microeconomics principles and analysis

MICROECONOMICS
Principles and Analysis
Frank A. Cowell
STICERD and Department of Economics
London School of Economics
December 2004
ii
Contents
Contents iii
List of Tables xiii
List of Figures xv
Preface xxiii
1 Introduction 1
1.1 The rôle of micro econ omic principles . . . . . . . . . . . . . . . . 1
1.2 Microeconomic models . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 The economic actors . . . . . . . . . . . . . . . . . . . . . 2
1.2.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.4 The economic environment . . . . . . . . . . . . . . . . . 3
1.2.5 Assumptions and axioms . . . . . . . . . . . . . . . . . . 4
1.2.6 “Testing” a model . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Equilibrium analysis . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 Equilibrium and economic context . . . . . . . . . . . . . 5
1.3.2 The comparative statics method . . . . . . . . . . . . . . 5
1.3.3 Dynamics and stability . . . . . . . . . . . . . . . . . . . 6
1.4 Background to this book . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.1 Economics . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.2 Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Using the book . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5.1 A route map . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5.2 Some tips . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 The Firm 9
2.1 Basic setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 The …rm: basic ingredients . . . . . . . . . . . . . . . . . 10
2.1.2 Properties of the production function . . . . . . . . . . . 12
2.2 The optimisation problem . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 Optimisation stage 1: cost minimisation . . . . . . . . . . 20
2.2.2 The cost function . . . . . . . . . . . . . . . . . . . . . . . 23
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iv CONTENTS
2.2.3 Optimisation stage 2: choosing output . . . . . . . . . . . 25
2.2.4 Assembling the solution . . . . . . . . . . . . . . . . . . . 26
2.3 The …rm as a “black box” . . . . . . . . . . . . . . . . . . . . . . 27
2.3.1 Demand and supply functions of the …rm . . . . . . . . . 29
2.3.2 Comparative statics: the general case . . . . . . . . . . . 31
2.4 The short run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.5 The multiproduct …rm . . . . . . . . . . . . . . . . . . . . . . . . 39
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.7 Reading notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3 The Firm and the Market 49
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2 The market supply curve . . . . . . . . . . . . . . . . . . . . . . 50
3.3 Large numbers and the supply curve . . . . . . . . . . . . . . . . 53
3.4 Interaction amongst …rms . . . . . . . . . . . . . . . . . . . . . . 55
3.5 The size of the industry . . . . . . . . . . . . . . . . . . . . . . . 56
3.6 Price-setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.6.1 Simple monopoly . . . . . . . . . . . . . . . . . . . . . . . 58
3.6.2 Discriminating monopolist . . . . . . . . . . . . . . . . . . 60
3.6.3 Entry fee . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.7 Product variety . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.9 Reading notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4 The Consumer 69
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 The consumer’s environment . . . . . . . . . . . . . . . . . . . . 70
4.3 Revealed preference . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.4 Preferences: axiomatic approach . . . . . . . . . . . . . . . . . . 75
4.5 Consumer optimisation: …xed income . . . . . . . . . . . . . . . . 80
4.5.1 Cost-minimisation . . . . . . . . . . . . . . . . . . . . . . 82
4.5.2 Utility-maximisation . . . . . . . . . . . . . . . . . . . . . 83
4.6 Welfare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.6.1 An application: price indices . . . . . . . . . . . . . . . . 92
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.8 Reading notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5 The Consumer and the Market 99
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.2 The market and incomes . . . . . . . . . . . . . . . . . . . . . . . 100
5.3 Supply by households . . . . . . . . . . . . . . . . . . . . . . . . 100
5.3.1 Labour supply . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3.2 Savings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
CONTENTS v
5.4 Household production . . . . . . . . . . . . . . . . . . . . . . . . 107
5.5 Aggregation over goods . . . . . . . . . . . . . . . . . . . . . . . 112
5.6 Aggregation of consumers . . . . . . . . . . . . . . . . . . . . . . 112
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.8 Reading notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6 A Simple Economy 121

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.2 Another look at production . . . . . . . . . . . . . . . . . . . . . 122
6.2.1 Processes and net outputs . . . . . . . . . . . . . . . . . . 122
6.2.2 The technology . . . . . . . . . . . . . . . . . . . . . . . . 124
6.2.3 The production function again . . . . . . . . . . . . . . . 128
6.2.4 Externalities and aggregation . . . . . . . . . . . . . . . . 128
6.3 The Robinson Crusoe economy . . . . . . . . . . . . . . . . . . . 129
6.4 Decentralisation and trade . . . . . . . . . . . . . . . . . . . . . . 132
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.6 Reading notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7 General Equilibrium 143
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.2 A more interesting economy . . . . . . . . . . . . . . . . . . . . . 144
7.2.1 Allocations . . . . . . . . . . . . . . . . . . . . . . . . . . 145
7.2.2 Incomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.2.3 An illustration: the exchange economy . . . . . . . . . . . 147
7.3 The logic of price-taking . . . . . . . . . . . . . . . . . . . . . . . 149
7.3.1 The core of the exchange economy . . . . . . . . . . . . . 151
7.3.2 Competitive equilibrium and the core: small economy . . 152
7.3.3 Competitive equilibrium and the core: large economy . . 152
7.4 The excess-demand approach . . . . . . . . . . . . . . . . . . . . 156
7.4.1 Properties of the excess demand function . . . . . . . . . 157
7.4.2 Existence . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
7.4.3 Uniqueness . . . . . . . . . . . . . . . . . . . . . . . . . . 162
7.4.4 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.5 The rôle of prices . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
7.5.1 The equilibrium allo cation . . . . . . . . . . . . . . . . . . 167
7.5.2 Decentralisation again . . . . . . . . . . . . . . . . . . . . 167
7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

