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Saturday, April 22, 2017

Kenneth Arrow and mathematical economics


Photo source: Wikimedia Commons, Linda A. Cicero

Photo license: CC BY 3.0


Kenneth Arrow (1921-2017) is an influential economist best known for his contributions to mathematical economics. He is also the recipient of the 1972 Nobel Prize in Economics. Economic journalist David Warsh said,


"Years late, when economist would argue among themselves about who had been the greatest economist of the twentieth century - Keynes? Schumpeter? Von Neumann? Samuelson? Friedman? - the answer that won out among the top economists, more often than not, was Kenneth Arrow." (The Knowledge and Wealth of Nations, 2006)


Economist Tyler Cohen said,


"In technical economics, I see a peak with Paul Samuelson and Kenneth Arrow and some of the core developments in game theory. Since then there are fewer iconic figures being generated in this area of research, even though there are plenty of accomplished papers being published." (Why Is There No New Milton Friedman Today? 2013)


The rest of this post is some quotes from Arrow,


General equilibrium theory


"Leon Walras first formulated the state of the economic system at any point of time as the solution of a system of simultaneous equations representing the demand for goods by consumers, the supply of goods by producers and the equilibrium condition that supply equal demand on every market." (Existence of an equilibrium for a competitive economy, 1954)


"The evidence is clear that the development of general equilibrium theory would have gone on quite as it did without me." (November 1984 lecture at Trinity University)


Welfare theory


"While economic theory in general may be defined as the theory of how an economic condition or an economic development is determined within an institutional framework, the welfare theory deals with how to judge whether one condition can be said to be better in some way than another and whether it is possible, by altering the institutional framework, to achieve a better condition than the present one." (Nobel Lectures, Economics 1972)


Decision theory


"Decision theory, as it has grown up in recent years, is a formalization of the problems involved in making optimal choices. In a certain sense - a very abstract sense, to be sure - it incorporates among others operations research, theoretical economics, and wide areas of statistics, among others." (The Economics of Information , 1984)


"The formal structure of a decision problem in any area can be put into four parts: 1. the choice of an objective function denning the relative desirability of different outcomes; 2. specification of the policy alternatives which are available to the agent, or decisionmaker, 3. specification of the model, that is, empirical relations that link the objective function, or the variables that enter into it, with the policy alternatives and possibly other variables; and 4. computational methods for choosing among the policy alternatives that one which performs best as measured by the objective function." (The Economics of Information , 1984)