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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 The rôle of microeconomic principles . . .

1.2 Microeconomic models . . . . . . . . . . .
1.2.1 Purpose . . . . . . . . . . . . . . .
1.2.2 The economic actors . . . . . . . .
1.2.3 Motivation . . . . . . . . . . . . .
1.2.4 The economic environment . . . .
1.2.5 Assumptions and axioms . . . . .
1.2.6 “Testing” a model . . . . . . . . .
1.3 Equilibrium analysis . . . . . . . . . . . .
1.3.1 Equilibrium and economic context
1.3.2 The comparative statics method .
1.3.3 Dynamics and stability . . . . . .
1.4 Background to this book . . . . . . . . . .
1.4.1 Economics . . . . . . . . . . . . . .
1.4.2 Mathematics . . . . . . . . . . . .
1.5 Using the book . . . . . . . . . . . . . . .
1.5.1 A route map . . . . . . . . . . . .
1.5.2 Some tips . . . . . . . . . . . . . .

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1
1
2
2
2
2
3
4
4
5
5
5
6

6
6
6
7
7
7

2 The Firm
2.1 Basic setting . . . . . . . . . . . . . . . . . . .
2.1.1 The …rm: basic ingredients . . . . . . .
2.1.2 Properties of the production function .
2.2 The optimisation problem . . . . . . . . . . . .
2.2.1 Optimisation stage 1: cost minimisation
2.2.2 The cost function . . . . . . . . . . . . .

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9
9
10
12
19

20
23

iii

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iv

CONTENTS

2.3

2.4
2.5
2.6
2.7
2.8

2.2.3 Optimisation stage 2: choosing output . .
2.2.4 Assembling the solution . . . . . . . . . .
The …rm as a “black box” . . . . . . . . . . . . .
2.3.1 Demand and supply functions of the …rm

2.3.2 Comparative statics: the general case . .
The short run . . . . . . . . . . . . . . . . . . . .
The multiproduct …rm . . . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . .
Reading notes . . . . . . . . . . . . . . . . . . . .
Exercises . . . . . . . . . . . . . . . . . . . . . .

3 The
3.1
3.2
3.3
3.4
3.5
3.6

Firm and the Market
Introduction . . . . . . . . . . . . . .
The market supply curve . . . . . .
Large numbers and the supply curve
Interaction amongst …rms . . . . . .
The size of the industry . . . . . . .
Price-setting . . . . . . . . . . . . . .
3.6.1 Simple monopoly . . . . . . .
3.6.2 Discriminating monopolist . .
3.6.3 Entry fee . . . . . . . . . . .
3.7 Product variety . . . . . . . . . . . .
3.8 Summary . . . . . . . . . . . . . . .
3.9 Reading notes . . . . . . . . . . . . .
3.10 Exercises . . . . . . . . . . . . . . .

4 The
4.1
4.2
4.3
4.4
4.5

4.6
4.7
4.8
4.9
5 The
5.1
5.2
5.3

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25
26
27
29
31

35
39
44
44
44

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49
49
50
53
55
56
58
58
60
61

62
64
64
64

Consumer
Introduction . . . . . . . . . . . . . .
The consumer’s environment . . . .
Revealed preference . . . . . . . . .
Preferences: axiomatic approach . .
Consumer optimisation: …xed income
4.5.1 Cost-minimisation . . . . . .
4.5.2 Utility-maximisation . . . . .
Welfare . . . . . . . . . . . . . . . .
4.6.1 An application: price indices
Summary . . . . . . . . . . . . . . .
Reading notes . . . . . . . . . . . . .
Exercises . . . . . . . . . . . . . . .

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69
69
70
72
75
80
82
83
87
92
93
93
94

Consumer and the Market
Introduction . . . . . . . . . . .
The market and incomes . . . .
Supply by households . . . . .
5.3.1 Labour supply . . . . .
5.3.2 Savings . . . . . . . . .

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99
99
100
100
103
104

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CONTENTS
5.4
5.5
5.6
5.7
5.8
5.9

Household production . .
Aggregation over goods .
Aggregation of consumers
Summary . . . . . . . . .
Reading notes . . . . . . .
Exercises . . . . . . . . .

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107
112
112
116
117
117

6 A Simple Economy
6.1 Introduction . . . . . . . . . . . . . . .
6.2 Another look at production . . . . . .
6.2.1 Processes and net outputs . . .
6.2.2 The technology . . . . . . . . .
6.2.3 The production function again
6.2.4 Externalities and aggregation .
6.3 The Robinson Crusoe economy . . . .
6.4 Decentralisation and trade . . . . . . .
6.5 Summary . . . . . . . . . . . . . . . .
6.6 Reading notes . . . . . . . . . . . . . .
6.7 Exercises . . . . . . . . . . . . . . . .