7.7 Reading notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
7.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
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8 Uncertainty and Risk 177
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
8.2 Consumption and uncertainty . . . . . . . . . . . . . . . . . . . . 177
8.2.1 The nature of choice . . . . . . . . . . . . . . . . . . . . . 179
8.2.2 State-space diagram . . . . . . . . . . . . . . . . . . . . . 180
8.3 A model of preferences . . . . . . . . . . . . . . . . . . . . . . . . 184
8.3.1 Key axioms . . . . . . . . . . . . . . . . . . . . . . . . . . 185
8.3.2 Von-Neumann- Morgenstern utility . . . . . . . . . . . . . 188
8.3.3 The “felicity”function . . . . . . . . . . . . . . . . . . . . 189
8.4 Risk aversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
8.4.1 Risk premium . . . . . . . . . . . . . . . . . . . . . . . . . 191
8.4.2 Indices of risk aversion . . . . . . . . . . . . . . . . . . . . 192
8.4.3 Special cases . . . . . . . . . . . . . . . . . . . . . . . . . 195
8.5 Lotteries and preferences . . . . . . . . . . . . . . . . . . . . . . . 197
8.5.1 The probability space . . . . . . . . . . . . . . . . . . . . 198
8.5.2 Axiomatic approach . . . . . . . . . . . . . . . . . . . . . 199
8.6 Trade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
8.6.1 Contingent goods: competitive equilibrium . . . . . . . . 203
8.6.2 Financial assets . . . . . . . . . . . . . . . . . . . . . . . . 203
8.7 Individual optimisation . . . . . . . . . . . . . . . . . . . . . . . 205
8.7.1 The attainable set . . . . . . . . . . . . . . . . . . . . . . 205
8.7.2 Components of the optimum . . . . . . . . . . . . . . . . 209
8.7.3 The portfolio problem . . . . . . . . . . . . . . . . . . . . 211
8.7.4 Insurance . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
8.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
8.9 Reading notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
8.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

9 Welfare 227
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
9.2 The constitution . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
9.3 Principles for social judgments: e¢ ciency . . . . . . . . . . . . . 234
9.3.1 Private go ods and the market . . . . . . . . . . . . . . . . 237
9.3.2 Departures from e¢ ciency . . . . . . . . . . . . . . . . . . 242
9.3.3 Externalities . . . . . . . . . . . . . . . . . . . . . . . . . 246
9.3.4 Public goods . . . . . . . . . . . . . . . . . . . . . . . . . 250
9.3.5 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . 251
9.3.6 Extending the e¢ ciency idea . . . . . . . . . . . . . . . . 254
9.4 Principles for social judgments: equity . . . . . . . . . . . . . . . 257
9.4.1 Fairness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
9.4.2 Concern for inequality . . . . . . . . . . . . . . . . . . . . 258
9.5 The social-welfare function . . . . . . . . . . . . . . . . . . . . . 258
9.5.1 Welfare, national income and expenditure . . . . . . . . . 259
9.5.2 Inequality and we lfare loss . . . . . . . . . . . . . . . . . . 261
9.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
9.7 Reading notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
CONTENTS vii
9.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
10 Strategic Behaviour 271
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
10.2 Games –basic concepts . . . . . . . . . . . . . . . . . . . . . . . 272
10.2.1 Players, rules and payo¤s . . . . . . . . . . . . . . . . . . 272
10.2.2 Information and Beliefs . . . . . . . . . . . . . . . . . . . 273
10.2.3 Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
10.2.4 Representing a game . . . . . . . . . . . . . . . . . . . . . 274
10.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
10.3.1 Multiple equilibria . . . . . . . . . . . . . . . . . . . . . . 278
10.3.2 E¢ ciency . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

10.3.3 Existence . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
10.4 Application: duopoly . . . . . . . . . . . . . . . . . . . . . . . . . 285
10.4.1 Competition in quantities . . . . . . . . . . . . . . . . . . 286
10.4.2 Competition in prices . . . . . . . . . . . . . . . . . . . . 291
10.5 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
10.5.1 Games and subgames . . . . . . . . . . . . . . . . . . . . 295
10.5.2 Equilibrium: more on concept and method . . . . . . . . 297
10.5.3 Repeated interactions . . . . . . . . . . . . . . . . . . . . 300
10.6 Application: market structure . . . . . . . . . . . . . . . . . . . . 305
10.6.1 Market leadership . . . . . . . . . . . . . . . . . . . . . . 305
10.6.2 Market entry . . . . . . . . . . . . . . . . . . . . . . . . . 306
10.6.3 Another look at duopoly . . . . . . . . . . . . . . . . . . 309
10.7 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
10.7.1 A basic model . . . . . . . . . . . . . . . . . . . . . . . . 311
10.7.2 An application: entry again . . . . . . . . . . . . . . . . . 314
10.7.3 Mixed strategies again . . . . . . . . . . . . . . . . . . . . 317
10.7.4 A “dynamic”approach . . . . . . . . . . . . . . . . . . . . 317
10.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
10.9 Reading notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
10.10Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
11 Information 327
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
11.2 Hidden characteristics: adverse selection . . . . . . . . . . . . . . 328
11.2.1 Information and monopoly power . . . . . . . . . . . . . . 329
11.2.2 One customer type . . . . . . . . . . . . . . . . . . . . . . 329
11.2.3 Multiple types: Full information . . . . . . . . . . . . . . 333
11.2.4 Imperfect information . . . . . . . . . . . . . . . . . . . . 336
11.2.5 Adverse selection: Competition . . . . . . . . . . . . . . . 345
11.2.6 Application: Insurance . . . . . . . . . . . . . . . . . . . . 346
11.3 Hidden characteristics: Signalling . . . . . . . . . . . . . . . . . . 352

