Kenneth Arrow

Kenneth J. Arrow
200px National Medal of Science award ceremony, 2004
Born	(1921-08-23) August 23, 1921 New York City, USA
Nationality	United States
Institution	Stanford University
Field	Microeconomics General equilibrium theory Social choice theory
School or tradition	Neoclassical economics
Alma mater	Columbia University City College of New York
Influences	Alfred Tarski Harold Hotelling
Influenced	Amartya Sen Allan Gibbard John C. Harsanyi Roger Myerson A. Michael Spence Eric S. Maskin Nancy Stokey Karl Shell Anthony Downs Wahidul Haque Takashi Negishi
Contributions	General equilibrium theory Fundamental theorems of welfare economics Arrow's impossibility theorem Endogenous growth theory
Awards	John Bates Clark Medal (1957) Nobel Prize in Economics (1972) von Neumann Theory Prize (1986) National Medal of Science (2004) ForMemRS (2006)
Information at IDEAS / RePEc

Kenneth Joseph "Ken" Arrow (born August 23, 1921) is an American economist, writer, and political theorist. He is the joint winner of the Nobel Memorial Prize in Economics with John Hicks in 1972. To date, he is the youngest person to have received this award, at 51.

In economics, he is a figure in post-World War II neo-classical economic theory. Many of his former graduate students have gone on to win the Nobel Memorial Prize themselves. 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 the economics of information.

Arrow remains active on the international scene through a variety of initiatives including trustee of Economists for Peace and Security and a member of the Advisory Board of Incentives for Global Health, the not-for-profit behind the Health Impact Fund.

Education and early career

Arrow was born on August 23, 1921, in New York City. Arrow's mother, Lilian, was from Iaşi (Romania), and his father, Harry, was from Podu Iloaiei (Iaşi, Romania). The Arrow family has Romanian Jewish origins. His family was very supportive of his education. Growing up during the Great Depression, he embraced socialism in his youth. He would later move away from socialism, but his views retained a left sensibility.

He graduated from Townsend Harris High School and then earned a Bachelor's degree from the City College of New York in 1940 in mathematics, where he was a member of Sigma Phi Epsilon. He attended Columbia University, for his graduate studies. While there, he studied under Harold Hotelling, and was greatly influenced by him. He received a Master's degree in 1941. He served as a weather officer in the United States Army Air Corps from 1942–1946.

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.

Arrow is brother to the economist Anita Summers, uncle to economist Larry Summers, and brother-in-law of the late economists Robert Summers and Paul Samuelson. In 1947, he married Selma Schweitzer; they have two children: David Michael and Andrew Seth, both actors. Andrew is married to actress Donna Lynne Champlin.

Academic career

He is currently the Joan Kenney Professor of Economics and Professor of Operations Research, Emeritus at Stanford University. He is also a founding member of the Pontifical Academy of Social Sciences. He is also currently a member of the Science Board of Santa Fe Institute.

He is a trustee of Economists for Peace and Security. He was a convening lead author for the Intergovernmental Panel on Climate Change. He is also Editor of the Annual Review of Economics.

Five of his former students have gone on to become Nobel Prize winners. These include Eric Maskin, John Harsanyi, Michael Spence and Roger Myerson.

He served in the government on the staff of the Council of Economic Advisers in the 1960s with Robert Solow. As a Fulbright Distinguished Chair, in 1995 he taught Economics at the University of Siena.

A collection of Arrow's papers is housed at the Rubenstein Library at Duke University.

Contributions

Arrow's impossibility theorem

Main article: Arrow's impossibility theorem

Arrow's monograph Social Choice and Individual Values derives from his Ph.D. thesis.

"If we exclude the possibility of interpersonal comparisons of utility, then the only methods of passing from individual tastes to social preferences which will be satisfactory and which will be defined for a wide range of sets of individual orderings are either imposed or dictatorial."

General Impossibility Theorem: It is impossible to formulate a social preference ordering that satisfies all of the following conditions:

1. Nondictatorship: The preferences of an individual should not become the group ranking without considering the preferences of others.
2. Individual Sovereignty: each individual should be able to order the choices in any way and indicate ties
3. Unanimity: If every individual prefers one choice to another, then the group ranking should do the same
4. Freedom From Irrelevant Alternatives: If a choice is removed, then the others' order should not change
5. Uniqueness of Group Rank: The method should yield the same result whenever applied to a set of preferences. The group ranking should be transitive.

The theorem has 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, if each person votes to get as much cake as possible, 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

Main articles: General equilibrium theory and Arrow–Debreu model

Working with Gérard Debreu, Arrow produced the first rigorous proof of the existence of a market clearing equilibrium, given certain restrictive assumptions. For this work and his other contributions, Debreu won the Nobel prize in 1983. Arrow went on to extend the model and its analysis to include uncertainty, the stability. His contributions to the general equilibrium theory were strongly influenced by Adam Smith's Wealth of Nations. Written in 1776, The Wealth of Nations is an examination of economic growth brought forward by the division of labor, by ensuring interdependence of individuals within society.

In 1974, The American Economic Association published the paper written by Kenneth Arrow, General Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice, where he states, '“From the time of Adam Smith’s Wealth of Nations in 1776, one recurrent theme of economic analysis has been the remarkable degree of coherence among the vast numbers of individual and seemingly separate decisions about the buying and selling of commodities. In everyday, normal experience, there is something of a balance between the amounts of goods and services that some individuals want to supply and the amounts that other, different individuals want to sell. Would-be buyers ordinarily count correctly on being able to carry out their intentions, and would-be sellers do not ordinarily find themselves producing great amounts of goods that they cannot sell. This experience of balance indeed so widespread that it raises no intellectual disquiet among laymen; they take it so much for granted that they are not supposed to understand the mechanism by which it occurs.”'

Fundamental theorems of welfare economics

He presents the first and second fundamental theorems of welfare economics and their proofs without requiring differentiability of utility, consumption, or technology, and including corner solutions.

Endogenous-growth theory

Arrow was researching 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 outside economic activities, and was outside (exogenous) to common economic models. At the same time there was no economic explanation for why it occurred. Endogenous-growth theory provided standard economic reasons for why firms innovate, leading economists to think of innovation and technical change as determined by economic actors, that is endogenously to economic activities, and thus belong inside the model. A literature on this theory has developed subsequently to Arrow's work.

Information economics

In other 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.

Awards and honors

Arrow was elected a Fellow of the American Academy of Arts and Sciences in 1959. He was the joint winner of the Nobel Memorial Prize in Economics with John Hicks in 1972. 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. He was elected a Foreign Member of the Royal Society (ForMemRS) in 2006.

Publications

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Including: Arrow, Kenneth J. Price-quantity adjustments in multiple markets with rising demands, pp. 3–15.

• Also available through: JSTOR 2295952.
• Pdf version.

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Also reprinted as a pdf.

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• Pdf.

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See also

• Arrow information paradox
• Learning by doing
• List of economists
• List of Jewish Nobel laureates
• List of think tanks

External links

• Collected Papers of Kenneth J. Arrow
• Kenneth Arrow at stanford.edu
• Ideological Profile from Econ Journal Watch
• Autobiography at nobel.se
• Kenneth Arrow Profile at cepa.newschool.edu
• Social Choice and Individual Values
• Photos of Kenneth Arrow
• Appearances on C-SPAN
• IDEAS/RePEc
• Kenneth J. Arrow: Nobel Prize in Economics Recipient by Seymour "Sy" Brody, Florida Atlantic University Libraries

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