Overlapping Generations Economies

by Tvede, Mich

• ISBN13: 9780230243330
• ISBN10: 0230243339
• Format: Hardcover
• Copyright: 2010-06-15
• Publisher: Red Globe Pr

Summary

In the past two decades the overlapping generations (OG) model has become a dominant framework in macroeconomic analysis. This book provides a clear and self-contained introduction to OG economies. Starting with the existence of equilibrium and the optimality of allocations, the discussion then turns to properties of equilibria, including the existence of fluctuations and sunspot equilibria, ending with applications to the theories of exchange rates and endogenous growth. Throughout the book, OG economies are compared and contrasted with optimal growth economies. The presentation includes detailed proofs of results as well as illustrative examples. Growing out of research and teaching experience on the subject, the book is suitable for advanced students and researchers.

Author Biography

PROFESSOR MICH TVEDE is at the Department of Economics, University of Copenhagen, Denmark. His research interests include consumer theory, economic dynamics, general equilibrium and incomplete financial markets

Table of Contents

Preface	p. xvii
Introduction	p. 1
Overlapping Generations Economies
Pure Exchange OG Economies	p. 7
Structure and Assumptions	p. 7
Expectations	p. 10
Demand	p. 11
Equilibria	p. 14
Forward Markets	p. 18
Exercises	p. 19
Optimality	p. 23
Allocations and Reallocations	p. 23
Improving Reallocations and Their Properties	p. 25
Notions of Pareto Optimality	p. 28
The Welfare Theorems	p. 31
Optimality of Allocations	p. 33
Parametric Reduced Models	p. 38
Optimality of Equilibrium Allocations	p. 41
Exercises	p. 44
Optimal Growth Economies	p. 47
Structure and Assumptions	p. 47
Forward Markets	p. 49
Optimality	p. 54
Spot Markets and Debt Constraints	p. 57
Comparison with OG Economies	p. 61
Exercises	p. 61
Stationary OG Economies	p. 63
Assumptions	p. 63
Equilibria	p. 64
Optimality	p. 66
Steady States	p. 68
On the Set of Equilibria	p. 70
Strongly Pareto Optimal Allocations	p. 73
Stationary Optimal Growth Economies	p. 77
Exercises	p. 78
Fluctuations	p. 81
Two-Cycles	p. 81
n-Cycles	p. 85
Sunspot Equilibria	p. 89
Endowment Vectors and Fluctuations	p. 96
Optimal Growth Economies	p. 98
Exercises	p. 99
Currencies	p. 101
Structure and Assumptions	p. 101
Consumers	p. 102
Equilibria	p. 103
On the Set of Equilibria	p. 108
Exercises	p. 113
OG Economies with Production	p. 115
Structure and Assumptions	p. 115
Demand, Supply and Equilibrium	p. 117
Allocations and Reallocations	p. 121
Optimality	p. 126
Steady States	p. 127
Fluctuations	p. 129
Optimal Growth Economies	p. 130
Exercises	p. 138
Endogenous Growth	p. 141
Structure and Assumptions	p. 141
Constant Returns to Scale	p. 142
Externalities	p. 144
Knowledge and Human Capital	p. 147
Endogenous Growth and Optimality	p. 152
Exercises	p. 153
Consumers and Firms
Consumers	p. 157
Assumptions and Their Implications	p. 157
Utility Maximization	p. 161
Demand: Price and Income	p. 164
Demand: Relative Price and Endowment	p. 169
Many Goods	p. 175
Exercises	p. 175
Preferred Sets and Support Functions	p. 177
Preferred Sets	p. 177
Support Functions	p. 179
Exercises	p. 188
Consumers under Uncertainty	p. 189
Assumptions and Their Implications	p. 189
Utility Maximization	p. 193
Demand: Price and Income	p. 195
Demand: Relative Price and Endowment	p. 197
Exercises	p. 199
Firms	p. 201
Assumptions and Their Implications	p. 201
Profit Maximization	p. 203
Supply	p. 206
Exercises	p. 210
Sequences, Sets and Functions	p. 213
Differentiability of Functions	p. 217
Separation of Convex Sets	p. 219
Dynamical Systems	p. 223
References	p. 229
Index	p. 233
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