Conservation Laws and Symmetry: Applications to Economics and Finance

Modem geometric methods combine the intuitiveness of spatial visualization with the rigor of analytical derivation. Classical analysis is shown to provide a foundation for the study of geometry while geometrical ideas lead to analytical concepts of intrinsic beauty. Arching over many subdisciplines of mathematics and branching out in applications to every quantitative science, these methods are, notes the Russian mathematician A.T. Fomenko, in tune with the Renais sance traditions. Economists and finance theorists are already familiar with some aspects of this synthetic tradition. Bifurcation and catastrophe theo ries have been used to analyze the instability of economic models. Differential topology provided useful techniques for deriving results in general equilibrium analysis. But they are less aware of the central role that Felix Klein and Sophus Lie gave to group theory in the study of geometrical systems. Lie went on to show that the special methods used in solving differential equations can be classified through the study of the invariance of these equations under a continuous group of transformations. Mathematicians and physicists later recognized the relation between Lie's work on differential equations and symme try and, combining the visions of Hamilton, Lie, Klein and Noether, embarked on a research program whose vitality is attested by the innumerable books and articles written by them as well as by biolo gists, chemists and philosophers.

Autorentext
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.

Zusammenfassung
' This book is recommendable to mathematicians in the field of differential geometry and calculus of variations, who take an interest in economic applications ' Journal of Economic 55:3 1992

Inhalt
1 Symmetry: An Overview of Geometric Methods in Economics.- 2 Law of Conservation of the Capital-Output Ratio in Closed von Neumann Systems.- 3 Two Conservation Laws in Theoretical Economics.- 4 The Invariance Principle and Income-Wealth Conservation Laws.- 5 Conservation Laws Derived via the Application of Helmholtz Conditions.- 6 Conservation Laws in Continuous and Discrete Models.- 7 Choice as Geometry.- 8 Symmetries, Dynamic Equilibria, and the Value Function.- 9 On Estimating Technical Progress and Returns to Scale.- 10 On the Functional Forms of Technical Change Functions.