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Lecture Notes on Microeconomic Theory pdf download
Shubham Goyal

Lecture Notes on Microeconomic Theory pdf download

Shubham Goyal | 08-Jul-2016 |
Microeconomic Theory , Preliminaries on Modern Economics and Mathematics , Individual Decision Making , Production Theory , Choice Under Uncertainty , Strategic Behavior and Markets , Game Theory , Theory of the Market , General Equilibrium Theory and Social Welfare , Normative Theory of Equilibrium: Its Welfare Properties , Positive Theory of Equilibrium: Existence , Uniqueness and Stability , Economic Core , Fair Allocations and Social Choice Theory , General Equilibrium Under Uncertainty , Externalities and Public Goods , Externalities , Public Goods , Information , Incentives , Mechanism Design and Contract Theory , General Mechanism Design: Contracts with Multi-Agents , Dynamic Mechanism Design ,

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Contents for Microeconomic Theory
1 Preliminaries on Modern Economics and Mathematics 1
1.1 Nature of Modern Economics . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Modern Economics and Economic Theory . . . . . . . . . . . . . . 1
1.1.2 Key Assumptions and Desired Properties Commonly Used Economics 3
1.1.3 The Basic Analytical Framework of Modern Economics . . . . . . . 4
1.1.4 Methodologies for Studying Modern Economics . . . . . . . . . . . 6
1.1.5 Roles, Generality, and Limitation of Economic Theory . . . . . . . 8
1.1.6 Roles of Mathematics in Modern Economics . . . . . . . . . . . . . 10
1.1.7 Conversion between Economic and Mathematical Languages . . . . 11
1.1.8 Distinguish between Necessary and Sufficient Conditions as well
Normative and Positive Statements . . . . . . . . . . . . . . . . . . 11
1.2 Language and Methods of Mathematics . . . . . . . . . . . . . . . . . . . . 12
1.2.1 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.2 Separating Hyperplane Theorem . . . . . . . . . . . . . . . . . . . . 14
1.2.3 Concave and Convex Functions . . . . . . . . . . . . . . . . . . . . 14
1.2.4 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2.5 The Envelope Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.2.6 Point-to-Set Mappings . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.2.7 Continuity of a Maximum . . . . . . . . . . . . . . . . . . . . . . . 25
1.2.8 Fixed Point Theorems . . . . . . . . . . . . . . . . . . . . . . . . . 26
I Individual Decision Making 30
2 Consumer Theory 32
i
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2 Consumption Set and Budget Constraint . . . . . . . . . . . . . . . . . . . 33
2.2.1 Consumption Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2.2 Budget Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Preferences and Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.3.1 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.3.2 The Utility Function . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.4 Utility Maximization and Optimal Choice . . . . . . . . . . . . . . . . . . 45
2.4.1 Consumer Behavior: Utility Maximization . . . . . . . . . . . . . . 45
2.4.2 Consumer’s Optimal Choice . . . . . . . . . . . . . . . . . . . . . . 45
2.4.3 Consumer’s First Order-Conditions . . . . . . . . . . . . . . . . . . 46
2.4.4 Sufficiency of Consumer’s First-Order Conditions . . . . . . . . . . 49
2.5 Indirect Utility, and Expenditure, and Money Metric Utility Functions . . 52
2.5.1 The Indirect Utility Function . . . . . . . . . . . . . . . . . . . . . 52
2.5.2 The Expenditure Function and Hicksian Demand . . . . . . . . . . 54
2.5.3 The Money Metric Utility Functions . . . . . . . . . . . . . . . . . 57
2.5.4 Some Important Identities . . . . . . . . . . . . . . . . . . . . . . . 60
2.6 Duality Between Direct and Indirect Utility . . . . . . . . . . . . . . . . . 64
2.7 Properties of Consumer Demand . . . . . . . . . . . . . . . . . . . . . . . 66
2.7.1 Income Changes and Consumption Choice . . . . . . . . . . . . . . 66
2.7.2 Price Changes and Consumption Choice . . . . . . . . . . . . . . . 66
2.7.3 Income-Substitution Effect: The Slutsky Equation . . . . . . . . . . 67
2.7.4 Continuity and Differentiability of Demand Functions . . . . . . . . 70
2.7.5 Inverse Demand Functions . . . . . . . . . . . . . . . . . . . . . . . 72
2.8 The Integrability Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.9 Revealed Preference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2.9.1 Axioms of Revealed Preferences . . . . . . . . . . . . . . . . . . . . 76
2.9.2 Characterization of Revealed Preference Maximization . . . . . . . 78
2.10 Recoverability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.11 Topics in Demand Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 82
2.11.1 Endowments in the Budget Constraint . . . . . . . . . . . . . . . . 82
ii
