfare 165
4.3. 1 Price and Individual Welfare 166
4.3.2 Efficiency of the Competitive 0\dcome 171
4.3.3 Efficiency aod Total Surplus Muimization 173
4.4 Exercises 175
CHAPTER 5 GENERAL EQUtlJBRIUM 181
5.1 Equ~brium in Exchange 181
5.2 EiquiNbrium in CompetiliYe Market
Sylleml 187
5.2.1 Existence of Equili~um 188
5.2.2 Efficiency 198
5.3 Equilibrium in Prodlldion 205
5.3.1 Producers 205
5.3.2 COII$Umers 208
5.3.3 Equilibrium 210
5.3.4 Welfare 217
5.4 ~ore and Equilibria 220
5.4.1 Replica Economies 221
5.5 Exercises 232
CHAPTER6 SOCIAL CHOICE AND WBIARE 239
6.1 The Nature of the Problem . 239
6.2 Social Choice and Arraw's 1heor.n 240
6.2.1 A Diagrammatic Proof 245
6.3 Measurability, Comparob~ity, and Some
Possibililie• 250
6.3.1 The Rawlsian Form 252
6.3.2 The Utilitarian Fom1 255
6.3.3 Flexible Fonn~ 256
6.4 Justice 258
X · ;;vi.;j'CN'tj
PARTUI
STRATEGIC BEHAV10R 265
OIAPTER 7 GAME THEORY 267
7.1 Stratlgic Decision Making 267
7.2 Strategic Fonn Games 269
7.2.1 Dominant Strategies 270
7.2.2 Nash Equilibrium 273
7.2.3 Incomplete Information 280
7.3 bten5i¥e Fonn Game5 285
7.3.1 Game Trees: A Diagrammatic
Representation 288
7.3.2 An lnfonnal Analysis of Take. Away 290
7.3.3 Extensive Form Game Strategies 291
7.3.4 Scrategies and Payoffs 292
7.3.5 Games of Perfect Infonnation and Backward
Induction Strategies 293
7.3.6 Games of Imperfect Information and Subgame
Perfect EquiJjbrium 297
7.3.7 Sequential Equilibrium 306
7.4 ExerciMS 322
CHAPTER 8 INFORMATION ECONOMICS 329
8.1 Adwne Selection 330
8.1.1 Information and tbe Efficiency of Matket
Outcomes 330
8.1.2 Signaling 335
8.1.3 Screening 353
8.2 Moral Hazard one! the Principal
Agent Problem 362
8.2.1 Symmetric Information 363
8.2.2 Asymmetric Information 366
8.3 Information one! Moritet Pttfonnance 369
8.4 Exercises 370
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CHAPTER 9 AUCT10NS AND MfCHANISM DESIGN 373
. ,
9.1 The fOUl' Standard AuctioN 373
9.2 The lndepetldent Priwte V<llues Model 374
9.2.1 Bidding Behavior in a First-Pri"'· Seai<»Bid
AUCiion 375
9.2.2 Bidding Behavior in a Dutch Auction 378
9.2.3 Bidding Behavior in a Second-Price, Sealed· Bid
Auction 378
9.2.4 Bidding Behavior in an English Auction 379
9.2.5 Revenue Comparisons 380
9.3 The Rwenue EquiYalence 1heorem 383
9.3.1 Incentive-Compatible Di= t SeUios Mechanisms 385
9.3.2 Efficiency 389
9.4 Reftnue-Maximimtion: All Applic;ation
of Mecha lism DeSign 389
9.4.1 Individual Rationality 390
9.4.2 An Optimal Selling Mechanism 390
9.4.3 A Closer Loolt at 1be Optimal SeUing Mechanism 395
9.4.4 Efficiency, SymmetJy. and Comparison to the
Four Standard Auctions 397
9.5 Exercises 399
MATHEMATlCAL APPENDIX 405
CHAPTER Al SETS AND MAPPINGS 407
A1.1 Elements of Logic 407
Al.l.l Necessity and Sufficiency 407
Al.1.2 lbeorems and Proofs 408
A1 .2 Elements of Set Theory 409
Al.2.1 Notation and Basic Concepts 409
Al.2.2 Convex Sel8 411
Al.2.3 Relations and Functions 41S
A1.3 A little Topology 417
Al.3.1 Continuity 426
Al.3.2 Some Existence lbeorems 431
xii · -·-curoltNiS
AU Reai·Valuecl Functions .436
A1.4.1 Related Sets 437
A1.4.2 Concave Functions 441
A1.4.3 Quasiconcave Functions 445
Al.4.4 Convex and Quasiconvex Functions 449
AI.S Exetmes 453
CHAPTER A2 CALCULUS AND OPTlMIZATION 459
A2.1 Calculus 459
A2.1.1 Functions of a Single Variable 459
A2.1.2 Functions of Several Variables 461
A2.1.3 Homogeneoos Functions 469
A2.2 Optimimtion 473
A2.2.1 Real· Valued Function& of Several Variables 41S
A2.2.2 Second-Order Conditions 478
A2.3 Constrained Optimization 484
A2.3.1 Equality Constraints 485
A2.3.2 Lagrange's Method 486
A2.3.3 Oeomeuic lnlerpretatioo 491
A2.3.4 Second-Order Conditions 494
A2.3.5 Inequality Constraints 498
A2.3.6 Kuhn·TIK:ker Conditions SOl
A2.4 Volue functians 504
A2.5 Exercises 509
UST OF THEOREMS 513
UST OF DEANITIONS 519
HINTS AND ANSWERS 523
REFERENCES 531
t4DEX 535
