Kenneth J. Arrow (b. 1921)

Kenneth Arrow was born in New York City, USA in 1921. As an undergraduate he studied mathematics at the City College of New York, from where he graduated with a BSc in 1940. Arrow undertook graduate work at Columbia University where he was awarded an MA in mathematics in 1941 and a PhD in 1951. His graduate schooling was, however, interrupted by wartime service in the US Army Air Corps from 1942 to 1946. After the Second World War Arrow worked, from 1946 to 1949, as a research associate at the Cowles Commission for Research in Economics at the University of Chicago, and was appointed Assistant Professor of Economics at Chicago in 1948. In 1949 he moved to Stanford University where he was promoted, in 1953, from Assistant Professor of Economics and Statistics, to Professor of Economics, Statistics and Operations Research. In 1968 he accepted an appointment as Professor of Economics at Harvard University, where he remained before returning to Stanford in 1979 as Joan Kenney Professor of Economics and Professor of Operations Research. Arrow retired in 1991, since when he has been Professor, Emeritus, at Stanford University.

Among his many offices and honours Arrow was awarded the John Bates Clark Medal of the American Economic Association in 1957 and the John von Neumann Theory Prize of ORSA/TIMS in 1986; served as president of the Econometric Society in 1956, the Institute of Management Sciences in 1963, the American Economic Association in 1973, and the International Economic Association from 1983 to 1986; and was a member of the US Council of Economic Advisers in 1962. In 1972 Arrow was awarded, jointly with the British economist John Hicks, the Nobel Memorial Prize in Economics ‘for their pioneering contributions to general economic equilibrium theory and welfare theory’ (Nobel Foundation, 2004).

Arrow is best known for his contributions to the fields of social choice and general equilibrium theory. His most famous and frequently cited work is his 1951 book Social Choice and Individual Values (Arrow, 1951a), which is based on his doctoral thesis. In this work, Arrow generalised Condorcet’s voting paradox (named after the eighteenth-century French politician) to show that it is impossible to derive a voting rule that allows rational individual preferences to be translated into rational social preferences or choices.

Table 2 Voting paradox

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Preference

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Voter 1 2 3
A X Y Z
B Y Z X
C Z X Y

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Arrow’s so-called ‘impossibility theorem’ can be illustrated as follows. Suppose there are three individuals A, B and C whose preferences between three options are summarised in Table 2. Reference to the table reveals that A prefers X to Y and Y to Z; B prefers Y to Z and Z to X; while C prefers Z to X and X to Y. In this situation a majority (two out of three voters, namely A and C) prefer X to Y. A majority (two out of three voters, namely A and B) prefer Y to Z. Unfortunately a majority do not prefer X to Z, as voters B and C prefer Z to X. What emerges under the democratic method of majority choice is a stalemate. In other words, Arrow demonstrated that it is impossible to aggregate an individual’s rational choices to produce an unambiguous, consistent social choice. Studying the consequences of Arrow’s impossibility theorem has resulted in much subsequent work both in political theory and in welfare economics. In the latter case the reader should refer to the entry on Amartya Sen, the 1998 Nobel Memorial Laureate, in this volume.

Arrow’s other main contribution to economics concerns his pioneering work on the existence, stability and optimality of general equilibrium systems. In his 1951 Berkeley Symposium paper, ‘An Extension of the Basic Theorems of Classical Welfare Economics’ (Arrow, 1951b), he showed that general (market) equilibrium states are Pareto optimal and that Pareto-optimal states can be obtained by achieving general (market) equilibrium. More importantly, in his seminal 1954 Econometrica paper, co-written with Gerard Debreu (see entry in this volume), on the ‘Existence of an Equilibrium for a Competitive Economy’, Arrow produced a rigorous and definitive mathematical proof of the existence of general equilibrium in a model of a market economy. Arrow and Debreu established that the proof of the existence of general equilibrium requires forward markets in all goods and services (that is, markets where one can pay today in order to obtain forward or future delivery, or accept delivery today against the promise of a forward or future payment). While this requirement led some economists to cast doubt on the usefulness of the Arrow–Debreu proof, in subsequent work with Frank Hahn, Arrow (1971a) demonstrated the relevance of general equilibrium analysis even to economies where forward markets are missing. In other work Arrow has extended the analysis to consider the stability of competitive equilibria – see, for example, his 1977 book co-edited with Leonid Hurwicz, Studies in Resource Allocation Processes.

