Overview

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.

Full Product Details

Author:   Ryuzo Sato ,  Rama V. Ramachandran ,  Rama V. Ramachandran
Publisher:   Springer Verlag, Japan
Imprint:   Springer Verlag, Japan
Edition:   2nd enhanced ed. 2014
Volume:   1
Dimensions:   Width: 15.50cm , Height: 1.80cm , Length: 23.50cm
Weight:   5.561kg
ISBN:  

9784431544296

ISBN 10:   4431544291
Pages:   273
Publication Date:   19 December 2013
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table 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

Reviews

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)

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)

Author Information

Ryuzo Sato Ryuzo Sato is 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 USA, and he conducts research, gives lectures, and writes on the subject of Japan–US relations. Recent work includes Biased Technical Change and Economic Conservation Laws (Springer, 2006), Growth Theory and Technical Change: The Selected Essays of Ryuzo Sato, vol. 1 (Edward Elgar, 1996), Production, Stability and DynamicSymmetry: The Selected Essays of Ryuzo Sato, vol. 2 (Edward Elgar, 1999), and Theory of Technical Change and Economic Invariance: Application of Lie Groups (Academic Press, 1981; reprint, new version, Edward Elgar, 1999). Professor Sato also writes columns regularly for several Japanese newspapers. 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. Rama V.Ramachandran Rama V.Ramachandran received his master’s degree from Madras University, India, and his Ph.D. from Brown University in the U.S.A. He was a faculty member of the Department of Economics of Southern Methodist University and the Department of Economics of the Stern School of Business, New York University. He was associate director of the Center for Japan–U.S. Business and Economics at the Stern School. His research interests were in microeconomics and growth theory. After retirement, he has focused on economic pedagogy and authored an innovative introduction to microeconomics, Opportunities and Choices: Understanding Our Economic Decisions. (http://www.visualeconomicanalysis.info/index.html)

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