2.11.2 Income-Leisure Choice Model . . . . . . . . . . . . . . . . . . . . . 83
2.11.3 Homothetic Utility Functions . . . . . . . . . . . . . . . . . . . . . 84
2.11.4 Aggregating Across Goods . . . . . . . . . . . . . . . . . . . . . . . 84
2.11.5 Aggregating Across Consumers . . . . . . . . . . . . . . . . . . . . 90
3 Production Theory 95
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.2 Production Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.2.1 Measurement of Inputs and Outputs . . . . . . . . . . . . . . . . . 96
3.2.2 Specification of Technology . . . . . . . . . . . . . . . . . . . . . . . 96
3.2.3 Common Properties of Production Sets . . . . . . . . . . . . . . . . 100
3.2.4 Returns to Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.2.5 The Marginal Rate of Technical Substitution . . . . . . . . . . . . . 103
3.2.6 The Elasticity of Substitution . . . . . . . . . . . . . . . . . . . . . 104
3.3 Profit Maximization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.3.1 Producer Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.3.2 Producer’s Optimal Choice . . . . . . . . . . . . . . . . . . . . . . . 107
3.3.3 Producer’s First-Order Conditions . . . . . . . . . . . . . . . . . . . 108
3.3.4 Sufficiency of Producer’s First-Order Condition . . . . . . . . . . . 109
3.3.5 Properties of Net Supply Functions . . . . . . . . . . . . . . . . . . 111
3.3.6 Weak Axiom of Profit Maximization . . . . . . . . . . . . . . . . . 112
3.3.7 Recoverability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.4 Profit Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.4.1 Properties of the Profit Function . . . . . . . . . . . . . . . . . . . 116
3.4.2 Deriving Net Supply Functions from Profit Function . . . . . . . . 117
3.5 Cost Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
3.5.1 First-Order Conditions of Cost Minimization . . . . . . . . . . . . . 119
3.5.2 Sufficiency of First-Order Conditions for Cost Minimization . . . . 120
3.6 Cost Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
3.6.1 Properties of Cost Functions . . . . . . . . . . . . . . . . . . . . . . 124
3.6.2 Properties of Conditional Input Demand . . . . . . . . . . . . . . . 125
3.6.3 Average and Marginal Costs . . . . . . . . . . . . . . . . . . . . . . 126
iii
3.6.4 The Geometry of Costs . . . . . . . . . . . . . . . . . . . . . . . . . 128
3.6.5 Long-Run and Short-Run Cost Curves . . . . . . . . . . . . . . . . 129
3.7 Duality in Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
3.7.1 Recovering a Production Set from a Cost Function . . . . . . . . . 131
3.7.2 Characterization of Cost Functions . . . . . . . . . . . . . . . . . . 135
3.7.3 The Integrability for Cost Functions . . . . . . . . . . . . . . . . . 136
4 Choice Under Uncertainty 139
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.2 Expected Utility Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
4.2.1 Lotteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
4.2.2 Expected Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.2.3 Uniqueness of the Expected Utility Function . . . . . . . . . . . . . 144
4.2.4 Other Notations for Expected Utility . . . . . . . . . . . . . . . . . 145
4.3 Risk aversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.3.1 Absolute Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.3.2 Global Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . . . 148
4.3.3 Relative Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . . 152
4.4 State Dependent Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
4.5 Subjective Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . . 154
II Strategic Behavior and Markets 159
5 Game Theory 161
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
5.2 Description of a game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
5.2.1 Strategic Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
5.3 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
5.3.1 Mixed Strategies and Pure Strategies . . . . . . . . . . . . . . . . . 166
5.3.2 Nash equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
5.3.3 Dominant strategies . . . . . . . . . . . . . . . . . . . . . . . . . . 171
5.4 Repeated games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
iv
5.5 Refinements of Nash equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 174
5.5.1 Elimination of dominated strategies . . . . . . . . . . . . . . . . . . 174
5.5.2 Sequential Games and Subgame Perfect Equilibrium . . . . . . . . . 175
5.5.3 Repeated games and subgame perfection . . . . . . . . . . . . . . . 180
5.6 Games with incomplete information . . . . . . . . . . . . . . . . . . . . . . 181
5.6.1 Bayes-Nash Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 181
5.6.2 Discussion of Bayesian-Nash equilibrium . . . . . . . . . . . . . . . 184
6 Theory of the Market 186
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
