Advanced_Microeconomic_Theory_3e_by_JEHLE_and_RENY

PREFACE xv
PART I
ECONOMIC AGENTS 1
CHAPTER 1 CONSUMER THEORY 3
1.1 Primitive Notions 3
1.2 Preferences and Utility 4
1.2.1 Preference Relations 5
1.2.2 The Utility Function 13
1.3 The Consumer’s Problem 19
1.4 Indirect Utility and Expenditure 28
1.4.1 The Indirect Utility Function 28
1.4.2 The Expenditure Function 33
1.4.3 Relations Between the Two 41
1.5 Properties of Consumer Demand 48
1.5.1 Relative Prices and Real Income 48
1.5.2 Income and Substitution Effects 50
1.5.3 Some Elasticity Relations 59
1.6 Exercises 63
CHAPTER 2 TOPICS IN CONSUMER THEORY 73
2.1 Duality: A Closer Look 73
2.1.1 Expenditure and Consumer Preferences 73
2.1.2 Convexity and Monotonicity 78
2.1.3 Indirect Utility and Consumer Preferences 81
2.2 Integrability 85
2.3 Revealed Preference 91
2.4 Uncertainty 97
2.4.1 Preferences 98
2.4.2 Von Neumann-Morgenstern Utility 102
2.4.3 Risk Aversion 110
2.5 Exercises 118
CHAPTER 3 THEORY OF THE FIRM 125
3.1 Primitive Notions 125
3.2 Production 126
3.2.1 Returns to Scale and Varying Proportions 132
3.3 Cost 135
3.4 Duality in Production 143
3.5 The Competitive Firm 145
3.5.1 Profit Maximisation 145
3.5.2 The Profit Function 147
3.6 Exercises 154
PART II
MARKETS AND WELFARE 163
CHAPTER 4 PARTIAL EQUILIBRIUM 165
4.1 Perfect Competition 165
4.2 Imperfect Competition 170
4.2.1 Cournot Oligopoly 174
4.2.2 Bertrand Oligopoly 175
4.2.3 Monopolistic Competition 177
4.3 Equilibrium and Welfare 179
4.3.1 Price and Individual Welfare 179
4.3.2 Efficiency of the Competitive Outcome 183
4.3.3 Efficiency and Total Surplus Maximisation 186
4.4 Exercises 188
CHAPTER 5 GENERAL EQUILIBRIUM 195
5.1 Equilibrium in Exchange 196
5.2 Equilibrium in Competitive Market
Systems 201
5.2.1 Existence of Equilibrium 203
5.2.2 Efficiency 212
5.3 Equilibrium in Production 220
5.3.1 Producers 220
5.3.2 Consumers 223
5.3.3 Equilibrium 225
5.3.4 Welfare 232
5.4 Contingent Plans 236
5.4.1 Time 236
5.4.2 Uncertainty 236
5.4.3 Walrasian Equilibrium with Contingent
Commodities 237
5.5 Core and Equilibria 239
5.5.1 Replica Economies 240
5.6 Exercises 251
CHAPTER 6 SOCIAL CHOICE AND WELFARE 267
6.1 The Nature of the Problem 267
6.2 Social Choice and Arrow’s Theorem 269
6.2.1 A Diagrammatic Proof 274
6.3 Measurability, Comparability, and Some
Possibilities 279
6.3.1 The Rawlsian Form 282
6.3.2 The Utilitarian Form 284
6.3.3 Flexible Forms 285
6.4 Justice 288
6.5 Social Choice and the
Gibbard-Satterthwaite Theorem 290
6.6 Exercises 296
PART III
STRATEGIC BEHAVIOUR 303
CHAPTER 7 GAME THEORY 305
7.1 Strategic Decision Making 305
7.2 Strategic Form Games 307
7.2.1 Dominant Strategies 308
7.2.2 Nash Equilibrium 311
7.2.3 Incomplete Information 319
7.3 Extensive Form Games 325
7.3.1 Game Trees: A Diagrammatic Representation 328
7.3.2 An Informal Analysis of Take-Away 330
7.3.3 Extensive Form Game Strategies 331
7.3.4 Strategies and Payoffs 332
7.3.5 Games of Perfect Information and Backward
Induction Strategies 333
7.3.6 Games of Imperfect Information and Subgame
