Variational Methods in Economics

✍ Scribed by George Hadley, Murray C. Kemp

• Publisher: Elsevier Science Publishing Co Inc.,U.S
• Year: 1971
• Tongue: English
• Leaves: 383
• Edition: First Edition
• Category: Library

✦ Synopsis

Advanced Textbooks in Economics, Volume 1: Variational Methods in Economics focuses on the application of variational methods in economics, including autonomous system, dynamic programming, and phase spaces and diagrams.

The manuscript first elaborates on growth models in economics and calculus of variations. Discussions focus on connection with dynamic programming, variable end points-free boundaries, transversality at infinity, sensitivity analysis-end point changes, Weierstrass and Legendre necessary conditions, and phase diagrams and phase spaces. The text then ponders on the constraints of classical theory, including unbounded intervals of integration, free boundary conditions, comparison functions, normality, and the problem of Bolza.

The publication explains two-sector models of optimal economic growth, optimal control theory, and connections with the classical theory. Topics include capital good immobile between industries, constrained state variables, linear control problems, conversion of a control problem into a problem of Lagrange, and the conversion of a nonautonomous system into an autonomous system.

The book is a valuable source of information for economists and researchers interested in the variational methods in economics.

✦ Table of Contents

Content:
ADVANCED TEXTBOOKS IN ECONOMICS, Page ii
Front Matter, Page iii
Copyright, Page iv
Preface, Pages v-vi
1 - Growth models in economics, Pages 1-5
2 - Calculus of variations — classical theory, Pages 6-174
3 - Classical theory — constraints, Pages 175-237
4 - Optimal control theory, Pages 238-281
5 - Connections with the classical theory, Pages 282-325
6 - Two-sector models of optimal economic growth, Pages 326-363
Appendix I - Uniqueness of the utility functional and the utility function, Pages 364-366
Appendix II - Implicit function theorems, Pages 367-369
Appendix III - Existence theorems for systems of ordinary differential equations, Pages 370-373
References, Pages 374-376
Index, Pages 377-378