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One of the most active, influential, and respected economists of the twentieth century, Kenneth J. Arrow was born in New York City in 1921 and remained in that city through his early adulthood. After receiving a bachelor of sciences degree in mathematics from the City College of New York in 1940, he obtained a master’s degree in the same field from Columbia University in 1941. During his graduate training in mathematical statistics his teachers Harold Hotelling (born 1895) and Abraham Wald nudged him toward economics. After working at the Cowles Commission in Chicago and the RAND Corporation in Santa Monica, Arrow received a doctorate in economics from Columbia University in 1951. He started his career at Stanford University and returned to that institution after spending the years from 1968 through 1979 at Harvard University. It was during that period, in 1972, that Arrow shared the Nobel Memorial Prize with John R. Hicks “for pioneering contributions to general equilibrium theory and welfare theory.” In welfare theory Arrow’s impossibility theorem is a towering achievement, and in general equilibrium theory Arrow is one of the founding fathers, along with Gerard Debreu.
Three distinct schools can be identified in post–World War II (1939–1945) American neoclassical demand theory (Mirowski and Hands 1998): the Chicago School, the Cowles Commission (at the University of Chicago), and Paul A. Samuelson’s Massachusetts Institute of Technology (MIT). All three offered different solutions to the problem of the relationship of the law of demand to utility maximization and the interdependence of income constraints and income effects.
Arrow’s contributions concern the so-called Cowles approach. Arrow’s impossibility theorem was developed in his doctoral dissertation and established that under certain assumptions about people’s preferences between options it is always impossible to find a collective choice rule in which one option emerges as the most preferred. In other words, it is logically impossible to add up or otherwise combine the choices of individuals into an unambiguous social choice. This has major implications for welfare economics and theories of justice. Along with Debreu, Arrow gave the first rigorous proof of the existence of a marketclearing equilibrium given certain restrictive assumptions. He extended the analysis to incorporate uncertainty, evaluate stability, and assess efficiency. The restrictive conditions under which the existence of equilibriums could be established, the difficulties encountered in efforts to prove the stability and uniqueness of competitive equilibriums, and the general perception of limited usefulness have caused a shift away from Arrow-Debreu general equilibrium theory toward game theory in microeconomics.
Areas in which Arrow’s legacy is most persistent are growth theory and information economics. In growth theory his research on innovation and learning by doing has served as a major inspiration for endogenous growth theory. For instance, Arrow was the first to construct a theoretical model of learning by doing, which was followed by many empirical studies by others. Yet whereas Arrow had imposed the restriction that increasing only capital (or only labor) does not lead to increasing returns, endogenous growth theorists such as Paul Romer (b. 1955) have gone to great lengths to disqualify that restriction. In information economics Arrow’s evaluations of problems caused by asymmetric information in markets endure in analyses of moral hazard, adverse selection, and so on. Arrow’s asymmetric information insights are of further importance for analyzing specific topics such as discrimination and education. For instance, Arrow offered the best and most complete model of racial wage differentials that are not based on productivity by making the phenomenon compatible with competitive equilibrium theory, more specifically by developing a model that includes signaling and screening mechanisms under conditions of asymmetric information.
Arrow’s insights have not gone without criticism. His impossibility theorem in particular has sparked a literature that has found other impossibilities as well as some possibility results. For example, if one weakens the requirement that the social choice rule must create a social preference ordering that satisfies transitivity and instead only requires acyclicity, there exist social choice rules that satisfy Arrow’s requirements. In addition, Amartya Sen (1982) has suggested at least two other alternatives based on relaxation of transitivity and removal of the Pareto principle. This has enabled Sen to show the existence of voting mechanisms that comply with all of Arrow’s criteria but supply only semitransitive results. In response to Arrow’s model of racial discrimination, others have developed a long list of criticisms and countered that the phenomenon must be understood in terms of the dual labor market hypothesis or radical models that build on the work of multiple labor analysts yet have added twists of their own. In spite of or perhaps as a result of these critical responses, Arrow’s legacy within the economics profession is as rich as his work.
- Arrow, Kenneth J. 1951. Social Choice and Individual Values. New York: Wiley.
- Arrow, Kenneth J. 1962. The Economic Implications of Learning by Doing. Review of Economic Studies 29: 155–173.
- Arrow, Kenneth J. 1963. Uncertainty and the Welfare Economics of Medical Care. American Economic Review 53: 941–973.
- Arrow, Kenneth J.  1964. The Role of Securities in the Optimal Allocation of Risk-Bearing. Review of Economics Studies 31: 91–96.
- Arrow, Kenneth J. 1971. Essays in the Theory of Risk Bearing. Chicago: Markham Publishing.
- Arrow, Kenneth J. 1974. The Limits of Organization. New York: Norton.
- Arrow, Kenneth J., and Gerard Debreu. 1954. The Existence of an Equilibrium for a Competitive Economy. Econometrica 22 (3): 265–290.
- Arrow, Kenneth J., and Frank H. Hahn. 1971. General Competitive Analysis. San Francisco: Holden-Day.
- Feiwel, George R., ed. 1987. Arrow and the Ascent of Modern Economic Theory. New York: New York University Press.
- Marshall, Ray. 1974. The Economics of Racial Discrimination: A Survey. Journal of Economic Literature 12: 849–871.
- Mirowski, Philip, and D. Wade Hands. 1998. A Paradox of Budgets: The Postwar Stabilization of American Neoclassical Demand Theory. In From Interwar Pluralism to Postwar Neoclassicism, eds. Mary Morgan and Malcolm Rutherford, 260–292. London and Durham, NC: Duke University Press.
- Sen, Amartya. 1982. Choice, Welfare, and Measurement. Oxford: Blackwell.
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