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121
121
122
122
124
128
128
129
132
139

139
139

7 General Equilibrium
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 A more interesting economy . . . . . . . . . . . . . . . . . . .
7.2.1 Allocations . . . . . . . . . . . . . . . . . . . . . . . .
7.2.2 Incomes . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.3 An illustration: the exchange economy . . . . . . . . .
7.3 The logic of price-taking . . . . . . . . . . . . . . . . . . . . .
7.3.1 The core of the exchange economy . . . . . . . . . . .
7.3.2 Competitive equilibrium and the core: small economy
7.3.3 Competitive equilibrium and the core: large economy
7.4 The excess-demand approach . . . . . . . . . . . . . . . . . .
7.4.1 Properties of the excess demand function . . . . . . .
7.4.2 Existence . . . . . . . . . . . . . . . . . . . . . . . . .
7.4.3 Uniqueness . . . . . . . . . . . . . . . . . . . . . . . .
7.4.4 Stability . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5 The rôle of prices . . . . . . . . . . . . . . . . . . . . . . . . .
7.5.1 The equilibrium allocation . . . . . . . . . . . . . . . .
7.5.2 Decentralisation again . . . . . . . . . . . . . . . . . .
7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.7 Reading notes . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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143
143
144
145
147
147
149
151
152
152
156
157
160
162
163
166
167
167
171
172
172

vi

CONTENTS

8 Uncertainty and Risk
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . .
8.2 Consumption and uncertainty . . . . . . . . . . . .
8.2.1 The nature of choice . . . . . . . . . . . . .
8.2.2 State-space diagram . . . . . . . . . . . . .
8.3 A model of preferences . . . . . . . . . . . . . . . .
8.3.1 Key axioms . . . . . . . . . . . . . . . . . .
8.3.2 Von-Neumann-Morgenstern utility . . . . .
8.3.3 The “felicity”function . . . . . . . . . . . .
8.4 Risk aversion . . . . . . . . . . . . . . . . . . . . .
8.4.1 Risk premium . . . . . . . . . . . . . . . . .
8.4.2 Indices of risk aversion . . . . . . . . . . . .
8.4.3 Special cases . . . . . . . . . . . . . . . . .
8.5 Lotteries and preferences . . . . . . . . . . . . . . .
8.5.1 The probability space . . . . . . . . . . . .
8.5.2 Axiomatic approach . . . . . . . . . . . . .
8.6 Trade . . . . . . . . . . . . . . . . . . . . . . . . .
8.6.1 Contingent goods: competitive equilibrium
8.6.2 Financial assets . . . . . . . . . . . . . . . .
8.7 Individual optimisation . . . . . . . . . . . . . . .
8.7.1 The attainable set . . . . . . . . . . . . . .
8.7.2 Components of the optimum . . . . . . . .
8.7.3 The portfolio problem . . . . . . . . . . . .
8.7.4 Insurance . . . . . . . . . . . . . . . . . . .
8.8 Summary . . . . . . . . . . . . . . . . . . . . . . .
8.9 Reading notes . . . . . . . . . . . . . . . . . . . . .

8.10 Exercises . . . . . . . . . . . . . . . . . . . . . . .

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177
177
177
179
180
184
185
188
189
190
191
192
195
197
198
199
202
203
203
205
205
209

211
217
219
220
220

9 Welfare
9.1 Introduction . . . . . . . . . . . . . . . . . . . . .
9.2 The constitution . . . . . . . . . . . . . . . . . .
9.3 Principles for social judgments: e¢ ciency . . . .
9.3.1 Private goods and the market . . . . . . .
9.3.2 Departures from e¢ ciency . . . . . . . . .
9.3.3 Externalities . . . . . . . . . . . . . . . .
9.3.4 Public goods . . . . . . . . . . . . . . . .
9.3.5 Uncertainty . . . . . . . . . . . . . . . . .
9.3.6 Extending the e¢ ciency idea . . . . . . .
9.4 Principles for social judgments: equity . . . . . .
9.4.1 Fairness . . . . . . . . . . . . . . . . . . .
9.4.2 Concern for inequality . . . . . . . . . . .
9.5 The social-welfare function . . . . . . . . . . . .
9.5.1 Welfare, national income and expenditure
9.5.2 Inequality and welfare loss . . . . . . . . .
9.6 Summary . . . . . . . . . . . . . . . . . . . . . .
9.7 Reading notes . . . . . . . . . . . . . . . . . . . .

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227
227
228
234
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242
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257

257
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259
261
264
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CONTENTS
9.8

Exercises

vii
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10 Strategic Behaviour
10.1 Introduction . . . . . . . . . . . . . .
10.2 Games –basic concepts . . . . . . .
10.2.1 Players, rules and payo¤s . .
10.2.2 Information and Beliefs . . .
10.2.3 Strategy . . . . . . . . . . . .
10.2.4 Representing a game . . . . .
10.3 Equilibrium . . . . . . . . . . . . . .
10.3.1 Multiple equilibria . . . . . .
10.3.2 E¢ ciency . . . . . . . . . . .
10.3.3 Existence . . . . . . . . . . .
10.4 Application: duopoly . . . . . . . . .
10.4.1 Competition in quantities . .
10.4.2 Competition in prices . . . .
10.5 Time . . . . . . . . . . . . . . . . . .
10.5.1 Games and subgames . . . .
10.5.2 Equilibrium: more on concept
10.5.3 Repeated interactions . . . .
10.6 Application: market structure . . . .
10.6.1 Market leadership . . . . . .
10.6.2 Market entry . . . . . . . . .
10.6.3 Another look at duopoly . .
10.7 Uncertainty . . . . . . . . . . . . . .
10.7.1 A basic model . . . . . . . .
10.7.2 An application: entry again .