11.3.1 Costly signals . . . . . . . . . . . . . . . . . . . . . . . . . 352
11.3.2 Costless signals . . . . . . . . . . . . . . . . . . . . . . . . 360
11.4 Hidden actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
viii CONTENTS
11.4.1 The issue . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
11.4.2 Outline of the problem . . . . . . . . . . . . . . . . . . . . 362
11.4.3 A simpli…ed model . . . . . . . . . . . . . . . . . . . . . . 362
11.4.4 Principal-and-Agent: a richer model . . . . . . . . . . . . 367
11.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
11.6 Reading notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
11.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
12 Design 381
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
12.2 Social choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
12.3 Markets and manipulation . . . . . . . . . . . . . . . . . . . . . . 385
12.3.1 Markets: another look . . . . . . . . . . . . . . . . . . . . 385
12.3.2 Simple trading . . . . . . . . . . . . . . . . . . . . . . . . 386
12.3.3 Manipulation: power and misrepresentation . . . . . . . . 387
12.3.4 A design issue? . . . . . . . . . . . . . . . . . . . . . . . . 388
12.4 Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
12.4.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . 390
12.4.2 Direct mechanisms . . . . . . . . . . . . . . . . . . . . . . 391
12.4.3 The revelation principle . . . . . . . . . . . . . . . . . . . 392
12.5 The design problem . . . . . . . . . . . . . . . . . . . . . . . . . 393
12.6 Design: applications . . . . . . . . . . . . . . . . . . . . . . . . . 395
12.6.1 Auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
12.6.2 A public project . . . . . . . . . . . . . . . . . . . . . . . 403
12.6.3 Contracting again . . . . . . . . . . . . . . . . . . . . . . 409
12.6.4 Taxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
12.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422

12.8 Reading notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424
12.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424
13 Government and the Individual 431
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
13.2 Market failure? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
13.3 Nonconvexities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
13.3.1 Large numbers and convexity . . . . . . . . . . . . . . . . 435
13.3.2 Interactions and convexity . . . . . . . . . . . . . . . . . . 435
13.3.3 The infrastructure problem . . . . . . . . . . . . . . . . . 436
13.3.4 Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . 438
13.4 Externalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
13.4.1 Production externalities: the e¢ ciency problem . . . . . . 443
13.4.2 Corrective taxes . . . . . . . . . . . . . . . . . . . . . . . 443
13.4.3 Production externalities: Private solutions . . . . . . . . . 444
13.4.4 Consumption externalities . . . . . . . . . . . . . . . . . . 447
13.4.5 Externalities: assessment . . . . . . . . . . . . . . . . . . 448
13.5 Public consumption . . . . . . . . . . . . . . . . . . . . . . . . . 448
13.5.1 Nonrivalness and e¢ ciency conditions . . . . . . . . . . . 449
CONTENTS ix
13.5.2 Club goo ds . . . . . . . . . . . . . . . . . . . . . . . . . . 449
13.6 Public goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
13.6.1 The issue . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
13.6.2 Voluntary provision . . . . . . . . . . . . . . . . . . . . . 452
13.6.3 Personalised prices? . . . . . . . . . . . . . . . . . . . . . 454
13.6.4 Public goo d s: market failure and the design problem . . . 457
13.6.5 Public goo d s: alternative mechanisms . . . . . . . . . . . 458
13.7 Optimal allocations? . . . . . . . . . . . . . . . . . . . . . . . . . 460
13.7.1 Optimum with lump-sum transfers . . . . . . . . . . . . . 461
13.7.2 Second-best approaches . . . . . . . . . . . . . . . . . . . 464
13.8 Conclusion: Economic Prescriptions . . . . . . . . . . . . . . . . 467

13.9 Reading notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468
13.10Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468
Bibliography 473
A Mathematics Background 485
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
A.2 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486
A.2.1 Sets in R
n
. . . . . . . . . . . . . . . . . . . . . . . . . . . 486
A.3 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
A.3.1 Linear and a¢ ne functions . . . . . . . . . . . . . . . . . 487
A.3.2 Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . 488
A.3.3 Homogeneous functions . . . . . . . . . . . . . . . . . . . 490
A.3.4 Homothetic functions . . . . . . . . . . . . . . . . . . . . 491
A.4 Di¤erentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
A.4.1 Function of one variable . . . . . . . . . . . . . . . . . . . 492
A.4.2 Function of several variables . . . . . . . . . . . . . . . . . 493
A.4.3 Function-of-a-Function Rule . . . . . . . . . . . . . . . . . 493
A.4.4 The Jacobian derivative . . . . . . . . . . . . . . . . . . . 494
A.4.5 The Taylor expansion . . . . . . . . . . . . . . . . . . . . 494
A.4.6 Elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . 494
A.5 Mappings and systems of equations . . . . . . . . . . . . . . . . . 496
A.5.1 Fixed-point results . . . . . . . . . . . . . . . . . . . . . . 496
A.5.2 Implicit functions . . . . . . . . . . . . . . . . . . . . . . . 497
A.6 Convexity and Concavity . . . . . . . . . . . . . . . . . . . . . . 499
A.6.1 Convex sets . . . . . . . . . . . . . . . . . . . . . . . . . . 499
A.6.2 Hyperplanes. . . . . . . . . . . . . . . . . . . . . . . . . . 500
A.6.3 Separation results . . . . . . . . . . . . . . . . . . . . . . 500
A.6.4 Convex and concave functions . . . . . . . . . . . . . . . . 503
A.6.5 quasiconcave functions . . . . . . . . . . . . . . . . . . . . 505

A.6.6 The Hessian property . . . . . . . . . . . . . . . . . . . . 507
A.7 Maximisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507
A.7.1 The basic technique . . . . . . . . . . . . . . . . . . . . . 508
A.7.2 Constrained maximisation . . . . . . . . . . . . . . . . . . 510
A.7.3 More on constrained maximisation . . . . . . . . . . . . . 511
x CONTENTS
A.7.4 Envelope theorem . . . . . . . . . . . . . . . . . . . . . . 514
A.7.5 A point on notation . . . . . . . . . . . . . . . . . . . . . 515
A.8 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
A.8.1 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 516
A.8.2 Bayes’rule . . . . . . . . . . . . . . . . . . . . . . . . . . 518
A.8.3 Probability distributions: examples . . . . . . . . . . . . . 518
A.9 Reading notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
B Answers to Footnote Questions 521
B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521
B.2 The …rm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521
B.3 The …rm and the market . . . . . . . . . . . . . . . . . . . . . . . 528
B.4 The consumer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529
B.5 The consumer and the market . . . . . . . . . . . . . . . . . . . . 535
B.6 A simple economy . . . . . . . . . . . . . . . . . . . . . . . . . . 539
B.7 General equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . 542
B.8 Uncertainty and risk . . . . . . . . . . . . . . . . . . . . . . . . . 548
B.9 Welfare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556
B.10 Strategic behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . 561
B.11 Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
B.12 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583
B.13 Government and individual . . . . . . . . . . . . . . . . . . . . . 598
C Selected Proofs 607
C.1 The …rm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607
C.1.1 Marginal cost and the Lagrange multiplier . . . . . . . . . 607

