Kenneth Arrow

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**Kenneth Arrow**
Image:KennethArrow.jpg National Medal of Science award ceremony, 2004
Born	August 23, 1921 New York City
Residence	Image:Flag of the United States.svg USA
Nationality	Image:Flag of the United States.svg American
Field	Economics
Institution	Stanford University
Alma mater	Columbia University
Academic advisor	Harold Hotelling
Notable students	John C. Harsanyi Thomas Marschak A. Michael Spence Nancy Stokey
Known for	General equilibrium theory Fundamental theorems of welfare economics Arrow's impossibility theorem Endogenous growth theory
Notable prizes	John Bates Clark Medal (1957) Nobel Prize in Economics (1972)

Kenneth Joseph Arrow (born August 23, 1921) is an American economist, winner of the Nobel Prize in Economics in 1972, and the youngest person ever to receive this award, at 51. He is considered one of the founders of modern (post World War II) 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.

He graduated from Townsend Harris High School and then earned a Bachelor's degree from the City College of New York in 1940. At Columbia University, he received a Master's degree in 1941. From 1946 to 1949 he spent his time partly as a graduate student at Columbia and partly as a research associate at the Cowles Commission for Research in Economics at the University of Chicago. During that time he also held the rank of Assistant Professor in Economics at the University of Chicago. In 1951 he earned his Ph.D. from Columbia. He is currently the Joan Kenney Professor of Economics and Professor of Operations Research, Emeritus at Stanford University. He was one of the recipients of the 2004 National Medal of Science, the nation's highest scientific honor, presented by President George W. Bush for his contributions to research on the problem of making decisions using imperfect information and his research on bearing risk. Ken Arrow's impact on the economics profession has been tremendous. For more than fifty years he has been one of the most listened to of all practicing economists.

1 Arrow's impossibility theorem
2 General equilibrium theory
3 Endogenous growth theory
4 Information economics
5 Works
6 Trivia
7 See also
8 External links

Arrow's impossibility theorem

Main article: Arrow's impossibility theorem

Arrow's monograph Social Choice and Individual Values derives from his Ph.D. thesis. In it he sets out a key result (in one final form).

General Possibility Theorem: It is impossible to formulate a social preference ordering that satisfies the following conditions (paraphrased):

Unrestricted Domain: For each state X and Y, based on the social preference ordering, society prefers either state X to Y or Y to X. i.e. society can compare any pair of candidates. (completeness)
Transitive Property: If society prefers (based on social rule aggregation of individual preferences) state X to Y and prefers Y to Z then society prefers X to Z.
Independence of Irrelevant Alternatives: If for some X, Y, and Z, X is preferred to Y, then changing the position in the ordering of Z does not affect the relative ordering of X and Y i.e. X is still preferred to Y. In other words, changing the position of Z in the preference ordering should not be allowed to "flip" the social choice between X and Y.
Weak Pareto Principle: If all individuals rank X above Y, then society should rank X above Y.
Non-Dictatorship: Societal preferences cannot be based on the preferences of only one person regardless of the preferences of other agents and of that person.

The theorem 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 top 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.

General equilibrium theory

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.

Endogenous growth theory

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.

Information economics

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.

Works

Arrow, Kenneth J. (1951). Social Choice and Individual Values. Wiley, New York. ISBN 0-300-01364-7. 2nd ed. 1963
Arrow, Kenneth J. (1962). "The Economic Implications of Learning by Doing". Review of Economic Studies 29: 155-73.
Arrow, Kenneth J. (1963). "Uncertainty and the Welfare Economics of Medical Care". American Economic Review 53 (5): 941-73.
Arrow, Kenneth J. (1971). Essays in the Theory of Risk-Bearing. North-Holland Pub. Co., Amsterdam. ISBN 072043047X.
Arrow, Kenneth J. (1974). The Limits of Organization. Norton, New York. ISBN 0-393-09323-9.
Arrow, Kenneth J. and Gerard Debreu (1954). "Existence of a Competitive Equilibrium for a Competitive Economy". Econometrica 22 (3): 265-90.
Arrow, Kenneth J. and Frank Hahn (1971). General Competitive Analysis. Holden-Day, San Francisco. ISBN 0816202753.

Trivia

Arrow and Paul Samuelson are related by marriage and they are both uncles of former United States Secretary of the Treasury Larry Summers. Arrow is the brother of Summers's mother, and Samuelson is the brother of Summers's father, who changed his family name.