10.7.3 Mixed strategies again . . . .
10.7.4 A “dynamic” approach . . . .
10.8 Summary . . . . . . . . . . . . . . .
10.9 Reading notes . . . . . . . . . . . . .
10.10Exercises . . . . . . . . . . . . . . .

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11 Information
11.1 Introduction . . . . . . . . . . . . . . . .
11.2 Hidden characteristics: adverse selection
11.2.1 Information and monopoly power
11.2.2 One customer type . . . . . . . .
11.2.3 Multiple types: Full information
11.2.4 Imperfect information . . . . . .
11.2.5 Adverse selection: Competition .
11.2.6 Application: Insurance . . . . . .
11.3 Hidden characteristics: Signalling . . . .
11.3.1 Costly signals . . . . . . . . . . .
11.3.2 Costless signals . . . . . . . . . .
11.4 Hidden actions . . . . . . . . . . . . . .

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271
271
272
272
273
274
274
276
278
279
281
285
286
291
293
295
297
300
305
305
306
309

310
311
314
317
317
318
319
320

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327
327
328
329
329
333
336

345
346
352
352
360
361


viii

CONTENTS
11.4.1 The issue . . . . . . . . . . . . . . .
11.4.2 Outline of the problem . . . . . . . .
11.4.3 A simpli…ed model . . . . . . . . . .
11.4.4 Principal-and-Agent: a richer model
11.5 Summary . . . . . . . . . . . . . . . . . . .
11.6 Reading notes . . . . . . . . . . . . . . . . .
11.7 Exercises . . . . . . . . . . . . . . . . . . .

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361
362
362
367
373

374
374

12 Design
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . .
12.2 Social choice . . . . . . . . . . . . . . . . . . . . .
12.3 Markets and manipulation . . . . . . . . . . . . . .
12.3.1 Markets: another look . . . . . . . . . . . .
12.3.2 Simple trading . . . . . . . . . . . . . . . .
12.3.3 Manipulation: power and misrepresentation
12.3.4 A design issue? . . . . . . . . . . . . . . . .
12.4 Mechanisms . . . . . . . . . . . . . . . . . . . . . .
12.4.1 Implementation . . . . . . . . . . . . . . . .
12.4.2 Direct mechanisms . . . . . . . . . . . . . .
12.4.3 The revelation principle . . . . . . . . . . .
12.5 The design problem . . . . . . . . . . . . . . . . .
12.6 Design: applications . . . . . . . . . . . . . . . . .
12.6.1 Auctions . . . . . . . . . . . . . . . . . . . .
12.6.2 A public project . . . . . . . . . . . . . . .
12.6.3 Contracting again . . . . . . . . . . . . . .
12.6.4 Taxation . . . . . . . . . . . . . . . . . . . .
12.7 Summary . . . . . . . . . . . . . . . . . . . . . . .
12.8 Reading notes . . . . . . . . . . . . . . . . . . . . .
12.9 Exercises . . . . . . . . . . . . . . . . . . . . . . .

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381
381
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385
385
386
387
388
388
390
391
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395
395
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409

415
422
424
424

13 Government and the Individual
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .
13.2 Market failure? . . . . . . . . . . . . . . . . . . . . . .
13.3 Nonconvexities . . . . . . . . . . . . . . . . . . . . . .
13.3.1 Large numbers and convexity . . . . . . . . . .
13.3.2 Interactions and convexity . . . . . . . . . . . .
13.3.3 The infrastructure problem . . . . . . . . . . .
13.3.4 Regulation . . . . . . . . . . . . . . . . . . . .
13.4 Externalities . . . . . . . . . . . . . . . . . . . . . . .
13.4.1 Production externalities: the e¢ ciency problem
13.4.2 Corrective taxes . . . . . . . . . . . . . . . . .
13.4.3 Production externalities: Private solutions . . .
13.4.4 Consumption externalities . . . . . . . . . . . .
13.4.5 Externalities: assessment . . . . . . . . . . . .
13.5 Public consumption . . . . . . . . . . . . . . . . . . .
13.5.1 Nonrivalness and e¢ ciency conditions . . . . .

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431
431

432
433
435
435
436
438
442
443
443
444
447
448
448
449


CONTENTS

ix

13.5.2 Club goods . . . . . . . . . . . . . . . . . .
13.6 Public goods . . . . . . . . . . . . . . . . . . . . .
13.6.1 The issue . . . . . . . . . . . . . . . . . . .
13.6.2 Voluntary provision . . . . . . . . . . . . .
13.6.3 Personalised prices? . . . . . . . . . . . . .
13.6.4 Public goods: market failure and the design
13.6.5 Public goods: alternative mechanisms . . .
13.7 Optimal allocations? . . . . . . . . . . . . . . . . .
13.7.1 Optimum with lump-sum transfers . . . . .
13.7.2 Second-best approaches . . . . . . . . . . .

13.8 Conclusion: Economic Prescriptions . . . . . . . .
13.9 Reading notes . . . . . . . . . . . . . . . . . . . . .
13.10Exercises . . . . . . . . . . . . . . . . . . . . . . .

