Symmetry and Economic Invariance

1. Front Matter

   Pages i-xii

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2. Introduction

   1. Front Matter

      Pages 1-1

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   2. Introduction

      • Ryuzo Sato, Rama V. Ramachandran

      Pages 3-12

   3. Technical Progress and Economies of Scale: Concept of Holotheticity

      • Ryuzo Sato, Rama V. Ramachandran

      Pages 13-28

   4. Holothetic Production Functions and Marginal Rate of Technical Substitution

      • Ryuzo Sato, Rama V. Ramachandran

      Pages 29-41

   5. Utility and Demand

      • Ryuzo Sato, Rama V. Ramachandran

      Pages 43-53

   6. Duality and Self Duality

      • Ryuzo Sato, Rama V. Ramachandran

      Pages 55-72

   7. The Theory of Index Numbers

      • Ryuzo Sato, Rama V. Ramachandran

      Pages 73-85

   8. Dynamics and Conservation Laws

      • Ryuzo Sato, Rama V. Ramachandran

      Pages 87-105

3. Back Matter

   Pages 107-109

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4. Recent Developments

   1. Front Matter

      Pages 111-111

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   2. The Invariance Principle and Income-Wealth Conservation Laws

      • Ryuzo Sato, Rama V. Ramachandran

      Pages 113-142

   3. Conservation Laws in Continuous and Discrete Models

      • Ryuzo Sato, Rama V. Ramachandran

      Pages 143-176

   4. Quantity or Quality: The Impact of Labour Saving Innovation on US and Japanese Growth Rates, 1960–2004

      • Ryuzo Sato, Rama V. Ramachandran

      Pages 177-208

   5. A Survey on Recent Developments

      • Ryuzo Sato, Rama V. Ramachandran

      Pages 209-229

   6. Appendix to Part II. Symmetry: An Overview of Geometric Methods in Economics

      • Ryuzo Sato, Rama V. Ramachandran

      Pages 231-266

5. Back Matter

   Pages 267-273

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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.

• Economic Equilibrium
• Economic Models
• Group-theoretic Analysis
• Lie Groups

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)

• New York University Stern School of Business, New York, USA

  Ryuzo Sato

• Plano, USA

  Rama V. Ramachandran

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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