6.2 The Role of Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
6.3 Perfect Competition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
6.3.1 Assumptions on Competitive Market . . . . . . . . . . . . . . . . . 188
6.3.2 The Competitive Firm . . . . . . . . . . . . . . . . . . . . . . . . . 188
6.3.3 The Competitive Firm’s Short-Run Supply Function . . . . . . . . 188
6.3.4 Partial Market Equilibrium . . . . . . . . . . . . . . . . . . . . . . 190
6.3.5 Competitive in the Long Run . . . . . . . . . . . . . . . . . . . . . 192
6.4 Pure Monopoly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
6.4.1 Profit Maximization Problem of Monopolist . . . . . . . . . . . . . 193
6.4.2 Inefficiency of Monopoly . . . . . . . . . . . . . . . . . . . . . . . . 195
6.4.3 Monopoly in the Long Run . . . . . . . . . . . . . . . . . . . . . . 196
6.5 Monopolistic Competition . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
6.6 Oligopoly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
6.6.1 Cournot Oligopoly . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
6.6.2 Stackelberg Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
6.6.3 Bertrand Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
6.6.4 Collusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
6.7 Monopsony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
III General Equilibrium Theory and Social Welfare 207
7 Positive Theory of Equilibrium: Existence, Uniqueness, and Stability 209
v
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
7.2 The Structure of General Equilibrium Model . . . . . . . . . . . . . . . . . 211
7.2.1 Economic Environments . . . . . . . . . . . . . . . . . . . . . . . . 211
7.2.2 Institutional Arrangement: Private Market Mechanism . . . . . . . 213
7.2.3 Individual Behavior Assumptions: . . . . . . . . . . . . . . . . . . . 214
7.2.4 Competitive Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 214
7.3 Some Examples of GE Models: Graphical Treatment . . . . . . . . . . . . 216
7.3.1 Pure Exchange Economies . . . . . . . . . . . . . . . . . . . . . . . 216
7.3.2 The One-Consumer and One Producer Economy . . . . . . . . . . . 222
7.4 The Existence of Competitive Equilibrium . . . . . . . . . . . . . . . . . . 225
7.4.1 The Existence of CE for Aggregate Excess Demand Functions . . . 226
7.4.2 The Existence of CE for Aggregate Excess Demand Correspondences245
7.4.3 The Existence of CE for General Production Economies . . . . . . . 247
7.5 The Uniqueness of Competitive Equilibria . . . . . . . . . . . . . . . . . . 247
7.6 Stability of Competitive Equilibrium . . . . . . . . . . . . . . . . . . . . . 251
7.7 Abstract Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
7.7.1 Equilibrium in Abstract Economy . . . . . . . . . . . . . . . . . . . 257
7.7.2 The Existence of Equilibrium for General Preferences . . . . . . . . 259
8 Normative Theory of Equilibrium: Its Welfare Properties 264
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
8.2 Pareto Efficiency of Allocation . . . . . . . . . . . . . . . . . . . . . . . . . 265
8.3 The First Fundamental Theorem of Welfare Economics . . . . . . . . . . . 271
8.4 Calculations of Pareto Optimum by First-Order Conditions . . . . . . . . . 273
8.4.1 Exchange Economies . . . . . . . . . . . . . . . . . . . . . . . . . . 274
8.4.2 Production Economies . . . . . . . . . . . . . . . . . . . . . . . . . 275
8.5 The Second Fundamental Theorem of Welfare Economics . . . . . . . . . . 276
8.6 Non-Convex Production Technologies and Marginal Cost Pricing . . . . . . 282
8.7 Pareto Optimality and Social Welfare Maximization . . . . . . . . . . . . . 285
8.7.1 Social Welfare Maximization for Exchange Economies . . . . . . . . 286
8.7.2 Welfare Maximization in Production Economy . . . . . . . . . . . . 287
8.8 Political Overtones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
vi
9 Economic Core, Fair Allocations, and Social Choice Theory 292
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
9.2 The Core of Exchange Economies . . . . . . . . . . . . . . . . . . . . . . . 293
9.3 Fairness of Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
9.4 Social Choice Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
9.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
9.4.2 Basic Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
9.4.3 Arrow’s Impossibility Theorem . . . . . . . . . . . . . . . . . . . . 306
9.4.4 Some Positive Result: Restricted Domain . . . . . . . . . . . . . . . 309
9.4.5 Gibbard-Satterthwaite Impossibility Theorem . . . . . . . . . . . . 311
10 General Equilibrium Under Uncertainty 318
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
10.2 A Market Economy with Contingent Commodities . . . . . . . . . . . . . . 319
10.3 Arrow-Debreu Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
10.4 Sequential Trade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