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Bibliography
A Mathematics Background
A.1 Introduction . . . . . . . . . . . . . . . . .
A.2 Sets . . . . . . . . . . . . . . . . . . . . .
A.2.1 Sets in Rn . . . . . . . . . . . . . .
A.3 Functions . . . . . . . . . . . . . . . . . .
A.3.1 Linear and a¢ ne functions . . . .
A.3.2 Continuity . . . . . . . . . . . . . .
A.3.3 Homogeneous functions . . . . . .
A.3.4 Homothetic functions . . . . . . .
A.4 Di¤erentiation . . . . . . . . . . . . . . .
A.4.1 Function of one variable . . . . . .
A.4.2 Function of several variables . . . .
A.4.3 Function-of-a-Function Rule . . . .
A.4.4 The Jacobian derivative . . . . . .
A.4.5 The Taylor expansion . . . . . . .
A.4.6 Elasticities . . . . . . . . . . . . .
A.5 Mappings and systems of equations . . . .
A.5.1 Fixed-point results . . . . . . . . .
A.5.2 Implicit functions . . . . . . . . . .
A.6 Convexity and Concavity . . . . . . . . .
A.6.1 Convex sets . . . . . . . . . . . . .
A.6.2 Hyperplanes. . . . . . . . . . . . .
A.6.3 Separation results . . . . . . . . .
A.6.4 Convex and concave functions . . .
A.6.5 quasiconcave functions . . . . . . .
A.6.6 The Hessian property . . . . . . .
A.7 Maximisation . . . . . . . . . . . . . . . .
A.7.1 The basic technique . . . . . . . .
A.7.2 Constrained maximisation . . . . .

A.7.3 More on constrained maximisation

449
451
451
452
454
457
458
460
461
464
467
468
468
473

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485
485
486
486
487
487
488
490
491
492
492
493
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494
494
494
496
496
497
499
499
500
500
503
505
507
507
508
510
511


x

CONTENTS
A.7.4 Envelope theorem . . . . . . . . .
A.7.5 A point on notation . . . . . . . .
A.8 Probability . . . . . . . . . . . . . . . . .
A.8.1 Statistics . . . . . . . . . . . . . .
A.8.2 Bayes’rule . . . . . . . . . . . . .
A.8.3 Probability distributions: examples
A.9 Reading notes . . . . . . . . . . . . . . . .

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514
515
515
516
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518
519

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521
521
521
528
529
535

539
542
548
556
561
570
583
598

C Selected Proofs
C.1 The …rm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C.1.1 Marginal cost and the Lagrange multiplier . . . . . . .
C.1.2 Properties of the cost function (Theorem 2.2) . . . . .
C.1.3 Firm’s demand and supply functions (Theorem 2.4) .
C.1.4 Firm’s demand and supply functions (continued) . . .
C.1.5 Properties of pro…t function (Theorem 2.7) . . . . . .
C.2 The consumer . . . . . . . . . . . . . . . . . . . . . . . . . . .
C.2.1 The representation theorem (Theorem 4.1) . . . . . .
C.2.2 Existence of ordinary demand functions (Theorem 4.5)
C.2.3 Quasiconvexity of the indirect utility function . . . . .
C.3 The consumer and the market . . . . . . . . . . . . . . . . . .
C.3.1 Composite commodity (Theorem 5.1): . . . . . . . . .
C.3.2 The representative consumer (Theorem 5.2): . . . . .
C.4 A simple economy . . . . . . . . . . . . . . . . . . . . . . . .
C.4.1 Decentralisation (Theorem 6.2) . . . . . . . . . . . . .
C.5 General equilibrium . . . . . . . . . . . . . . . . . . . . . . .
C.5.1 Competitive equilibrium and the core (Theorem 7.1) .
C.5.2 Existence of competitive equilibrium (Theorem 7.4) .
C.5.3 Uniqueness of competitive equilibrium (Theorem 7.5)
C.5.4 Valuation in general equilibrium (Theorem 7.6) . . . .

C.6 Uncertainty and risk . . . . . . . . . . . . . . . . . . . . . . .
C.6.1 Risk-taking and wealth (Theorem 8.7) . . . . . . . . .

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607
607
607
608
611
612
613
614
614
615
615

616
616
616
617
617
617
617
618
619
619
620
620

B Answers to Footnote Questions
B.1 Introduction . . . . . . . . . . .
B.2 The …rm . . . . . . . . . . . . .
B.3 The …rm and the market . . . .
B.4 The consumer . . . . . . . . . .
B.5 The consumer and the market .
B.6 A simple economy . . . . . . .
B.7 General equilibrium . . . . . .
B.8 Uncertainty and risk . . . . . .
B.9 Welfare . . . . . . . . . . . . .
B.10 Strategic behaviour . . . . . . .
B.11 Information . . . . . . . . . . .
B.12 Design . . . . . . . . . . . . . .
B.13 Government and individual . .

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CONTENTS
C.7 Welfare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C.7.1 Arrow’s theorem (Theorem 9.1) . . . . . . . . . . . . . . .
C.7.2 Black’s theorem (Theorem 9.2) . . . . . . . . . . . . . . .
C.7.3 The support theorem (Theorem 9.5) . . . . . . . . . . . .
C.7.4 Potential superiority (Theorem 9.10) . . . . . . . . . . . .
C.8 Strategic behaviour . . . . . . . . . . . . . . . . . . . . . . . . . .

