The theory of existence of general equilibrium in the history of mathematical economics (1838-1976).

摘要

This dissertation is an attempt at providing different paradigms involved in the development of the existence of general equilibrium proofs based on historiographical approach. The following issues have been highlighted in this dissertation: the factors which lead the general equilibrium theorists to develop the model of existence of general equilibrium; the individuals responsible for identifying the problem associated with the earlier general equilibrium theory; the link between earlier and the modern theory of existence of equilibrium; the individual or group who develop the first existence proofs; the contributions of the modern existence theorists of general equilibrium and the approach finally did emerge. Cournot, Walras, Pareto and Cassel are identified as the contributors on the existence issue at the earlier analysis. The lag between the development of mathematical tools and the application of it in the theory of existence of general equilibrium are also investigated.;The existence of equilibrium proofs during the 1930s connect the Vienna circle of the mathematician Karl Menger, Mathematical Colloquium, Morgenstern to Karl Schlesinger, Abraham Wald and John von Neumann. Schlesinger is shown to be the real link between the earlier and the 1930s existence proof of general equilibrium. The 1930s is considered to be a period when the axiomatic approach revisited for the first time in the existence question. Hick's Value and Capital is shown to have profound influence on the existence of general equilibrium proofs in the 1950s.;The next step focuses on the events that paves the way to the proof of existence of general equilibrium in the 1950s in the United States. Linear programming, activity analysis, game theory, Nash equilibrium, Kakutani fixed point theorem and the Econometric Society are shown to be related to the development of the existence proofs of general equilibrium. The results achieved by Arrow and Debreu in the 1950s (and all subsequent developments in the existence proofs of general equilibrium opened up by them) demonstrate the existence of general equilibrium under very general assumptions. The assumptions are, in fact, those traditionally and fundamentally inherent to Walrasian theory. It is also shown that differential calculus revisited in the existence proof in the 1970s.