10.5 Incomplete Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
IV Externalities and Public Goods 336
11 Externalities 339
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
11.2 Consumption Externalities . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
11.3 Production Externality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
11.4 Solutions to Externalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
11.4.1 Pigovian Tax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
11.4.2 Coase’ Voluntary Negotiation and Enforceable Property Rights Approach
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
11.4.3 Missing Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
11.4.4 The Compensation Mechanism . . . . . . . . . . . . . . . . . . . . 362
12 Public Goods 367
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
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12.2 Notations and Basic Settings . . . . . . . . . . . . . . . . . . . . . . . . . . 367
12.3 Discrete Public Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
12.3.1 Efficient Provision of Public Goods . . . . . . . . . . . . . . . . . . 369
12.3.2 Free-Rider Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
12.3.3 Voting for a Discrete Public Good . . . . . . . . . . . . . . . . . . . 371
12.4 Continuous Public Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
12.4.1 Efficient Provision of Public Goods . . . . . . . . . . . . . . . . . . 372
12.4.2 Lindahl Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . 374
12.4.3 Free-Rider Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 378
V Information, Incentives, Mechanism Design, and Contract
Theory 382
13 Optimal Mechanism Design: Contracts with One-Agent and Hidden
Information 387
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
13.2 Basic Settings of Principal-Agent Model with Adverse Selection . . . . . . 389
13.2.1 Economic Environment (Technology, Preferences, and Information) 389
13.2.2 Contracting Variables: Outcomes . . . . . . . . . . . . . . . . . . . 389
13.2.3 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
13.3 The Complete Information Optimal Contract(Benchmark Case) . . . . . . 390
13.3.1 First-Best Production Levels . . . . . . . . . . . . . . . . . . . . . . 390
13.3.2 Implementation of the First-Best . . . . . . . . . . . . . . . . . . . 391
13.3.3 A Graphical Representation of the Complete Information Optimal
Contract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
13.4 Incentive Feasible Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . 393
13.4.1 Incentive Compatibility and Participation . . . . . . . . . . . . . . 393
13.4.2 Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
13.4.3 Monotonicity Constraints . . . . . . . . . . . . . . . . . . . . . . . 395
13.5 Information Rents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
13.6 The Optimization Program of the Principal . . . . . . . . . . . . . . . . . 396
13.7 The Rent Extraction-Efficiency Trade-Off . . . . . . . . . . . . . . . . . . . 397
viii
13.7.1 The Optimal Contract Under Asymmetric Information . . . . . . . 397
13.7.2 A Graphical Representation of the Second-Best Outcome . . . . . . 400
13.7.3 Shutdown Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
13.8 The Theory of the Firm Under Asymmetric Information . . . . . . . . . . 402
13.9 Asymmetric Information and Marginal Cost Pricing . . . . . . . . . . . . . 402
13.10The Revelation Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
13.11A More General Utility Function for the Agent . . . . . . . . . . . . . . . . 405
13.11.1 The Optimal Contract . . . . . . . . . . . . . . . . . . . . . . . . . 405
13.11.2 More than One Good . . . . . . . . . . . . . . . . . . . . . . . . . . 407
13.12Ex Ante versus Ex Post Participation Constraints . . . . . . . . . . . . . . 408
13.12.1 Risk Neutrality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
13.12.2 Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410
13.13Commitment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
13.13.1 Renegotiating a Contract . . . . . . . . . . . . . . . . . . . . . . . . 414
13.13.2 Reneging on a Contract . . . . . . . . . . . . . . . . . . . . . . . . 415
13.14Informative Signals to Improve Contracting . . . . . . . . . . . . . . . . . 415
13.14.1Ex Post Verifiable Signal . . . . . . . . . . . . . . . . . . . . . . . . 416
13.14.2Ex Ante Nonverifiable Signal . . . . . . . . . . . . . . . . . . . . . . 417
13.15Contract Theory at Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
13.15.1 Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
13.15.2 Nonlinear Pricing by a Monopoly . . . . . . . . . . . . . . . . . . . 418
13.15.3 Quality and Price Discrimination . . . . . . . . . . . . . . . . . . . 419
13.15.4 Financial Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . . 420