C.1.2 Properties of the cost function (Theorem 2.2) . . . . . . . 608
C.1.3 Firm’s demand and supply functions (Theorem 2.4) . . . 611
C.1.4 Firm’s demand and supply functions (continued) . . . . . 612
C.1.5 Properties of pro…t function (Theorem 2.7) . . . . . . . . 613
C.2 The consumer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614
C.2.1 The representation theorem (Theorem 4.1) . . . . . . . . 614
C.2.2 Existence of ordinary demand functions (Theorem 4.5) . . 615
C.2.3 Quasiconvexity of the indirect utility function . . . . . . . 615
C.3 The consumer and the market . . . . . . . . . . . . . . . . . . . . 616
C.3.1 Composite commodity (Theorem 5.1): . . . . . . . . . . . 616
C.3.2 The representative consumer (Theorem 5.2): . . . . . . . 616
C.4 A simple economy . . . . . . . . . . . . . . . . . . . . . . . . . . 617
C.4.1 Decentralisation (Theorem 6.2) . . . . . . . . . . . . . . . 617
C.5 General equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . 617
C.5.1 Competitive equilibrium and the core (Theorem 7.1) . . . 617
C.5.2 Existence of competitive equilibrium (Theorem 7.4) . . . 618
C.5.3 Uniqueness of competitive equilibrium (Theorem 7.5) . . 619
C.5.4 Valuation in general equilibrium (Theorem 7.6) . . . . . . 619
C.6 Uncertainty and risk . . . . . . . . . . . . . . . . . . . . . . . . . 620
C.6.1 Risk-taking and wealth (Theorem 8.7) . . . . . . . . . . . 620
CONTENTS xi
C.7 Welfare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620
C.7.1 Arrow’s theorem (Theorem 9.1) . . . . . . . . . . . . . . . 620
C.7.2 Black’s theorem (Theorem 9.2) . . . . . . . . . . . . . . . 622
C.7.3 The support theorem (Theorem 9.5) . . . . . . . . . . . . 623
C.7.4 Potential superiority (Theorem 9.10) . . . . . . . . . . . . 625
C.8 Strategic behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . 626
C.8.1 Nash equilibrium in pure strategies with in…nite strategy
sets (Theorem 10.2) . . . . . . . . . . . . . . . . . . . . . 626
C.8.2 Existence of Nash equilibrium (Theorem 10.1) . . . . . . 627

C.8.3 The Folk theorem . . . . . . . . . . . . . . . . . . . . . . 627
C.9 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 628
C.9.1 Revenue equivalence (Theorem 12.6) . . . . . . . . . . . . 628
C.9.2 The Clark-Groves mechanism (Theorem 12.7) . . . . . . 630
Index 632
xii CONTENTS
List of Tables
2.1 The Firm: Basic Notation . . . . . . . . . . . . . . . . . . . . . . 10
2.2 The Firm: Solution Functions . . . . . . . . . . . . . . . . . . . . 35
4.1 The Consumer: Basic Notation . . . . . . . . . . . . . . . . . . . 73
5.1 Own-wage labour-supply responses for di¤erent types of UK work-
ers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.1 The Desert Island Economy . . . . . . . . . . . . . . . . . . . . . 130
7.1 Elements of the Economy . . . . . . . . . . . . . . . . . . . . . . 144
7.2 Alf, Arthur and Bill cut Ben out of the coalition . . . . . . . . . 154
8.1 Two simple decision problems under uncertainty . . . . . . . . . 178
8.2 Example for Independence Axiom . . . . . . . . . . . . . . . . . . 185
8.3 Prospects with fruit . . . . . . . . . . . . . . . . . . . . . . . . . 187
8.4 Prospects with di¤erent fruit . . . . . . . . . . . . . . . . . . . . 187
8.5 Uncertainty and risk: notation . . . . . . . . . . . . . . . . . . . 202
9.1 How the IOC voted 1993 . . . . . . . . . . . . . . . . . . . . . . . 234
9.2 Classi…cation of goods . . . . . . . . . . . . . . . . . . . . . . . . 236
9.3 Elements of the e¢ ciency problem . . . . . . . . . . . . . . . . . 237
9.4 Left-handed and right-handed voters . . . . . . . . . . . . . . . . 267
10.1 Simultaneous move, strategic form . . . . . . . . . . . . . . . . . 276
10.2 Multiple equilibria 1 . . . . . . . . . . . . . . . . . . . . . . . . . 279
10.3 Multiple equilibria 2 . . . . . . . . . . . . . . . . . . . . . . . . . 279
10.4 No equilibrium in pure strategies . . . . . . . . . . . . . . . . . . 281
10.5 Cournot model as Prisoner’s Dilemma . . . . . . . . . . . . . . . 290
10.6 Strategic behaviour: notation . . . . . . . . . . . . . . . . . . . . 293

