Conservation Laws and Symmetry: Applications to Economics and Finance

Editors: Ryuzo Sato, Rama V. Ramachandran



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.

Table of contents

Front Matter
Pages i-xiii

Symmetry: An Overview of Geometric Methods in Economics
Pages 1-51

Law of Conservation of the Capital-Output Ratio in Closed von Neumann Systems
Pages 53-56

Two Conservation Laws in Theoretical Economics
Pages 57-70

The Invariance Principle and Income-Wealth Conservation Laws
Pages 71-106

Conservation Laws Derived via the Application of Helmholtz Conditions
Pages 107-134

Conservation Laws in Continuous and Discrete Models
Pages 135-174

Choice as Geometry
Pages 175-224

Symmetries, Dynamic Equilibria, and the Value Function
Pages 225-259

On Estimating Technical Progress and Returns to Scale
Pages 261-274

On the Functional Forms of Technical Change Functions
Pages 275-299

Back Matter
Pages 301-304