C.8.1 Nash equilibrium in pure strategies with in…nite strategy
sets (Theorem 10.2) . . . . . . . . . . . . . . . . . . . . .
C.8.2 Existence of Nash equilibrium (Theorem 10.1) . . . . . .
C.8.3 The Folk theorem . . . . . . . . . . . . . . . . . . . . . .
C.9 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C.9.1 Revenue equivalence (Theorem 12.6) . . . . . . . . . . . .
C.9.2 The Clark-Groves mechanism (Theorem 12.7) . . . . . .
Index

xi
620
620
622
623
625
626
626
627
627
628
628
630
632


xii

CONTENTS

List of Tables
2.1
2.2

The Firm: Basic Notation . . . . . . . . . . . . . . . . . . . . . .
The Firm: Solution Functions . . . . . . . . . . . . . . . . . . . .

10
35

4.1

The Consumer: Basic Notation . . . . . . . . . . . . . . . . . . .

73

5.1

Own-wage labour-supply responses for di¤erent types of UK workers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6.1

The Desert Island Economy . . . . . . . . . . . . . . . . . . . . . 130

7.1
7.2

Elements of the Economy . . . . . . . . . . . . . . . . . . . . . . 144
Alf, Arthur and Bill cut Ben out of the coalition . . . . . . . . . 154

8.1
8.2
8.3
8.4
8.5

Two simple decision problems under uncertainty
Example for Independence Axiom . . . . . . . . .
Prospects with fruit . . . . . . . . . . . . . . . .
Prospects with di¤erent fruit . . . . . . . . . . .
Uncertainty and risk: notation . . . . . . . . . .

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178
185
187
187
202

9.1
9.2
9.3
9.4

How the IOC voted 1993 . . . . . . .
Classi…cation of goods . . . . . . . .
Elements of the e¢ ciency problem .
Left-handed and right-handed voters

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234
236
237
267

10.1 Simultaneous move, strategic form . .
10.2 Multiple equilibria 1 . . . . . . . . . .
10.3 Multiple equilibria 2 . . . . . . . . . .
10.4 No equilibrium in pure strategies . . .
10.5 Cournot model as Prisoner’s Dilemma
10.6 Strategic behaviour: notation . . . . .
10.7 Simultaneous move, strategic form . .
10.8 Incredible threat: strategic view . . . .
10.9 Bill’s trigger strategy sbT . . . . . . .
10.10Elimination and equilibrium . . . . . .
10.11Pure-strategy Nash equilibria . . . . .

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276

279
279
281
290
293
294
299
303
320
320

xiii


xiv

LIST OF TABLES
11.1
11.2
11.3
11.4

Types of incentive problem . . . . . . . . . . .
Adverse selection: Elements of the problem . .
Signalling: Elements of the problem . . . . . .
Principal and Agent: Elements of the Problem

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328
332
355
368

12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9

Social-choice functions: Notation . . . . . . . .
The Trading Game . . . . . . . . . . . . . . . .
Mechanism: Notation . . . . . . . . . . . . . .

Types of auction . . . . . . . . . . . . . . . . .
Auctions: notation . . . . . . . . . . . . . . . .
A public project: Elements of the problem . . .
Penalty table for public projects . . . . . . . .
Contracting with hidden information: Elements
Optimal taxation: Elements of the problem . .

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of the problem
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383
386
389

396
400
404
408
410
418

B.1
B.2
B.3
B.4
B.5

“Battle of the sexes” –strategic form
The Prisoner’s Dilemma . . . . . . .
Bertrand model with integer prices .
Strong incumbent . . . . . . . . . . .
Lots of uninteresting Nash equilibria

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562
563
567
568
585

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List of Figures
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18

Input requirement sets for four di¤erent technologies
Marginal rate of technical substitution . . . . . . . .
Low and high elasticity of substitution . . . . . . . .

Homothetic and homogeneous functions . . . . . . .
An IRTS production function . . . . . . . . . . . . .
A DRTS production function . . . . . . . . . . . . .
A CRTS production function . . . . . . . . . . . . .
Four di¤erent technologies . . . . . . . . . . . . . . .
The marginal product . . . . . . . . . . . . . . . . .
Cost minimisation . . . . . . . . . . . . . . . . . . .
Cost and input price . . . . . . . . . . . . . . . . . .
Optimal output may be multivalued . . . . . . . . .
Convexity and input demands . . . . . . . . . . . .
The substitution e¤ect of a fall in price . . . . . . .
Input-price fall: total e¤ect . . . . . . . . . . . . . .
Marginal and average costs in the short and long run
Firm’s transformation curve . . . . . . . . . . . . .
Pro…t maximisation: multiproduct …rm . . . . . . .

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12

14
14
15
17
17
18
19
20
21
24
27
28
33
34
38
40
42

3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12

3.13

A market with two …rms . . . . . . . . . . . . .
Another market with two …rms . . . . . . . . .
Absence of market equilibrium . . . . . . . . .
Average supply of two identical …rms . . . . . .
Average supply of lots of …rms . . . . . . . . .
Industry supply with negative externality . . .
Industry supply with positive externality . . . .
Temporary equilibrium of one …rm . . . . . . .
Equilibrium of the marginal competitive …rm .
Equilibrium of the monopolist . . . . . . . . . .
Monopolistic market with an entry fee . . . . .
Equilibrium for the local monopolist . . . . . .
The marginal …rm in monopolistic competition

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50
51
52
53
54
55

56
57
58
59
62
63
63

4.1

The consumption set: standard assumptions . . . . . . . . . . . .

