Mathematical Methods in Dynamic... | Buy

This book 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. Mixing traditional and modern materials, the study covers dynamics with and without optimization, naiuml;ve and rational expectations, respectively. In addition to standard models of growth and cycles, the book also contains original studies on control of a multisector economy and expectations-derived multicohort economy.

Andrßs Simonovits is Scientific Advisor at the Institute of Economics, Hungarian Academy of Sciences.

Foreword

Introduction

1

(14)

PART I. DYNAMICS WITHOUT OPTIMIZATION

15

(140)

Linear Difference Equations

17

(32)

Difference equations

17

(6)

General Linear systems

23

(12)

Planar Linear systems

35

(6)

Linear control systems

41

(8)

Discrete-Time Linear Models

49

(19)

Linear model of accelerator--multiplier

49

(7)

Linear models of control by stock signals

56

(5)

Linear decentralized control with expectations

61

(7)

Nonlinear Difference Equations

68

(21)

Existence and stability of fixed points

68

(8)

Limit cycles

76

(2)

Chaos

78

(11)

Discrete-Time Nonlinear Models

89

(25)

Irregular growth cycles

89

(2)

Nonlinear model of accelerator--multiplier

91

(7)

Nonlinear model of control by stock signals

98

(3)

Nonlinear stock control with expectations

101

(4)

Mixed expectations

105

(6)

Related issues

111

(3)

Ordinary Differential Equations

114

(22)

Basic concepts and theorems

114

(9)

Linear systems

123

(6)

Nonlinear systems

129

(4)

Control in continuous time

133

(3)

Continuous-Time Models

136

(19)

Growth models

136

(5)

Government stabilization

141

(3)

Competitive price adjustment

144

(11)

PART II. DYNAMICS WITH OPTIMIZATION

155

(72)

Dynamic Programming

157

(17)

Deterministic principle of optimality

157

(9)

Stochastic principle of optimality

166

(2)

Optimal LQ control with perfect observation

168

(4)

Optimal LQG control with imperfect observation

172

(2)

Applications of Dynamic Programming

174

(17)

Optimal saving

174

(4)

One-sector optimal accumulation

178

(5)

Multisector optimal accumulation

183

(3)

The great fish war

186

(5)

Optimal Control

191

(17)

Basic problem

191

(6)

Calculus of Variations

197

(4)

Supplements

201

(7)

Optimal Consumption Paths

208

(19)

Exogenous wage and interest

208

(5)

Endogenous wage and interest: infinite horizon

213

(5)

Constant capital-output ratio: finite horizon

218

(9)

PART III. SUPPLEMENTS

227

(2)

Appendix A. Linear Algebra

229

(11)

Appendix B. Overlapping Generations

240

(13)

Appendix C. Overlapping Cohorts

253

(30)

C.1 An exchange economy

253

(9)

C.2 Steady states

262

(4)

C.3 Dynamics with rational expectations

266

(9)

C.4 Dynamics with naive expectations

275

(8)

Solutions

283

(12)

References

295

(15)

Index of subjects

310

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