# Kenneth Arrow

## (1921 - )

Kenneth Joseph Arrow was born in New York City on August 23, 1921. He earned a Bachelor of Science degree in Social Science from the City College of New York in 1940. At Columbia, he received a Master's degree in Mathematics in 1941 and a Ph.D. in Economics in 1951. In 1949, he was appointed Acting Assistant Professor of Economics and Statistics at Stanford, eventually becoming Professor of Economics, Statistics, and Operations Research. In 1968, Arrow moved to Harvard to be the Professor of Economics.

Arrow was awarded the John Bates Clark Medal of the American Economic Association in 1957. He was elected president of the American Economic Association in 1972. Arrow has also been a member of the National Academy of Sciences and the American Statistical Association.

Arrow is considered, along with Paul Samuelson, one of the founders of modern neo-classical economics. His most significant works are his contributions to social choice theory, notably "Arrow's impossibility theorem," and his work on general equilibrium analysis. He has also provided foundational work in many other areas of economics, including endogenous growth theory and information economics. In 1972, Kenneth Arrow received the Nobel Prize for Economics.

Arrow's impossibility theorem was set out in his Ph.D. thesis,

Social choice and individual values.In its final form it states the following: given the conditions of Pareto Optimality (P), Unbounded social choice (S), Independence of choices (I) and non-Dictatorship (D), it is impossible to formulate a social choice function which satisfies all of them. This has tremendous implications for welfare economics and theories of justice. It was extended by Amartya Sen to the Liberal Paradox which argued that given a status of "Minimal Liberty" there was no way to obtain Pareto Optimality, nor to avoid the problem of social choice of neutral but unequal results.

An example of this would be to have the following choices to divide a cake between three people. Let us call them A, B and C.

Choice 1: A gets nothing, B and C get half each. Choice 2: B gets nothing, A and C get half each. Choice 3: C gets nothing, A and B get half each. Choice 4: divide the cake equally.

Thus choice 4 would be third from the bottom in everyone's list, and would, in any direct choice lose 2 to 1 against an unequal distribution. Since all of these choices are Pareto optimal - no one's welfare can be improved without reducing the welfare of others - choice 4 would not be chosen, since there would always be other preferred choices.

Working with Gerard Debreu (who won the Nobel prize for this work in 1983), Arrow produced the first rigorous proof of the existence of a market clearing equilibrium, given certain restrictive assumptions. See general equilibrium. Arrow went on to extend the model to deal with issues relating to uncertainty, stability of the equilibrium, and whether a competitive equilibrium is efficient.

Arrow was instrumental in kick-starting research into endogenous growth theory (also known as

new growth theory) which sought to explain the source of technical change, which is a key driver of economic growth. Until this theory came to prominence, technical change was assumed to occur exogenously - that is, it was assumed to occur with no explanation of why it occurred. Endogenous growth theory provided standard economic reasons for why firms innovate - so innovation and technical change are determined endogenously - that is, within the model (hence the name). A vast literature on this theory has developed subsequently to Arrow's pioneering work.

In yet more pioneering research, Arrow investigated the problems caused by asymmetric information in markets. In many transactions, one party (usually the seller) has more information about the product being sold than the other party. Asymmetric information creates incentives for the party with more information to cheat the party with less information; as a result, a number of market structures have developed, including warranties and third party authentication, which enable markets with asymmetric information to function. Arrow analysed this issue for medical care (a 1963 paper entitled "Uncertainty and the Welfare Economics of Medical Care," in the American Economic Review); later researchers investigated many other markets, particularly second-hand assets, online auctions and insurance.

**Arrow’s Works Include**

•

The Economic Implications of Learning by DoingReview of Economic Studies 29 (June 1962) pp 155-73

•Essays in the Theory of Risk-Bearing1971

•Existence of a Competitive Equilibrium for a Competitive EconomyEconometrica 22, no 3 (July 1954) pp 265-90, with Gerard Debreu

•General Competitive Analysis1971, with Frank Hahn

•Uncertainty and the Welfare Economics of Medical CareAmerican Economic Review 1963

•Existence of an equilibrium for a competitive economyEconometrica (1954) Vol 22 No 3, with Gerard Debreu

•Social Choice and Individual Values1951

•The Limits of Organization1974

The following press release from the Royal Swedish Academy of Sciences describes Arrow's work:

The progress of thc economic sciences has led to a profound transformation of the general equilibrium theory. To a high degree, this development is marked by the pioneering works of Sir John Hicks and of Professor Kenneth Arrow. Both have opened up new productive paths for research in this area and thereby made fundamental contributions to the renewal of the theory. Hicks initiated this recreative process in the 1930s and Arrow provided it with fresh nourishment in the 1950s and 60s. As the distance in time between these contributions indicates, Hicks and Arrow belong to two different generations of scientists, a fact which can be traced in their choice of problems and methods of analysis.

Gcneral equilibrium theory had, earlier, essentially the character of formal analysis. In his most well-known work, the monography, Value and Capital, published in 1939, Hicks abandoned this tradition and gave the theory an increased economic relevance. He presented a complete economic equilibrium model with aggregated markets for commodities, factors of production, credit and money. The construction of this model included a number of innovations, i.e., a further development of older theories of consumption and of production, the formulation of conditions for multimarket stability, an extension of the applicability of the static method of analysis to include multiperiod analysis, and the introduction of a capital theory based on profit maximization assumptions. By being deeply anchored in theories of the behaviour of consumers and of entrepreneurs, Hicks's model offered far better possibilities to study the consequences of changes in externally given variables than earlier models in this field, and Hicks succeeded in formulating a number of economically interesting theorems. His model became of great importance also as a connecting link between general equilibrium theory and current theories of business cycles.

As his mathematical tool, Hicks used traditional differential analysis. When, later on, more modern mathematical methods were introduced in economic sciences, Arrow applied these methods in his studies of general equilibrium systems. In a series of papers, which preferentially treated the properties of solubility and stability of such systems, he provided the basis for a radical reformulation of the traditional equilibrium theory. Through this reformulation, which was based on the mathematical theory of convex sets, the general equilibrium theory gained both in generality and in simplicity. The pioneering work, a paper from 1954, was written together with Gerhard Debreu. The model presented in this paper became the starting point for the major part of further research in this field. Among Arrow's many important contributions should also be mentioned his development of the theory of uncertainty and its incorporation within the frame of general equilibrium theory and, furthermore, his analysis of the possibilities for decentralized decisions in a society where the price system is fixed by the central authority. This analysis was made in collaboration with Leonid Hurwicz.

From general equilibrium theory to welfare theory is but a short step, and both Hicks and Arrow have, on several points, developed the welfare economic consequences of their achievements indicated above. The most well-known contributions by Hicks to welfare theory are his analysis of criteria for comparisons bctween different economic situations, and his revision of thc concept of consumer surplus. In its new form this concept has had a great impact, i.e., within the cost-benefit analysis. Arrow has generalized the well-known theorem about pareto-optimality of a competitive equilibrium, and he has demonstrated that there exist general tendencies towards inoptimality in the allocation of resources between research and investments in real capital. As perhaps the most important of Arrow's many contributions to welfare theory appears his "possibility theorem", according to which it is impossible to construct a social welfare function out of individual preference functions.

Both Hicks and Arrow have made important contributions also to other fields than those mentioned above - Hicks to monetary theory and to the theory of business cycles, and Arrow to growth theory and decision theory.

**Sources:** Wikipedia; "Kenneth Arrow Autobiography"; Nobelprize.org. Photo courtesy of Prof. Kenneth Arrow