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. 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