Symmetry and Economic Invariance

Symmetry and Economic Invariance (second enhanced edition) explores how the symmetry and invariance of economic models can provide insights into their properties. Although the professional economist of today is adept at many of the mathematical techniques used in static and dynamic optimization models, group theory is still not among his or her repertoire of tools. The authors aim to show that group theoretic methods form a natural extension of the techniques commonly used in economics and that they can be easily mastered. Part I provides an introduction that minimizes prerequisites including prior knowledge of group theory. Part II discusses recent developments in the field.

List of contents

Part I Introduction
1 Introduction
1.1 GROUP THEORY AND CLASSIFICATION OF MATHEMATICAL STRUCTURE
1.2 LIE GROUPS AND INVARIANCE
1.3 ECONOMIC APPLICATIONS OF LIE GROUPS

2 Technical Progress and Economies of Scale: Concept of Holotheticity
2.1 A REFORMULATION OF THE PROBLEM
2.2 LIE GROUPS
2.3 HOLOTHETICITY
2.4 CONCLUSION

3 Holothetic Production Functions and Marginal Rate of Technical Substitution
3.1 TYPES OF TECHNICAL PROGRESS FUNCTIONS AND HOLOTHETICITY
3.2 MARGINAL RATE OF TRANSFORMATION AND EXTENDED TRANSFORMATION
3.3 HOLOTHETICITY AND LIE BRACKET
3.4 CONCLUSION

4 Utility and Demand
4.1 INTEGRABILITY CONDITIONS
4.2 CONCLUSION

5 Duality and Self Duality
5.1 DUALITY IN CONSUMER THEORY
5.2 SEPARABILITY AND ADDITIVITY
5.3 SELF-DUALITY IN DEMAND THEORY
5.4 A METHOD OF DERIVING SELF-DUAL DEMAND FUNCTIONS
5.5EMPIRICAL ESTIMATION OF SELF-DUAL DEMAND FUNCTIONS
5.6 IMPLICIT SELF-DUALITY OF PRODUCTION AND COST FUNCTIONS
5.7 CONCLUSION

6 The Theory of Index Numbers
6.1 STATISTICAL APPROACH
6.2 TEST APPROACH
6.3 ECONOMIC INDEX NUMBERS
6.4 DIVISIA INDEX

7 Dynamics and Conservation Laws
7.1 THE VARIATIONAL PROBLEM AND THE RAMSEY RULE
7.2 STEADY STATE AND THE GOLDEN RULES
7.3 THE HAMILTONIAN FORMULATION AND CONTROL THEORY
7.4 NOETHER THEOREM AND ITS IMPLICATIONS
7.5 CONSERVATION LAWS IN VON NEUMANN MODEL
7.6 MEASUREMENT OF NATIONAL INCOME AND INCOME-WEALTH RATIOS
7.7 CONCLUSION

Part II Recent Developments
8 The Invariance Principle and Income-Wealth Conservation Laws
8.1 INTRODUCTION
8.2 BRIEF SUMMARY OF THE LITERATURE
8.3 A MODEL WITH HETEROGENEOUS CAPITAL GOODS
8.4 NOETHER'S THEOREM (INVARIANCE PRINCIPLE
8.5 INCOME-WEALTH CONSERVATION LAWS
8.6 SPECIAL CASES
8.7 GENERALIZED INCOME/ WEALTH CONSERVATION LAWS
8.8 INCOME-CAPITAL (WEALTH) CONSERVATION LAW
IN THE VON NEUMANN MODEL
8.9 THE TOTAL VALUE CONSERVATION LAWOF THE FIRM
8.10 EMPIRICAL APPLICATIONS
8.11 SUMMARY

9 Conservation Laws in Continuous and Discrete Models---In memory of Professor Mineo Ikeda
9.1 INTRODUCTION
9.2 CONTINUOUS MODELS
9.3 DISCRETE MODELS (2012 VERSION) BY SHIGERU MAEDA
9.4 SUMMARY

10 Quantity or Quality: The Impact of Labour Saving Innovation on US and Japanese Growth Rates, 1960-2004
10.1 INTRODUCTION
10.2 A MODEL OF BIASED (LABOUR SAVING) TECHNICAL CHANGE
10.3 APPLICATIONS TO THE US AND JAPANESE DATA
10.4 CONCLUSION

11 A Survey on Recent Developments
11.1 Introduction
11.2 Extensions of the Income-Wealth Conservation Law
11.3 Externalities and Policy Interventions
11.4 Stochastic Income and Wealth Conservation Law
11.5 Warning
11.6 Conservation Laws and Helmholtz Conditions
11.7 Comparisons: Three Approaches
11.8 Hartwick Rule and Conservation Laws
11.9 More Abstract Applications of Group Theory to Economics and Finance

12 Appendix to Part II---Symmetry: An Overview of Geometric Methods in Economics
12.1 INTRODUCTION
12.2 TOOLBOX
12.3 HOLOTHETICITY: SYMMETRY OF THE ISOQUANT MAP
12.4 EXAMPLES OF CONSERVATION LAWS IN ECONOMICS
12.5 CONCLUSION

About the author

Ryuzo Sato is a C. V. Starr Professor Emeritus of Economics at the Stern School of Business, New York University. He was director of the Center for Japan U.S. Business and Economic Studies at the Stern School. Prior to becoming a Stern faculty member, he was a professor of economics at Brown University. Professor Sato also taught at Harvard University, The University of Tokyo, Kyoto University, and Bonn University. He was the founding chief editor of Japan and the World Economy, an international theory and policy journal. For more than 40 years, Professor Sato has divided his time between Japan and the United States, and he conducts research, gives lectures, and writes on the subject of Japan U.S. relations. Professor Sato, who was a Fulbright Scholar, received his B.A. in economics and his Dr. Economics from Hitotsubashi University in Tokyo, and his Ph.D. in economics from Johns Hopkins University. His principal areas of research interest are mathematical economics and economic growth.

Summary

Symmetry and Economic Invariance (second enhanced edition) explores how the symmetry and invariance of economic models can provide insights into their properties. Although the professional economist of today is adept at many of the mathematical techniques used in static and dynamic optimization models, group theory is still not among his or her repertoire of tools. The authors aim to show that group theoretic methods form a natural extension of the techniques commonly used in economics and that they can be easily mastered. Part I provides an introduction that minimizes prerequisites including prior knowledge of group theory. Part II discusses recent developments in the field.

Additional text

From the book reviews:
“The monograph provides an introduction to the application of group theory, a mathematical tool, to examine the structure of economic models. … It will be useful for postgraduate students and researches specializing in dynamical models of economics.” (Sergei Georgievich Zhuravlev, zbMATH, Vol. 1291, 2014)

Report

From the book reviews:
"The monograph provides an introduction to the application of group theory, a mathematical tool, to examine the structure of economic models. ... It will be useful for postgraduate students and researches specializing in dynamical models of economics." (Sergei Georgievich Zhuravlev, zbMATH, Vol. 1291, 2014)

Product details

• Authors: T. Kobayashi, Rama V Ramachandran, Rama V. Ramachandran, Ryuz Sato, Ryuzo Sato
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 01.02.2014
• EAN: 9784431544296
• ISBN: 978-4-431-54429-6
• No. of pages: 273
• Dimensions: 163 mm x 242 mm x 17 mm
• Weight: 574 g
• Illustrations: XII, 273 p. 44 illus.
• Series: Advances in Japanese Business and Economics; Advances in Japanese Business and Economics
• Subject: Social sciences, law, business > Business > Economics