70

xv

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xvi

LIST OF FIGURES
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13

Two versions of the budget constraint . . . . . . . . . .
x is chosen Monday; x0 is chosen Tuesday . . . . . . . .
Extension of the revealed preference concept . . . . . . .
The continuity axiom . . . . . . . . . . . . . . . . . . . .
Two utility functions representing the same preferences
A bliss point . . . . . . . . . . . . . . . . . . . . . . . .
Strictly quasicconcave (concave-contoured) preferences .
Two views of the consumer’s optimisation problem . . .
The e¤ects of a price fall . . . . . . . . . . . . . . . . . .
Compensated demand and the value of a price fall . . .
Compensated demand and the value of a price fall (2) .
Three ways of measuring the bene…ts of a price fall . . .

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71
74
74
76
77
78

79
81
86
90
91
91

5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9

The o¤er curve . . . . . . . . . . . . . . . . . . . . . . . . . . .
The household’s supply of good 1 . . . . . . . . . . . . . . . . .
The savings problem . . . . . . . . . . . . . . . . . . . . . . . .
General household production model . . . . . . . . . . . . . . .
Consumption in the household-production model . . . . . . . .
Market price change causes a switch . . . . . . . . . . . . . . .
Aggregation of consumer demand . . . . . . . . . . . . . . . . .
Aggregable demand functions . . . . . . . . . . . . . . . . . . .
Odd things happen when Alf and Bill’s demands are combined

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102
103
106
109
110
111
114
115
116

6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.12

Three basic production processes . .
Labour and pigs produce sausages .
The technology set Q . . . . . . . . .
The potato-sausage tradeo¤ . . . . .
Smooth potato-sausage tradeo¤ . . .
Crusoe’s attainable set . . . . . . . .
Robinson Crusoe problem: summary
Crusoe problem: another view . . . .
The separating role of prices . . . . .
Optimum cannot be decentralised . .
Crusoe’s island trades . . . . . . . .
Convexi…cation of the attainable set

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125
126
127
129
131
132
133
134
136
137
138

7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10

Utility-maximising choices for Alf and Bill .
Competitive equilibrium: exchange economy
The contract curve . . . . . . . . . . . . . .
The core in the two-person case . . . . . . .

Any CE must lie in the core . . . . . . . .
An allocation that blocks [xa ] . . . . . . . .
Construction of excess demand curve . . . .
Normalised prices, n = 2. . . . . . . . . . .
Existence of a unique equilibrium price . . .
Discontinuous excess demand . . . . . . . .

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148
149
150
151
153
155
157
159
160
161

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LIST OF FIGURES

xvii

7.11
7.12
7.13
7.14
7.15
7.16
7.17

Excess demand for good 2 unbounded below . . . .
Multiple equilibria . . . . . . . . . . . . . . . . . .
Global stability . . . . . . . . . . . . . . . . . . . .
Local instability . . . . . . . . . . . . . . . . . . .
Decentralisation in general equilibrium . . . . . . .
Convexi…cation of production through aggregation
Non-convex preferences . . . . . . . . . . . . . . .

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161
163
164

165
168
169
170

8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
8.12
8.13
8.14
8.15
8.16
8.17
8.18
8.19
8.20
8.21
8.22
8.23
8.24
8.25

8.26
8.27
8.28
8.29
8.30
8.31

The ex-ante/ex-post distinction . . . . . . . . . . . . . .
The state-space diagram: # = 2 . . . . . . . . . . . . .
The state-space diagram: # = 3 . . . . . . . . . . . . .
Preference contours in state-space . . . . . . . . . . . .
The certainty equivalent . . . . . . . . . . . . . . . . . .
Quasiconcavity reinterpreted . . . . . . . . . . . . . . .
A change in perception . . . . . . . . . . . . . . . . . . .
Independence axiom: illustration . . . . . . . . . . . . .
Contours of the Expected-Utility function . . . . . . . .
Attitudes to risk . . . . . . . . . . . . . . . . . . . . . .
The “felicity” or “cardinal utility” function u. . . . . . .
Concavity of u and risk aversion . . . . . . . . . . . . .
Di¤erences in risk attitudes . . . . . . . . . . . . . . . .
Indi¤erence curves with constant absolute risk aversion .
Indi¤erence curves with constant relative risk aversion .
Estimates of % by quintiles from Barsky et al. (1997) . .
The probability diagram: # = 2 . . . . . . . . . . . . .
The probability diagram: # = 3 . . . . . . . . . . . . .
The probability diagram: # = 3 (close-up) . . . . . . .
-indi¤erence curves . . . . . . . . . . . . . . . . . . . .
Contingent goods: equilibrium trade . . . . . . . . . . .
Attainable set: safe and risky assets . . . . . . . . . . .
Attainable set: safe and risky assets (2) . . . . . . . . .