Perfect Equilibrium 337
7.3.7 Sequential Equilibrium 347
7.4 Exercises 364
CHAPTER 8 INFORMATION ECONOMICS 379
8.1 Adverse Selection 380
8.1.1 Information and the Efficiency of Market Outcomes 380
8.1.2 Signalling 385
8.1.3 Screening 404
8.2 Moral Hazard and the Principal–Agent
Problem 413
8.2.1 Symmetric Information 414
8.2.2 Asymmetric Information 416
8.3 Information and Market Performance 420
8.4 Exercises 421
CHAPTER 9 AUCTIONS AND MECHANISM DESIGN 427
9.1 The Four Standard Auctions 427
9.2 The Independent Private Values
Model 428
9.2.1 Bidding Behaviour in a First-Price, Sealed-Bid
Auction 429
9.2.2 Bidding Behaviour in a Dutch Auction 432
9.2.3 Bidding Behaviour in a Second-Price, Sealed-Bid
Auction 433
9.2.4 Bidding Behaviour in an English Auction 434
9.2.5 Revenue Comparisons 435
9.3 The Revenue Equivalence Theorem 437
9.3.1 Incentive-Compatible Direct Selling Mechanisms:
A Characterisation 441
9.3.2 Efficiency 444
9.4 Designing a Revenue Maximising
Mechanism 444
9.4.1 The Revelation Principle 444
9.4.2 Individual Rationality 445
9.4.3 An Optimal Selling Mechanism 446
9.4.4 A Closer Look at the Optimal Selling Mechanism 451
9.4.5 Efficiency, Symmetry, and Comparison to the Four
Standard Auctions 453
9.5 Designing Allocatively Efficient
Mechanisms 455
9.5.1 Quasi-Linear Utility and Private Values 456
9.5.2 Ex Post Pareto Efficiency 458
9.5.3 Direct Mechanisms, Incentive Compatibility
and the Revelation Principle 458
9.5.4 The Vickrey-Clarke-Groves Mechanism 461
9.5.5 Achieving a Balanced Budget: Expected
Externality Mechanisms 466
9.5.6 Property Rights, Outside Options, and Individual
Rationality Constraints 469
9.5.7 The IR-VCG Mechanism: Sufficiency of
Expected Surplus 472
9.5.8 The Necessity of IR-VCG Expected Surplus 478
9.6 Exercises 484
MATHEMATICAL APPENDICES 493
CHAPTER A1 SETS AND MAPPINGS 495
A1.1 Elements of Logic 495
A1.1.1 Necessity and Sufficiency 495
A1.1.2 Theorems and Proofs 496
A1.2 Elements of Set Theory 497
A1.2.1 Notation and Basic Concepts 497
A1.2.2 Convex Sets 499
A1.2.3 Relations and Functions 503
A1.3 A Little Topology 505
A1.3.1 Continuity 515
A1.3.2 Some Existence Theorems 521
A1.4 Real-Valued Functions 529
A1.4.1 Related Sets 530
A1.4.2 Concave Functions 533
A1.4.3 Quasiconcave Functions 538
A1.4.4 Convex and Quasiconvex Functions 542
A1.5 Exercises 546
CHAPTER A2 CALCULUS AND OPTIMISATION 551
A2.1 Calculus 551
A2.1.1 Functions of a Single Variable 551
A2.1.2 Functions of Several Variables 553
A2.1.3 Homogeneous Functions 561
A2.2 Optimisation 566
A2.2.1 Real-Valued Functions of Several Variables 567
A2.2.2 Second-Order Conditions 570
A2.3 Constrained Optimisation 577
A2.3.1 Equality Constraints 577
A2.3.2 Lagrange’s Method 579
A2.3.3 Geometric Interpretation 584
A2.3.4 Second-Order Conditions 588
A2.3.5 Inequality Constraints 591
A2.3.6 Kuhn-Tucker Conditions 595
A2.4 Optimality Theorems 601
A2.5 Separation Theorems 607
A2.6 Exercises 611
LIST OF THEOREMS 619
LIST OF DEFINITIONS 625
HINTS AND ANSWERS 631
REFERENCES 641
INDEX 645