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These essays illustrate Ryuzo Sato's contribution to the analysis of the theories of production, preference, stability and dynamic symmetry in economics. He examines production and preference functions containing both goods and money, and studies the stability of general equilibium systems.
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.
Symmetry and Economic Invariance: An Introduction explores how symmetry and invariance of economic models can provide insights into their properties. While the professional economist is nowadays 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.
The johansen schema; An integrated system of production: comments and criticisms; The ex ante function; The ex ante function and the ex post micro function; Aggregate putty-clay functions; Agtregate neoclassical production functions; Neoclassical production functions: fact or fantasy? Production functions - some conclusions.
Production economics is that branch of microeconomics that examines producer decisions. This book focuses on the empirical estimation of these relationships using primal, dual, and differential specifications. The primal specification models production decisions based on the production function — estimation of the input/output relationship and the derivation of optimization behavior from this technical relationship. The dual approach estimates production decisions using economic information such as input and output prices. The textbook then develops the linkages between these relationships. The differential specification is an alternative approach derived from changes in the first-order conditions from cost minimizing behavior. In each case, the theoretical development is followed by different empirical specifications that can be used to estimate the producer's choice.
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.
This work offers detailed coverage of every important aspect of symmetric structures in function of a single real variable, providing a historical perspective, proofs and useful methods for addressing problems. It provides assistance for real analysis problems involving symmetric derivatives, symmetric continuity and local symmetric structure of sets or functions.