10.7 Simultaneous move, strategic form . . . . . . . . . . . . . . . . . 294
10.8 Incredible threat: strategic view . . . . . . . . . . . . . . . . . . . 299
10.9 Bill’s trigger strategy s
b
T
. . . . . . . . . . . . . . . . . . . . . . 303
10.10Elimination and equilibrium . . . . . . . . . . . . . . . . . . . . . 320
10.11Pure-strategy Nash equilibria . . . . . . . . . . . . . . . . . . . . 320
xiii
xiv LIST OF TABLES
11.1 Types of incentive problem . . . . . . . . . . . . . . . . . . . . . 328
11.2 Adverse selection: Elements of the problem . . . . . . . . . . . . 332
11.3 Signalling: Elements of the problem . . . . . . . . . . . . . . . . 355
11.4 Principal and Agent: Elements of the Problem . . . . . . . . . . 368
12.1 Social-choice functions: Notation . . . . . . . . . . . . . . . . . . 383
12.2 The Trading Game . . . . . . . . . . . . . . . . . . . . . . . . . . 386
12.3 Mechanism: Notation . . . . . . . . . . . . . . . . . . . . . . . . 389
12.4 Types of auction . . . . . . . . . . . . . . . . . . . . . . . . . . . 396
12.5 Auctions: notation . . . . . . . . . . . . . . . . . . . . . . . . . . 400
12.6 A public project: Elements of the problem . . . . . . . . . . . . . 404
12.7 Penalty table for public projects . . . . . . . . . . . . . . . . . . 408
12.8 Contracting with hidden information: Elements of the problem . 410
12.9 Optimal taxation: Elements of the problem . . . . . . . . . . . . 418
B.1 “Battle of the sexes” –strategic form . . . . . . . . . . . . . . . . 562
B.2 The Prisoner’s Dilemma . . . . . . . . . . . . . . . . . . . . . . . 563
B.3 Bertrand model with integer prices . . . . . . . . . . . . . . . . . 567
B.4 Strong incumbent . . . . . . . . . . . . . . . . . . . . . . . . . . . 568
B.5 Lots of uninteresting Nash equilibria . . . . . . . . . . . . . . . . 585
List of Figures
2.1 Input requirement sets for four di¤erent technologies . . . . . . . 12

2.2 Marginal rate of techn ical substitution . . . . . . . . . . . . . . . 14
2.3 Low and high elasticity of substitution . . . . . . . . . . . . . . . 14
2.4 Homothetic and homogeneous functions . . . . . . . . . . . . . . 15
2.5 An IRTS production function . . . . . . . . . . . . . . . . . . . . 17
2.6 A DRTS production function . . . . . . . . . . . . . . . . . . . . 17
2.7 A CRTS production function . . . . . . . . . . . . . . . . . . . . 18
2.8 Four di¤erent technologies . . . . . . . . . . . . . . . . . . . . . . 19
2.9 The marginal pro d uct . . . . . . . . . . . . . . . . . . . . . . . . 20
2.10 Cost minimisation . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.11 Cost and input price . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.12 Optimal output may be multivalued . . . . . . . . . . . . . . . . 27
2.13 Convexity and input demands . . . . . . . . . . . . . . . . . . . 28
2.14 The substitution e¤ect of a fall in price . . . . . . . . . . . . . . 33
2.15 Input-price fall: total e¤ect . . . . . . . . . . . . . . . . . . . . . 34
2.16 Marginal and average costs in the short and long run . . . . . . . 38
2.17 Firm’s transformation curve . . . . . . . . . . . . . . . . . . . . 40
2.18 Pro…t maximisation: multiproduct …rm . . . . . . . . . . . . . . 42
3.1 A market with two …rms . . . . . . . . . . . . . . . . . . . . . . . 50
3.2 Another market with two …rms . . . . . . . . . . . . . . . . . . . 51
3.3 Absence of market equilibrium . . . . . . . . . . . . . . . . . . . 52
3.4 Average supply of two identical …rms . . . . . . . . . . . . . . . . 53
3.5 Average supply of lots of …rms . . . . . . . . . . . . . . . . . . . 54
3.6 Industry supply with negative externality . . . . . . . . . . . . . 55
3.7 Industry supply with positive externality . . . . . . . . . . . . . . 56
3.8 Temporary equilibrium of one …rm . . . . . . . . . . . . . . . . . 57
3.9 Equilibrium of the marginal compe titive …rm . . . . . . . . . . . 58
3.10 Equilibrium of the monopolist . . . . . . . . . . . . . . . . . . . . 59
3.11 Monopolistic market with an entry fee . . . . . . . . . . . . . . . 62
3.12 Equilibrium for the local monopolist . . . . . . . . . . . . . . . . 63
3.13 The marginal …rm in monopolistic competition . . . . . . . . . . 63

4.1 The consumption set: standard assumptions . . . . . . . . . . . . 70
xv
xvi LIST OF FIGURES
4.2 Two versions of the budget constraint . . . . . . . . . . . . . . . 71
4.3 x is chosen Monday; x
0
is chosen Tuesd ay . . . . . . . . . . . . . 74
4.4 Extension of the revealed preference concept . . . . . . . . . . . . 74
4.5 The continuity axiom . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.6 Two utility functions represe nting the same preferences . . . . . 77
4.7 A bliss point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.8 Strictly quasicconcave (concave-c ontoured) preferences . . . . . . 79
4.9 Two views of the consumer’s optimisation problem . . . . . . . . 81
4.10 The e¤ects of a price fall . . . . . . . . . . . . . . . . . . . . . . . 86
4.11 Compensated demand and the value of a price fall . . . . . . . . 90
4.12 Compensated demand and the value of a price fall (2) . . . . . . 91
4.13 Three ways of measuring the bene…ts of a price fall . . . . . . . . 91
5.1 The o¤er curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.2 The household’s supply of good 1 . . . . . . . . . . . . . . . . . . 103
5.3 The savings problem . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.4 General household production model . . . . . . . . . . . . . . . . 109
5.5 Consumption in the household-production model . . . . . . . . . 110
5.6 Market price ch ange cause s a switch . . . . . . . . . . . . . . . . 111
5.7 Aggregation of consumer demand . . . . . . . . . . . . . . . . . . 114
5.8 Aggregable demand functions . . . . . . . . . . . . . . . . . . . . 115
5.9 Odd things happen when Alf and Bill’s demands are combined . 116
6.1 Three basic production processes . . . . . . . . . . . . . . . . . . 122
6.2 Labour and pigs produce sausages . . . . . . . . . . . . . . . . . 125
6.3 The technology set Q . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.4 The potato-sausage tradeo¤ . . . . . . . . . . . . . . . . . . . . . 127