Attainable set: insurance . . . . . . . . . . . . . . . . .
Consumer choice with a variety of …nancial assets . . . .
Distribution of returns . . . . . . . . . . . . . . . . . . .
Consumer choice: safe and risky assets . . . . . . . . . .
E¤ect of an increase in endowment . . . . . . . . . . . .
A rightward shift . . . . . . . . . . . . . . . . . . . . . .
E¤ect of a rightward shift in the distribution . . . . . .
E¤ect of numbers . . . . . . . . . . . . . . . . . . . . . .

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179
180
181
182
182
183
184
186
188
190
191

193
194
195
196
197
198
199
200
201
204
206
208
209
210
212
213
215
215
217
218

9.1
9.2
9.3
9.4
9.5
9.6

Alf, Bill, Charlie and the Bomb . .
Alf, Bill, Charlie and the Bomb (2)

The utility possibility set . . . . .
Household h will choose x
~h not x
^h .
Firm f will choose q
~f not q
^f . . . .
Component of e¢ ciency loss . . . .

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231
232
235
241
241
245

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xviii
9.7
9.8
9.9
9.10
9.11
9.12

LIST OF FIGURES
The e¤ect of pollution on a victim’s production set . .
Production boundary and e¢ ciency with externalities
Conditions for e¢ cient provision of public goods . . .
Ex-ante and ex-post e¢ ciency . . . . . . . . . . . . . .
is accessible from 0 and 0 is accessible from
. .
The social-welfare function . . . . . . . . . . . . . . .

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247
248
252
254
256
263

10.1 Simultaneous move, extensive form . . . . . . . . . . . .
10.2 Utility possibilities: Prisoner’s Dilemma . . . . . . . . .
10.3 Equilibrium in mixed strategy . . . . . . . . . . . . . . .
10.4 Alf’s pure and mixed strategies . . . . . . . . . . . . . .
10.5 Cournot –the reaction function . . . . . . . . . . . . . .
10.6 Cournot-Nash equilibrium . . . . . . . . . . . . . . . . .
10.7 Simpli…ed one-shot Cournot game . . . . . . . . . . . .
10.8 Bertrand model . . . . . . . . . . . . . . . . . . . . . . .
10.9 Sequential move –extensive form . . . . . . . . . . . . .
10.10Game and subgame (1) . . . . . . . . . . . . . . . . . .
10.11Game and subgame (2) . . . . . . . . . . . . . . . . . .
10.12An incredible threat . . . . . . . . . . . . . . . . . . . .
10.13Repeated Prisoner’s Dilemma . . . . . . . . . . . . . . .
10.14Utility possibilities: Prisoner’s Dilemma with “mixing” .
10.15Leader-follower . . . . . . . . . . . . . . . . . . . . . . .
10.16Entry deterrence . . . . . . . . . . . . . . . . . . . . . .
10.17Alf’s beliefs about Bill . . . . . . . . . . . . . . . . . . .
10.18Entry with incomplete information . . . . . . . . . . . .
10.19Bene…ts of restricting information . . . . . . . . . . . . .

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275
280
282
283
287
288
290
292
294
296
296
299
301
302
306
307
312
316
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 . . . . . . . . . . . . . . . . . .
12.2 The revelation principle . . . . . . . . . . . . . . . .
12.3 Distribution of tastes –Beta(2,7) . . . . . . . . . . .
12.4 First-price auction: bid and probability of winning .
12.5 Distribution of price paid . . . . . . . . . . . . . . .
12.6 A …xed-size project . . . . . . . . . . . . . . . . . . .

12.7 Indi¤erence curves in (z; y)-space and (q; y)-space . .
12.8 Two types of Agent: Full-information solution . . . .
12.9 Two types of Agent: contract design . . . . . . . . .
12.10Output and disposable income under the optimal tax

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387
392
399
400
404
406
411
413
416
423

13.1 Implementation through the market . . . . . . . . . . .
13.2 Non-convexities in production and e¢ ciency: Two cases
13.3 Nonconvexity: e¤ect of the competitive market . . . . .
13.4 Nonconvexity: an e¢ cient fee schedule . . . . . . . . . .
13.5 Nonconvexity: uncertain trade o¤ . . . . . . . . . . . . .
13.6 A fundamental nonconvexity . . . . . . . . . . . . . . .
13.7 Myopic rationality underprovides public good . . . . . .
13.8 The Cournot-Nash solution underprovides . . . . . . . .

13.9 Lindahl solution . . . . . . . . . . . . . . . . . . . . . .
13.10Opportunities for redistribution . . . . . . . . . . . . . .

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434
437

438
439
441
446
454
455
456
463

A.1 (a) A continuous function (b) An upper-hemicontinuous correspondence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.2 Continuous mapping with a …xed point . . . . . . . . . . . . . . .
A.3 Upper hemicontinuous mapping with a …xed point . . . . . . . .
A.4 A strictly convex set in R2 . . . . . . . . . . . . . . . . . . . . . .
A.5 A hyperplane in R2 . . . . . . . . . . . . . . . . . . . . . . . . . .
A.6 A hyperplane separating A and y . . . . . . . . . . . . . . . . . .
A.7 Supporting hyperplane . . . . . . . . . . . . . . . . . . . . . . . .
A.8 A strictly convex function of one variable . . . . . . . . . . . . .
A.9 A strictly concave-contoured (strictly quasiconcave) function . .
A.10 Di¤erent types of stationary point . . . . . . . . . . . . . . . . .
A.11 A case where xi = 0 at the optimum . . . . . . . . . . . . . . . .

