Symmetry and Economic Invariance

Ryuzo SatoRyuzo 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.RamachandranRama 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)

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)

• Part I  Introduction1  Introduction1.1 GROUP THEORY AND CLASSIFICATION OF MATHEMATICAL STRUCTURE1.2 LIE GROUPS AND INVARIANCE1.3 ECONOMIC APPLICATIONS OF LIE GROUPS 2  Technical Progress and Economies of Scale: Concept of Holotheticity2.1 A REFORMULATION OF THE PROBLEM2.2 LIE GROUPS2.3 HOLOTHETICITY2.4 CONCLUSION 3  Holothetic Production Functions and Marginal Rate of Technical Substitution3.1 TYPES OF TECHNICAL PROGRESS FUNCTIONS AND HOLOTHETICITY3.2 MARGINAL RATE OF TRANSFORMATION AND EXTENDED TRANSFORMATION3.3 HOLOTHETICITY AND LIE BRACKET3.4 CONCLUSION 4 Utility and Demand4.1 INTEGRABILITY CONDITIONS4.2 CONCLUSION 5  Duality and Self Duality5.1 DUALITY IN CONSUMER THEORY5.2 SEPARABILITY AND ADDITIVITY5.3 SELF-DUALITY IN DEMAND THEORY5.4 A METHOD OF DERIVING SELF-DUAL DEMAND FUNCTIONS5.5EMPIRICAL ESTIMATION OF SELF-DUAL DEMAND FUNCTIONS5.6 IMPLICIT SELF-DUALITY OF PRODUCTION AND COST FUNCTIONS5.7 CONCLUSION 6  The Theory of Index Numbers6.1 STATISTICAL APPROACH6.2 TEST APPROACH6.3 ECONOMIC INDEX NUMBERS6.4 DIVISIA INDEX 7  Dynamics and Conservation Laws7.1 THE VARIATIONAL PROBLEM AND THE RAMSEY RULE7.2 STEADY STATE AND THE GOLDEN RULES7.3 THE HAMILTONIAN FORMULATION AND CONTROL THEORY7.4 NOETHER THEOREM AND ITS IMPLICATIONS7.5 CONSERVATION LAWS IN VON NEUMANN MODEL7.6 MEASUREMENT OF NATIONAL INCOME AND INCOME-WEALTH RATIOS7.7 CONCLUSION Part II  Recent Developments8  The Invariance Principle and Income-Wealth Conservation Laws8.1 INTRODUCTION8.2 BRIEF SUMMARY OF THE LITERATURE8.3 A MODEL WITH HETEROGENEOUS CAPITAL GOODS8.4 NOETHER’S THEOREM (INVARIANCE PRINCIPLE8.5 INCOME-WEALTH CONSERVATION LAWS8.6 SPECIAL CASES8.7 GENERALIZED INCOME/ WEALTH CONSERVATION LAWS8.8 INCOME-CAPITAL (WEALTH) CONSERVATION LAWIN THE VON NEUMANN MODEL8.9 THE TOTAL VALUE CONSERVATION LAWOF THE FIRM8.10 EMPIRICAL APPLICATIONS8.11 SUMMARY 9  Conservation Laws in Continuous and Discrete Models---In memory of Professor Mineo Ikeda9.1 INTRODUCTION9.2 CONTINUOUS MODELS9.3 DISCRETE MODELS (2012 VERSION) BY SHIGERU MAEDA9.4 SUMMARY 10  Quantity or Quality: The Impact of Labour Saving Innovation on US and Japanese Growth Rates, 1960–200410.1 INTRODUCTION10.2 A MODEL OF BIASED (LABOUR SAVING) TECHNICAL CHANGE10.3 APPLICATIONS TO THE US AND JAPANESE DATA10.4 CONCLUSION 11  A Survey on Recent Developments11.1 Introduction11.2 Extensions of the Income-Wealth Conservation Law11.3 Externalities and Policy Interventions 11.4 Stochastic Income and Wealth Conservation Law11.5 Warning11.6 Conservation Laws and Helmholtz Conditions11.7 Comparisons: Three Approaches11.8 Hartwick Rule and Conservation Laws11.9 More Abstract Applications of Group Theory to Economics and Finance 12  Appendix to Part II---Symmetry: An Overview of Geometric Methods in Economics12.1 INTRODUCTION12.2 TOOLBOX12.3 HOLOTHETICITY: SYMMETRY OF THE ISOQUANT MAP12.4 EXAMPLES OF CONSERVATION LAWS IN ECONOMICS12.5 CONCLUSION