Optimal Control of the Growth of Wealth of Nations

by Chukwu; E.N.

• ISBN13: 9780415269667
• ISBN10: 0415269660
• Format: Hardcover
• Copyright: 2003-01-23
• Publisher: CRC Press

Summary

Students and researchers in applied mathematics and applied economics can use this introductory-level graduate text. It looks at the current problems of the development of the global economy by studying the dynamics of key economic variables, such as gross national product, interest rates, employment, value of capital stock, prices (inflation) and balance of payments. Validation of the model is attempted using the economic time series of several countries. The constructed models explain the macroeconomic data of nations as dynamic games of pursuit, which are equivalent to "control" problems and are used to study mathematical optimal control of the growth of the wealth of nations. This invaluable reference for graduates and researchers compares the extent of government intervention in the economy with private firms to ensure the controllability of the economy.

Author Biography

E. N. Chukwu is Professor at the Department of Mathematics, North Carolina State University.

Table of Contents

Dedication	p. ix
Introduction to Series	p. ix
Preface	p. xi
Foreword	p. xvii
References	p. xx
Acknowledgements	p. xxiii
Introduction	p. 1
References	p. 4
Competition and Cooperation: The Social Environment for Economic Activity	p. 7
Introduction	p. 7
Competition: Predator-Prey [40]	p. 9
Density of Wealth	p. 13
Competitive Systems: Uniform Persistence and Extinction	p. 19
A Modern Example of Cooperation [63]	p. 22
A Modern Example of Competition	p. 36
Fundamental Principles	p. 36
Validation from Nobel Laureate Dr. Sen	p. 36
References	p. 38
Economic Dynamics	p. 43
Introduction	p. 43
Balance of Payments	p. 55
Numerical Solutions of Ordinary Differential Equations	p. 62
Parameter Identification	p. 70
Parameter Identification Optimization	p. 75
Validity of Model	p. 81
Appendix 1	p. 90
Appendix 2	p. 93
Appendix 3	p. 101
References	p. 108
Program Nigeria.M	p. 110
Controllable Economic Systems	p. 119
Introduction	p. 119
Differential Games of Pursuit	p. 124
Controllability to a Nonzero Target	p. 128
Cores of Target Sets	p. 133
Are Real National Economies Controllable?	p. 134
Optimal Control	p. 135
Example: Differential Game	p. 145
Ordinary Differential Systems Model of National Economies	p. 151
Ordinary Differential Equation Models	p. 151
The Control Set	p. 179
References Chapters 2-4	p. 181
Oscillation: Conditions for Economic Boom and Criteria for the Prevention of Depression	p. 185
History of Cycle Theory	p. 185
References	p. 186
Oscillation--Introduction	p. 189
Oscillation with Forcing Term in Ordinary Differential Dynamics	p. 192
Non-Linear Oscillatory and Nonoscillatory Models	p. 194
References	p. 198
Chaos in the Deterministic Models of National Economy	p. 198
References	p. 202
References	p. 228
Hereditary Economic Systems	p. 229
Control of Nonlinear Delay Differential Equations in W[subscript 2 superscript (1)] with Economic Applications	p. 229
Introduction	p. 229
Economic Models with Delay	p. 230
Definitions and Main Results	p. 237
Applications	p. 252
Model Structure	p. 254
System Identification	p. 256
References	p. 259
On the Controllability of Nonlinear Economic Systems with Delay: The Italian, Indian, and U.S. Examples	p. 260
Motivation--Economic Models with Delay, the Neutral Case	p. 260
The Theory	p. 275
Nonlinear Government and Private Strategies	p. 282
References	p. 283
Control of Hereditary Linear Models	p. 285
Remark: Economic Systems with Delay in Control	p. 300
References	p. 303
Control Under Scarcity of the Growth of Wealth of Nations: India, Italy and U.S.A. Examples	p. 303
Introduction	p. 303
U.S. Model	p. 305
U.S. Data	p. 308
Function Space Controllability	p. 316
Constrained Controllability: Soft Landing	p. 317
References	p. 320
Programs and Results: Italy and India	p. 323
Oscillation of Hereditary Systems, Conditions for Economic Boom; Criteria for the Prevention of Depression	p. 369
Linear Delay Equations	p. 369
Chaotic Economic System with Delay	p. 376
References	p. 378
Remarks on Nonlinear Hereditary Economic Systems	p. 379
References	p. 379
Index	p. 381
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