6.5 Smooth potato-sausage tradeo¤ . . . . . . . . . . . . . . . . . . . 129
6.6 Crusoe’s attainable set . . . . . . . . . . . . . . . . . . . . . . . . 131
6.7 Robinson Crusoe problem: summary . . . . . . . . . . . . . . . . 132
6.8 Crusoe problem: another view . . . . . . . . . . . . . . . . . . . . 133
6.9 The separating role of prices . . . . . . . . . . . . . . . . . . . . . 134
6.10 Optimum cannot be decentralised . . . . . . . . . . . . . . . . . . 136
6.11 Crusoe’s island trades . . . . . . . . . . . . . . . . . . . . . . . . 137
6.12 Convexi…cation of the attainable set . . . . . . . . . . . . . . . . 138
7.1 Utility-maximising choices for Alf and Bill . . . . . . . . . . . . . 148
7.2 Competitive equilibrium: exchange economy . . . . . . . . . . . . 149
7.3 The contract curve . . . . . . . . . . . . . . . . . . . . . . . . . . 150
7.4 The core in the two-person case . . . . . . . . . . . . . . . . . . . 151
7.5 Any CE must lie in the core . . . . . . . . . . . . . . . . . . . . 153
7.6 An allocation that blocks [x
a
] . . . . . . . . . . . . . . . . . . . . 155
7.7 Construction of excess demand curve . . . . . . . . . . . . . . . . 157
7.8 Normalised prices, n = 2. . . . . . . . . . . . . . . . . . . . . . . 159
7.9 Existence of a unique equilibrium price . . . . . . . . . . . . . . . 160
7.10 Discontinuous excess demand . . . . . . . . . . . . . . . . . . . . 161
LIST OF FIGURES xvii
7.11 Excess demand for good 2 unbounded below . . . . . . . . . . . . 161
7.12 Multiple equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.13 Global stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
7.14 Local instability . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.15 Decentralisation in general equilibrium . . . . . . . . . . . . . . . 168
7.16 Convexi…cation of produ ction through aggregation . . . . . . . . 169
7.17 Non-convex preferences . . . . . . . . . . . . . . . . . . . . . . . 170
8.1 The ex-ante/ex-post distinction . . . . . . . . . . . . . . . . . . . 179
8.2 The state-space diagram: # = 2 . . . . . . . . . . . . . . . . . . 180

8.3 The state-space diagram: # = 3 . . . . . . . . . . . . . . . . . . 181
8.4 Preference contours in state-space . . . . . . . . . . . . . . . . . 182
8.5 The certainty equivalent . . . . . . . . . . . . . . . . . . . . . . . 182
8.6 Quasiconcavity reinterpreted . . . . . . . . . . . . . . . . . . . . 183
8.7 A change in perception . . . . . . . . . . . . . . . . . . . . . . . . 184
8.8 Independence axiom: illustration . . . . . . . . . . . . . . . . . . 186
8.9 Contours of the Expected-Utility function . . . . . . . . . . . . . 188
8.10 Attitudes to risk . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
8.11 The “felicity”or “cardinal utility”function u. . . . . . . . . . . . 191
8.12 Concavity of u and risk aversion . . . . . . . . . . . . . . . . . . 193
8.13 Di¤erences in risk attitudes . . . . . . . . . . . . . . . . . . . . . 194
8.14 Indi¤erence curves with constant absolute risk aversion . . . . . . 195
8.15 Indi¤erence curves with constant relative risk aversion . . . . . . 196
8.16 Estimates of % by quintiles from Barsky et al. (1997) . . . . . . . 197
8.17 The probability diagram: # = 2 . . . . . . . . . . . . . . . . . . 198
8.18 The probability diagram: # = 3 . . . . . . . . . . . . . . . . . . 199
8.19 The probability diagram: # = 3 (close-up) . . . . . . . . . . . . 200
8.20 -indi¤erence curves . . . . . . . . . . . . . . . . . . . . . . . . . 201
8.21 Contingent goods: equilibrium trade . . . . . . . . . . . . . . . . 204
8.22 Attainable set: safe and risky assets . . . . . . . . . . . . . . . . 206
8.23 Attainable set: safe and risky assets (2) . . . . . . . . . . . . . . 208
8.24 Attainable set: insurance . . . . . . . . . . . . . . . . . . . . . . 209
8.25 Consumer choice with a variety of …nancial assets . . . . . . . . . 210
8.26 Distribution of returns . . . . . . . . . . . . . . . . . . . . . . . . 212
8.27 Consumer choice: safe and risky assets . . . . . . . . . . . . . . . 213
8.28 E¤ect of an increase in endowment . . . . . . . . . . . . . . . . . 215
8.29 A rightward shift . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
8.30 E¤ect of a rightward shift in the distribution . . . . . . . . . . . 217
8.31 E¤ect of numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
9.1 Alf, Bill, Charlie and the Bomb . . . . . . . . . . . . . . . . . . . 231

9.2 Alf, Bill, Charlie and the Bomb (2) . . . . . . . . . . . . . . . . . 232
9.3 The utility possibility set . . . . . . . . . . . . . . . . . . . . . . 235
9.4 Household h will choose ~x
h
not ^x
h
. . . . . . . . . . . . . . . . . . 241
9.5 Firm f will choose ~q
f
not ^q
f
. . . . . . . . . . . . . . . . . . . . . 241
9.6 Component of e¢ ciency loss . . . . . . . . . . . . . . . . . . . . . 245
xviii LIST OF FIGURES
9.7 The e¤ect of pollution on a victim’s production set . . . . . . . . 247
9.8 Production boundary and e¢ ciency with externalities . . . . . . 248
9.9 Conditions for e¢ cient provision of public goods . . . . . . . . . 252
9.10 Ex-ante and ex-post e¢ ciency . . . . . . . . . . . . . . . . . . . . 254
9.11 

is accessible from 
0
and 
0
is accessible from 

. . . . . . . . 256
9.12 The social-welfare function . . . . . . . . . . . . . . . . . . . . . 263
10.1 Simultaneous move, extensive form . . . . . . . . . . . . . . . . . 275
10.2 Utility possibilities: Prisoner’s Dilemma . . . . . . . . . . . . . . 280

