Advanced Microeconomics

625 Pages·2021·5.825 MB·english

by  Harald Wiese

Harald Wiese
Advanced
Microeconomics
Advanced Microeconomics
Harald Wiese
Advanced Microeconomics
Harald Wiese
Fakultät Wirtschaftswissenschaften
Universität Leipzig
Leipzig, Germany
ISBN 978-3-658-34958-5 ISBN 978-3-658-34959-2 (eBook)
https://doi.org/10.1007/978-3-658-34959-2
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Für Corinna, Ben, Jasper und Samuel
Preface
What is this book about?
This is a course on advanced microeconomics. It covers a lot of ground,
from decision theory to game theory, from bargaining to auction theory,
from household theory to oligopoly theory, and from the theory of general
equilibrium to regulation theory. It has been used for several years at the
university of Leipzig in the Master program “Economics”. A lecturer may
find advisable to make some more difficult material non-obligatory, as I do
in Leipzig.
What about mathematics ... ?
A course in advanced microeconomics can use more advanced mathematics,
such as open sets or Brouwer’s fix-point theorem. I decided not to relegate
theseconceptstoanappendixbuttodealwiththemwheretheyareneeded.
Exercises and solutions
The main text is interspersed with questions and problems. Solutions or
hints are given at the end of each chapter. On top, we add a few exercises
without solutions.
Thank you!
Frank Hüttner translated some of the material from German to English.
He and Andreas Tutic suggested both interesting and boring exercises.
Franziska Beltz improved the quality of the many figures in the textbook.
Somegenerationsofstudentsalsoprovidedfeedbackthathelpedtoimprove
the manuscript. Michael Diemer, Pavel Brendler, Mathias Klein, Hendrik
Kohrs,MaxLillack,KatharinaLotzen,andKatharinaZalewskideservespe-
cial mention. Hendrik Kohrs and Katharina Lotzen checked the manuscript
and the corresponding slides in detail. The latter also produced the index.
Vital last-minute help with technical matters was provided by Alexander
Singer. He and Johanna Freistühler checked the manuscript for remaining
mistakes.
Leipzig, June 2021 Harald Wiese
Contents
Chapter I. Cooperation as the central focus of microeconomics 1
1. Three modes of cooperation 1
2. This book 3
Part A. Basic decision and preference theory 7
Chapter II. Decisions in strategic form 9
1. Introduction and three examples 9
2. Sets, functions, and real numbers 12
3. Dominance and best responses 15
4. Mixed strategies and beliefs 17
5. Rationalizability 23
6. Topics and literature 25
7. Solutions 25
8. Further exercises without solutions 29
Chapter III. Decisions in extensive form 31
1. Introduction and two examples 31
2. Decision trees and actions 33
3. Strategies and subtrees: perfect information 35
4. Strategies and subtrees: imperfect information 42
5. Moves by nature, imperfect information, and perfect recall 47
6. Topics 51
7. Solutions 51
8. Further exercises without solutions 56
Chapter IV. Ordinal preference theory 59
1. The vector space of goods and its topology 59
2. Preference relations 65
3. Axioms: convexity, monotonicity, and continuity 69
4. Utility functions 74
5. Quasi-concave utility functions and convex preferences 79
6. Marginal rate of substitution 82
IX
X CONTENTS
7. Topics 87
8. Solutions 88
9. Further exercises without solutions 92
Chapter V. Decisions under risk 93
1. Simple and compound lotteries 93
2. The St.Petersburg lottery 96
3. Preference axioms for lotteries 100
4. Risk attitudes 103
5. Stochastic dominance 110
6. Topics 118
7. Solutions 119
8. Further exercises without solutions 125
Part B. Household theory and theory of the firm 127
Chapter VI. The household optimum 129
1. Budget 129
2. The household optimum 135
3. Comparative statics and vocabulary 142
4. Solution theory 151
5. Indirect utility function 159
6. Consumer’s rent and Marshallian demand 162
7. Topics 165
8. Solutions 165
9. Further exercises without solutions 171
Chapter VII. Comparative statics and duality theory 173
1. The duality approach 173
2. Envelope theorems and Shephard’s lemma 180
3. Concavity, the Hesse matrix, and the Hicksian law of demand 184
4. Slutsky equations 190
5. Compensating and equivalent variations 196
6. Topics 205
7. Solutions 205
8. Further exercises without solutions 208
Chapter VIII. Production theory 209
1. The production set 209
2. Efficiency 213
3. Convex production sets and convave production functions 219
CONTENTS XI
4. Exploring the production mountain (function) 222
5. Topics 228
6. Solutions 228
7. Further exercises without solutions 230
Chapter IX. Cost minimization and profit maximization 231
1. Revisiting the production set 231
2. Cost minimization 233
3. Long-run and short-run cost minimization 238
4. Profit maximization 240
5. Profit maximization? 244
6. The separation function of markets 253
7. Topics 255
8. Solutions 255
9. Further exercises without solutions 260
Part C. Games and industrial organization 261
Chapter X. Games in strategic form 263
1. Introduction, examples, and definition 263
2. Dominance 269
3. Best responses and Nash equilibria 274
4. ... for mixed strategies, also 276
5. Existence and number of mixed-strategy equilibria 281
6. Critical reflections on game theory 283
7. Topics 285
8. Solutions 285
9. Further exercises without solutions 288
Chapter XI. Price and quantity competition 289
1. Monopoly: Pricing policy 289
2. Price competition 294
3. Monopoly: quantity policy 299
4. Quantity competition 312
5. Topics and literature 322
6. Solutions 323
7. Further exercises without solutions 328
Chapter XII. Games in extensive form 329
1. Examples 329
2. Defining strategies 341
XII CONTENTS
3. Subgame perfection and backward induction 344
4. Multi-stage games 346
5. Product differentiation 349
6. Application: Strategic trade policy 356
7. Topics and literature 361
8. Solutions 361
9. Further exercises without solutions 366
Chapter XIII. Repeated games 367
1. Example: Repeating the pricing game 367
2. Definitions 371
3. Equilibria of stage games and of repeated games 372
4. The infinitely repeated prisoners’ dilemma 374
5. Topics 378
6. Solutions 378
7. Further exercises without solutions 380
Part D. Bargaining theory and Pareto optimality 381
Chapter XIV. Pareto optimality in microeconomics 383
1. Introduction: Pareto improvements 383
2. Identical marginal rates of substitution 384
3. Identical marginal rates of transformation 390
4. Equality of marginal rates of substitution and transformation 392
5. Topics 398
6. Solutions 398
7. Further exercises without solutions 402
Chapter XV. Cooperative game theory 403
1. Introduction 403
2. The coalition function 403
3. Summing and zeros 405
4. Solution correspondences 406
5. The Shapley value 411
6. Simple games 416
7. Five non-simple games 420
8. Topics and literature 425
9. Solutions 425
Chapter XVI. The Rubinstein bargaining model 433
1. Introduction 433