# Kenneth Arrow

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Kenneth Joseph Arrow (born August 23, 1921) is an American economist, winner of the Nobel Prize in Economics in 1972. 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 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 and Ph.D. in 1951.

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### General Possibility Theorem

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.

### 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

• The Economic Implications of Learning by Doing Review of Economic Studies 29 (June 1962) pp 155-73
• Essays in the Theory of Risk-Bearing 1971
• Existence of a Competitive Equilibrium for a Competitive Economy Econometrica 22, no 3 (July 1954) pp 265-90, with Gerard Debreu
• General Competitive Analysis 1971, with Frank Hahn
• Uncertainty and the Welfare Economics of Medical Care American Economic Review 1963
• Existence of an equilibrium for a competitive economy Econometrica (1954) Vol 22 No 3, with Gerard Debreu
• Social Choice and Individual Values 1951
• The Limits of Organization 1974

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