10.3 Equilibrium in mixed strategy . . . . . . . . . . . . . . . . . . . . 282
10.4 Alf’s pure and mixed strategies . . . . . . . . . . . . . . . . . . . 283
10.5 Cournot –the reaction function . . . . . . . . . . . . . . . . . . . 287
10.6 Cournot-Nash equilibrium . . . . . . . . . . . . . . . . . . . . . . 288
10.7 Simpli…ed one-shot Cournot game . . . . . . . . . . . . . . . . . 290
10.8 Bertrand model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
10.9 Sequential move –extensive form . . . . . . . . . . . . . . . . . . 294
10.10Game and subgame (1) . . . . . . . . . . . . . . . . . . . . . . . 296
10.11Game and subgame (2) . . . . . . . . . . . . . . . . . . . . . . . 296
10.12An incredible threat . . . . . . . . . . . . . . . . . . . . . . . . . 299
10.13Repeated Prisoner’s Dilemma . . . . . . . . . . . . . . . . . . . . 301
10.14Utility possibilities: Prisoner’s Dilemma with “mixing” . . . . . . 302
10.15Leader-follower . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
10.16Entry deterrence . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
10.17Alf’s beliefs about Bill . . . . . . . . . . . . . . . . . . . . . . . . 312
10.18Entry with incomplete information . . . . . . . . . . . . . . . . . 316
10.19Bene…ts of restricting information . . . . . . . . . . . . . . . . . . 322
11.1 Alternative fee schedules . . . . . . . . . . . . . . . . . . . . . . . 330
11.2 An exploitative contract: fee schedule and consumption possibilities333
11.3 Two types: single-crossing condition . . . . . . . . . . . . . . . . 334
11.4 Full-information contracts: Consumption possibilities for each type335
11.5 Screening: extensive-form game . . . . . . . . . . . . . . . . . . . 337
11.6 Possibility of masquerading . . . . . . . . . . . . . . . . . . . . . 338
11.7 Second-best contracts: consumption for each of the two types . . 344
11.8 Second best contract: fee schedule and attainable set . . . . . . . 345
11.9 Pro…t on the contract . . . . . . . . . . . . . . . . . . . . . . . . 346
11.10Insurance: e¢ cient risk allocation . . . . . . . . . . . . . . . . . . 348
11.11Insurance: pooling . . . . . . . . . . . . . . . . . . . . . . . . . . 351
11.12Insurance: Separating equilibrium? . . . . . . . . . . . . . . . . 352
11.13Signalling by workers . . . . . . . . . . . . . . . . . . . . . . . . . 353

11.14Costly signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
11.15Separating equilibria . . . . . . . . . . . . . . . . . . . . . . . . . 358
11.16Pooling equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
11.17Principal-and-Agent . . . . . . . . . . . . . . . . . . . . . . . . . 363
11.18Full-information contracts . . . . . . . . . . . . . . . . . . . . . . 365
11.19Second-best contracts . . . . . . . . . . . . . . . . . . . . . . . . 368
LIST OF FIGURES xix
11.20E¤ort shifts the frequency distribution . . . . . . . . . . . . . . . 372
12.1 Manipulated trading . . . . . . . . . . . . . . . . . . . . . . . . . 387
12.2 The revelation principle . . . . . . . . . . . . . . . . . . . . . . . 392
12.3 Distribution of tastes –Beta(2,7) . . . . . . . . . . . . . . . . . . 399
12.4 First-price auction: bid and probability of winning . . . . . . . . 400
12.5 Distribution of price paid . . . . . . . . . . . . . . . . . . . . . . 404
12.6 A …xed-size project . . . . . . . . . . . . . . . . . . . . . . . . . . 406
12.7 Indi¤erence curves in (z; y)-space and (q; y)-space . . . . . . . . . 411
12.8 Two types of Agent: Full-information solution . . . . . . . . . . . 413
12.9 Two types of Agent: contract design . . . . . . . . . . . . . . . . 416
12.10Output and disposable income under the optimal tax . . . . . . . 423
13.1 Implementation through the market . . . . . . . . . . . . . . . . 434
13.2 Non-convexities in production and e¢ ciency: Two cases . . . . . 437
13.3 Nonconvexity: e¤ect of the competitive market . . . . . . . . . . 438
13.4 Nonconvexity: an e¢ cient fee schedule . . . . . . . . . . . . . . . 439
13.5 Nonconvexity: uncertain trade o¤ . . . . . . . . . . . . . . . . . . 441
13.6 A fundamental nonconvexity . . . . . . . . . . . . . . . . . . . . 446
13.7 Myopic rationality underprovides public good . . . . . . . . . . . 454
13.8 The Cournot-Nash solution underprovides . . . . . . . . . . . . . 455
13.9 Lindahl solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
13.10Opportunities for redistribution . . . . . . . . . . . . . . . . . . . 463
A.1 (a) A continuous function (b) An upper-hemicontinuous corre-
spondence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489

A.2 Continuous mapping with a …xed point . . . . . . . . . . . . . . . 497
A.3 Upper hemicontinuous mapping with a …xed point . . . . . . . . 498
A.4 A strictly convex set in R
2
. . . . . . . . . . . . . . . . . . . . . . 500
A.5 A hyperplane in R
2
. . . . . . . . . . . . . . . . . . . . . . . . . . 501
A.6 A hyperplane separating A and y . . . . . . . . . . . . . . . . . . 501
A.7 Supporting hyperplane . . . . . . . . . . . . . . . . . . . . . . . . 503
A.8 A strictly convex function of one variable . . . . . . . . . . . . . 504
A.9 A strictly concave-contoured (strictly quasiconcave) function . . 506
A.10 Di¤erent types of stationary point . . . . . . . . . . . . . . . . . 509
A.11 A case where x

i
= 0 at the optimum . . . . . . . . . . . . . . . . 513
B.1 Labour input in two locations . . . . . . . . . . . . . . . . . . . . 522
B.2 Cost minimisation: a corner solution . . . . . . . . . . . . . . . . 523
B.3 Pro…t maximisation: corner solution . . . . . . . . . . . . . . . . 528
B.4 Price changes (i) and (ii) in two cases . . . . . . . . . . . . . . . 530
B.5 Prices di¤er for buying and selling . . . . . . . . . . . . . . . . . 530
B.6 Lexicographic preferences . . . . . . . . . . . . . . . . . . . . . . 531
B.7 Utility maximisation: corner solution . . . . . . . . . . . . . . . . 532
B.8 Quantity discount . . . . . . . . . . . . . . . . . . . . . . . . . . 533
B.9 Gi¤en good . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
xx LIST OF FIGURES
B.10 Supply of good 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 536
B.11 Budget constraint with overtime . . . . . . . . . . . . . . . . . . 537
B.12 Indivisibility in production . . . . . . . . . . . . . . . . . . . . . 539