489
497
498
500
501
501
503
504
506

509
513

B.1
B.2
B.3
B.4
B.5
B.6
B.7
B.8
B.9

522
523
528
530
530
531
532
533
535

Labour input in two locations . . . . .
Cost minimisation: a corner solution .
Pro…t maximisation: corner solution .
Price changes (i) and (ii) in two cases
Prices di¤er for buying and selling . .
Lexicographic preferences . . . . . . .
Utility maximisation: corner solution .

Quantity discount . . . . . . . . . . .
Gi¤en good . . . . . . . . . . . . . . .

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xx

LIST OF FIGURES
B.10
B.11
B.12
B.13
B.14
B.15
B.16
B.17
B.18
B.19
B.20
B.21

B.22
B.23
B.24
B.25
B.26
B.27
B.28
B.29
B.30
B.31
B.32
B.33
B.34
B.35
B.36
B.37
B.38
B.39
B.40
B.41
B.42
B.43
B.44
B.45
B.46
B.47
B.48
B.49
B.50
B.51

B.52
B.53
B.54

Supply of good 1 . . . . . . . . . . . . . . . . . . . . . . . . . . .
Budget constraint with overtime . . . . . . . . . . . . . . . . . .
Indivisibility in production . . . . . . . . . . . . . . . . . . . . .
Combination of technology sets . . . . . . . . . . . . . . . . . . .
Answer to 2a . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Answer to 2b . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-input, 1-output production function . . . . . . . . . . . . . . .
The attainable set . . . . . . . . . . . . . . . . . . . . . . . . . .
Imports and exports . . . . . . . . . . . . . . . . . . . . . . . . .
The o¤er curves and equilibrium . . . . . . . . . . . . . . . . . .
O¤er curves and multiple equilibria . . . . . . . . . . . . . . . . .
Normalised prices, n = 3 . . . . . . . . . . . . . . . . . . . . . . .
Ambiguous risk attitude . . . . . . . . . . . . . . . . . . . . . . .
CARA: changing . . . . . . . . . . . . . . . . . . . . . . . . . .
CARA: = 2 and = 5 . . . . . . . . . . . . . . . . . . . . . . .
Portfolio choice: playing safe . . . . . . . . . . . . . . . . . . . .
Portfolio choice: plunging in the risky asset . . . . . . . . . . . .
E¤ect of an increase in spread . . . . . . . . . . . . . . . . . . . .
Points that cannot be supported in an equilibrium . . . . . . . .
Utility loss through price distortion . . . . . . . . . . . . . . . . .
Battle of the sexes: extensive form . . . . . . . . . . . . . . . . .
Extensive form: alternative representation . . . . . . . . . . . . .
(a) Battle of sexes (b) Chicken . . . . . . . . . . . . . . . . . . .
Payo¤ possibilities . . . . . . . . . . . . . . . . . . . . . . . . . .
Payo¤s consistent with Nash equilibrium in a repeated Cournot
game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Full-information contracts: fee schedule . . . . . . . . . . . . . .
Full-information contracts: Labour supply for each type . . . . .
Bill masquerades as an a-type in labour supply . . . . . . . . . .
Second best contract: quantity discount . . . . . . . . . . . . . .
Second-best labour contracts . . . . . . . . . . . . . . . . . . . .
Second-best labour contract: attainable set . . . . . . . . . . . .
Indi¤erence curves for quadratic cost . . . . . . . . . . . . . . . .
Bounds on education (1) . . . . . . . . . . . . . . . . . . . . . . .
A simple set of beliefs . . . . . . . . . . . . . . . . . . . . . . . .
No-signalling dominates . . . . . . . . . . . . . . . . . . . . . . .
Bounds on education (2) . . . . . . . . . . . . . . . . . . . . . . .
Equilibrium under the intuitive criterion . . . . . . . . . . . . . .
Implications of monotonicity . . . . . . . . . . . . . . . . . . . .
Monopolistic trading . . . . . . . . . . . . . . . . . . . . . . . . .
A …xed-size project (2) . . . . . . . . . . . . . . . . . . . . . . . .
Two types of Agent: Second-best solution . . . . . . . . . . . . .
Three types of Agent: Second-best solution . . . . . . . . . . . .
Compensating variation measure of welfare . . . . . . . . . . . .
Pro…ts in the nonconvexity example . . . . . . . . . . . . . . . .
High-e¢ ciency type masquerades as low-e¢ ciency type . . . . . .

536
537
539
539
540
540
541
542
543

544
545
547
549
552
552
554
555
556
557
558
562
563
564
566
569
571
572
573
575
576
577
578
579
580
581
582
583
584
585

588
593
595
599
600
601


LIST OF FIGURES

xxi

B.55 Public good provision under lottery . . . . . . . . . . . . . . . . . 605


xxii

LIST OF FIGURES


Preface
Acknowledgements for 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 actions logically to certain
principles; he therefore invents these a posteriori in order to justify
his actions. –Vilfredo Pareto, “The rise and fall of the elites”(1968,
p. 27)

1.1

The rôle of microeconomic principles

Why principles in microeconomics? Principles take you further than pure economic theory; principles show you the reasons underlying good practice in applied economics; principles 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 understanding 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 technical 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 microeconomics 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