Mathematical Models in Dynamic Economics

✍ Scribed by Andras Simonovitis

• Publisher: Palgrave Macmillan
• Year: 2000
• Tongue: English
• Leaves: 333
• Category: Library

✦ Synopsis

Recently dynamics have begun to play a central role in economics. This book tries to survey the whole field in a unique way. It contains a concise description of important mathematical methods of dynamics and suitable economic models. It covers discrete as well as continuous-time systems, linear and nonlinear models. The book goes beyond the elementary parts of the field by including the treatment of the theory of chaos and dynamic optimization. The book often contains sketches rather than full proofs of difficult topics. Mixing traditional and modern materials, the study covers dynamics with and without optimization. The author compares naive and rational expectations and demonstrates the strengths and weaknesses of both approaches. In addition to standard models of growth and cycle, the book also contains original studies on control of multisector economy and expectations-driven multicohort economy. The study contains numerous examples, problems (with solutions) and figures.

✦ Table of Contents

Cover......Page 1
Half Title......Page 4
Title......Page 6
Copyright......Page 7
Contents......Page 8
Foreword......Page 11
Introduction......Page 14
PART I. DYNAMICS WITHOUT OPTIMIZATION......Page 28
1.1 Difference equations......Page 30
1.2 General linear systems......Page 36
1.3 Planar linear systems......Page 48
1.4 Linear control systems......Page 54
2.1 Linear model of accelerator-multiplier......Page 62
2.2 Linear models of control by stock signals......Page 69
2.3 Linear decentralized control with expectations......Page 74
3.1 Existence and stability of fixed points......Page 81
3.2 Limit cycles......Page 89
3.3 Chaos......Page 91
4.1 Irregular growth cycles......Page 102
4.2 Nonlinear model of accelerator-multiplier......Page 104
4.3 Nonlinear model of control by stock signals......Page 111
4.4 Nonlinear stock control with expectations......Page 114
4.5 Mixed expectations......Page 118
4.6 Related issues......Page 124
5.1 Basic concepts and theorems......Page 127
5.2 Linear systems......Page 136
5.3 Nonlinear systems......Page 142
5.4 Control in continuous time......Page 146
6.1 Growth models......Page 149
6.2 Government stabilization......Page 154
6.3 Competitive price adjustment......Page 157
PART II. DYNAMICS WITH OPTIMIZATION......Page 168
7.1 Deterministic principle of optimality......Page 170
7.2 Stochastic principle of optimality......Page 179
7.3 Optimal LQ control with perfect observation......Page 181
7.4 Optimal LQG control with imperfect observation......Page 185
8.1 Optimal saving......Page 187
8.2 One-sector optimal accumulation......Page 191
8.3 Multisector optimal accumulation......Page 196
8.4 The great fish war......Page 199
9.1 Basic problem......Page 204
9.2 Calculus of Variations......Page 210
9.3 Supplements......Page 214
10.1 Exogenous wage and interest......Page 221
10.2 Endogenous wage and interest: infinite horizon......Page 226
10.3 Constant capital-output ratio: finite horizon......Page 231
PART III. SUPPLEMENTS......Page 240
Appendix A. Linear Algebra......Page 242
Appendix B. Overlapping Generations......Page 253
C.1 An exchange economy......Page 266
C.2 Steady states......Page 275
C.3 Dynamics with rational expectations......Page 279
C.4 Dynamics with naive expectations......Page 288
Solutions......Page 296
References......Page 308
Index of subjects......Page 323