B.13 Combination of technology sets . . . . . . . . . . . . . . . . . . . 539
B.14 Answer to 2a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540
B.15 Answer to 2b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540
B.16 2-input, 1-output production function . . . . . . . . . . . . . . . 541
B.17 The attainable set . . . . . . . . . . . . . . . . . . . . . . . . . . 542
B.18 Imports and exports . . . . . . . . . . . . . . . . . . . . . . . . . 543
B.19 The o¤er curves and equilibrium . . . . . . . . . . . . . . . . . . 544
B.20 O¤er curves and multiple equilibria . . . . . . . . . . . . . . . . . 545
B.21 Normalised prices, n = 3 . . . . . . . . . . . . . . . . . . . . . . . 547
B.22 Ambiguous risk attitude . . . . . . . . . . . . . . . . . . . . . . . 549
B.23 CARA: changing  . . . . . . . . . . . . . . . . . . . . . . . . . . 552
B.24 CARA:  = 2 and  = 5 . . . . . . . . . . . . . . . . . . . . . . . 552
B.25 Portfolio choice: playing safe . . . . . . . . . . . . . . . . . . . . 554
B.26 Portfolio choice: plunging in the risky asset . . . . . . . . . . . . 555
B.27 E¤ec t of an increase in spread . . . . . . . . . . . . . . . . . . . . 556
B.28 Points that cannot be supported in an equilibrium . . . . . . . . 557
B.29 Utility loss through price distortion . . . . . . . . . . . . . . . . . 558
B.30 Battle of the sexes: extensive form . . . . . . . . . . . . . . . . . 562
B.31 Extensive form: alternative representation . . . . . . . . . . . . . 563
B.32 (a) Battle of sexes (b) Chicken . . . . . . . . . . . . . . . . . . . 564
B.33 Payo¤ possibilities . . . . . . . . . . . . . . . . . . . . . . . . . . 566
B.34 Payo¤s consistent with Nash equilibrium in a repeated Cournot
game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569
B.35 Full-information contracts: fee schedule . . . . . . . . . . . . . . 571
B.36 Full-information contracts: Lab our supp ly for each type . . . . . 572
B.37 Bill masquerades as an a-type in labour supply . . . . . . . . . . 573
B.38 Second best contract: quantity discount . . . . . . . . . . . . . . 575
B.39 Second-best labour contracts . . . . . . . . . . . . . . . . . . . . 576
B.40 Second-best labour contract: attainable set . . . . . . . . . . . . 577
B.41 Indi¤eren ce curves for quadratic cost . . . . . . . . . . . . . . . . 578

B.42 Bounds on education (1) . . . . . . . . . . . . . . . . . . . . . . . 579
B.43 A simple set of beliefs . . . . . . . . . . . . . . . . . . . . . . . . 580
B.44 No-signalling dominates . . . . . . . . . . . . . . . . . . . . . . . 581
B.45 Bounds on education (2) . . . . . . . . . . . . . . . . . . . . . . . 582
B.46 Equilibrium under the intuitive criterion . . . . . . . . . . . . . . 583
B.47 Implications of monotonicity . . . . . . . . . . . . . . . . . . . . 584
B.48 Monopolistic trading . . . . . . . . . . . . . . . . . . . . . . . . . 585
B.49 A …xed-size project (2) . . . . . . . . . . . . . . . . . . . . . . . . 588
B.50 Two types of Agent: Second-best solution . . . . . . . . . . . . . 593
B.51 Three types of Agent: Second-best solution . . . . . . . . . . . . 595
B.52 Compensating variation measure of welfare . . . . . . . . . . . . 599
B.53 Pro…ts in the nonconvexity example . . . . . . . . . . . . . . . . 600
B.54 High-e¢ ciency type masquerades as low-e¢ ciency type . . . . . . 601
LIST OF FIGURES xxi
B.55 Public good provision under lottery . . . . . . . . . . . . . . . . . 605
xxii LIST OF FIGURES
Preface
Acknowledgements f or the continuous help and encouragement from @@[usual
blah]
xxiii
xxiv PREFACE
Chapter 1
Introduction
the greater part of human actions have their origin not in logical
reasoning but in sentiment. This is particularly true for actions that
are not motivated economically . Man, although impelled to act
by nonlogical motives, likes to tie his ac tions logically to certain
principles; he therefore invents these a posteriori in order to justify
his actions. –Vilfredo Pareto, “The rise and f all of the elites”(1968,
p. 27)

1.1 The rôle of microeconomic principles
Why principles in microeconomics? Principles take you further than pure eco-
nomic theory; principles show you the reason s underlying good practice in ap-
plied economics; princip les help you tie together issues in microeconomics that
might otherwise remain as isolated topics.
This book aims to introduce these principles: it does not try cover everything
in the …eld of microeconomics nor to explore all the rami…cations of standard
abstract models. Rather its purpose is to conduct you through an account of
the central canon of microeconomics, showing you how it can assist in under-
standing everyday economic phenomena and helping you to develop a ‡air for
economic reasoning. If you grasp some basic principles in theoretical and applied
economics you can often make considerable headway through a mixture of tech-
nical expertise and healthy common sense. There are a lot of rules-of-thumb,
standard analytical procedures and simple theorems that can be applied again
and again to apparently dissimilar economic problems. The student of microeco-
nomics can exploit the fact that many basic problems have a common structure
and that they can be analysed using the same insights and methods. I hope
that this book will help students to do just that.
1