13.15.5 Labor Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
13.16The Optimal Contract with a Continuum of Types . . . . . . . . . . . . . 422
13.17Further Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426
14 Optimal Mechanism Design: Contracts with One-Agent and Hidden
Action 429
14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
14.2 Basic Settings of Principal-Agent Model with Moral Hazard . . . . . . . . 430
14.2.1 Effort and Production . . . . . . . . . . . . . . . . . . . . . . . . . 430
ix
14.2.2 Incentive Feasible Contracts . . . . . . . . . . . . . . . . . . . . . . 431
14.2.3 The Complete Information Optimal Contract . . . . . . . . . . . . 432
14.3 Risk Neutrality and First-Best Implementation . . . . . . . . . . . . . . . . 433
14.4 The Trade-Off Between Limited Liability Rent Extraction and Efficiency . 435
14.5 The Trade-Off Between Insurance and Efficiency . . . . . . . . . . . . . . . 437
14.5.1 Optimal Transfers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437
14.5.2 The Optimal Second-Best Effort . . . . . . . . . . . . . . . . . . . . 439
14.6 More than Two Levels of Performance . . . . . . . . . . . . . . . . . . . . 440
14.6.1 Limited Liability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
14.6.2 Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
14.7 Contract Theory at Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 443
14.7.1 Efficiency Wage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443
14.7.2 Sharecropping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444
14.7.3 Wholesale Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . 446
14.7.4 Financial Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . . 446
14.8 A Continuum of Performances . . . . . . . . . . . . . . . . . . . . . . . . . 448
14.9 Further Extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
15 General Mechanism Design: Contracts with Multi-Agents 452
15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452
15.2 Basic Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454
15.2.1 Economic Environments . . . . . . . . . . . . . . . . . . . . . . . . 454
15.2.2 Social Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
15.2.3 Economic Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . 456
15.2.4 Solution Concept of Self-Interested Behavior . . . . . . . . . . . . . 457
15.2.5 Implementation and Incentive Compatibility . . . . . . . . . . . . . 458
15.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460
15.4 Dominant Strategy and Truthful Revelation Mechanisms . . . . . . . . . . 461
15.5 Gibbard-Satterthwaite Impossibility Theorem . . . . . . . . . . . . . . . . 464
15.6 Hurwicz Impossibility Theorem . . . . . . . . . . . . . . . . . . . . . . . . 465
15.7 Vickrey-Clark-Groves Mechanisms . . . . . . . . . . . . . . . . . . . . . . . 468
15.7.1 Vickrey-Clark-Groves Mechanisms for Discrete Public Good . . . . 468
x
15.7.2 The Vickrey-Clark-Groves Mechanisms with Continuous Public Goods
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472
15.7.3 Balanced VCG Mechanisms . . . . . . . . . . . . . . . . . . . . . . 477
15.8 Nash Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479
15.8.1 Nash Equilibrium and General Mechanism Design . . . . . . . . . . 479
15.8.2 Characterization of Nash Implementation . . . . . . . . . . . . . . . 481
15.9 Better Mechanism Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
15.9.1 Groves-Ledyard Mechanism . . . . . . . . . . . . . . . . . . . . . . 487
15.9.2 Walker’s Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . 489
15.9.3 Tian’s Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
15.10Incomplete Information and Bayesian-Nash Implementation . . . . . . . . 494
15.10.1Bayesian-Nash Implementation Problem . . . . . . . . . . . . . . . 494
15.10.2 Ex-Post Efficient Implementation by the Expected Externality Mechanism
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497
15.10.3Participation Constraints . . . . . . . . . . . . . . . . . . . . . . . . 501
15.10.4 The Revenue Equivalence Theorem in Auctions . . . . . . . . . . . 506
15.10.5 Correlated Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510
15.10.6 Ex Post Implementation . . . . . . . . . . . . . . . . . . . . . . . . 513
15.10.7Ex post Implementation with Common Values . . . . . . . . . . . . 514
16 Dynamic Mechanism Design 523
16.1 Dynamic Contracts with Commitment . . . . . . . . . . . . . . . . . . . . 523
16.1.1 Dynamic P-A Model with Constant Type . . . . . . . . . . . . . . . 524
16.1.2 Dynamic P-A Model with Markov Types . . . . . . . . . . . . . . . 525
16.2 Dynamic Contracts without Full Commitment . . . . . . . . . . . . . . . . 527
16.2.1 Basic Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
16.2.2 Full Analysis of A Simple Model . . . . . . . . . . . . . . . . . . . . 530

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