In addition to his pioneering work on welfare theory and general equilibrium theory, Arrow has made a number of important contributions to other areas of study. Four examples will suffice. First, he has undertaken work on the theory of inventory and production (for example, Arrow et al., 1958), including the problems of optimal capital investment and optimal production scheduling for private firms. Second, in a famous 1961 paper published in the Review of Economics and Statistics, co-written with Hollis Chenery, Bagicha Minhas and Robert Solow, Arrow introduced a production function that has a constant elasticity of substitution (CES) between labour and capital. Third, in a frequently cited paper published in 1962 in the Review of Economic Studies, ‘The Economic Implications of Learning by Doing’, he constructed a model in which ideas are a byproduct of production or investment that contribute to productivity. Other leading economists (such as Paul Romer) have subsequently built upon this work as part of what has come to be known as the new endogenous growth theory. Fourth, some of Arrow’s most important contributions to the economics of uncertainty can be found in his book Essays in the Theory of Risk-Bearing (Arrow, 1971b), which include work on adverse selection, moral hazard, measures of risk aversion and optimal insurance.
Arrow is a highly respected economist who has made important contributions to a wide range of areas, most notably in economic theory, but also in applied economics. The breadth (and depth) of his work is reflected in the six volumes of his Collected Papers (Arrow, 1983–85) published by Harvard University Press: Social Choice and Justice; General Equilibrium; Individual Choice under Certainty and Uncertainty; The Economics of Information; Production and Capital; and Applied Economics.

Main Published Works
(1951a), Social Choice and Individual Values, New York: John Wiley & Sons; 2nd edn 1963.
(1951b), ‘An Extension of the Basic Theorems of Classical Welfare Economics’, in J. Neyman (ed.), Proceedings of the Second Berkeley Symposium of Mathematical Statistics and Probability, Berkeley, CA: University of California Press, pp. 507–32.
(1954), ‘Existence of an Equilibrium for a Competitive Economy’ (with G. Debreu), Econometrica, 22, July, pp. 265–90.

(1958), Studies in the Mathematical Theory of Inventory and Production (ed. with S. Karlin and
H. Scarf), Stanford, CA: Stanford University Press.

(1961), ‘Capital–Labour Substitution and Economic Efficiency’ (with H.B. Chenery, B.S. Minhas and R.M. Solow), Review of Economics and Statistics, 43, August, pp. 225–50.

(1962), ‘The Economic Implications of Learning by Doing’, Review of Economic Studies, 29, June, pp. 155–73. (1971a), General Competitive Analysis (with F.H. Hahn), San Francisco: Holden-Day.

(1971b), Essays in the Theory of Risk Bearing, Amsterdam: North-Holland.

(1977), Studies in Resource Allocation Processes (ed. with L. Hurwicz), Cambridge: Cambridge
University Press.

(1983), Collected Papers of Kenneth J. Arrow, vol. 1, Social Choice and Justice; vol. 2, General Equilibrium, Cambridge, MA: Harvard University Press.
(1984), Collected Papers of Kenneth J. Arrow, vol. 3, Individual Choice under Certainty and Uncertainty; vol. 4, The Economics of Information, Cambridge, MA: Harvard University Press.
(1985), Collected Papers of Kenneth J. Arrow, vol. 5, Production and Capital; vol. 6, Applied Economics, Cambridge, MA: Harvard University Press.