Debreu, Gerard
Debreu, Gerard 19212005
Gerard Debreu, a Frenchborn American mathematical economist and 1983 Nobel laureate, was a major force in the advancement of the theory of general equilibrium. His early influence came from the 1988 French Nobel laureate, Maurice Allais, who introduced him to the writings of Leon Walras (18341910), the founder of the mathematical theory of general equilibrium analysis.
In 1949 Debreu visited several premier universities, including Harvard and the University of California, Berkeley, on a Rockefeller fellowship. Following the fellowship, he spent a decade with the Cowles Commission, then attached to the University of Chicago, working on Pareto optima, the existence of a general economics equilibrium, and utility theory. Subsequently, after one year at Stanford, he moved to Berkeley in 1962 where he remained until his retirement in 1991. Besides mathematics, Debreu was so taken by the U.S. rule of law during the Watergate scandal that he became an American citizen in 1975.
Debreu’s research interest was general equilibrium analysis, in line with Walras, whose method was to equate equations and unknowns. The essential idea is to show how prices gravitate from disequilibrium to their natural or equilibrium levels. Debreu liberated the analysis by opting for fixedpoint and convex tools for general equilibrium analysis.
Convexity requires that the production and consumption sets be bowlshaped. Debreu would “slip a hyperplane,” as he would say, through the tangent of those convex sets. He first revealed a proof at the 1950 meeting of the Econometric Society at Harvard that did not use the convexity solution. Many optimal solutions of the Pareto type and some possible competitive solutions resulted where prices are given and agents maximize their affairs. In 1954, in collaboration with Kenneth Arrow and using topological methods, which Debreu had used previously, he proved the existence of general equilibrium in an “epochmaking” paper, “Existence of an Equilibrium for a Competitive Economy.”
Debreu’s early book, The Theory of Value (1959), produced the hardcore ideas of his lifetime research program.
He expressed the economy as , where each consumer, i = 1.… m, has an initial endowment, ω_{i}, a share of j^{th} producer’s profit, θ_{i, j}, and an underlying utility function for his or her preferences. Each producer, j = 1.… n, takes the prices that are announced, and maximizes profits, π_{j }. The innerbracketed terms represent the consumer budget from the initial endowment and shares of profits. Consumers will maximize their utility subject to their budget constraints, yielding demand functions. Excess demand functions are now possible by summing all the demand functions less endowment. Thus we can derive the equilibrium prices from the excess demand functions, which in two dimensions are usually the zeros or solutions of a quadratic equation.
Debreu built his theories on axioms, where a primitive such as a commodity becomes a mathematical object with spatiotemporal and physical characteristics. He urged his students to be concise, mentioning that John Nash demonstrated the equilibrium for finite games on only one page. During his lectures his eyes would light up when he demonstrated the superiority of mathematical reasoning. He used to say that mathematical economists have the best of two worlds—mathematical discoveries when they are young and economic discoveries when they are old.
SEE ALSO ArrowDebreu Model; General Equilibrium; Pareto Optimum; Tatonnement
BIBLIOGRAPHY
Arrow, Kenneth J., and Gerard Debreu. 1954. Existence of an Equilibrium for a Competitive Economy. Econometrica 22: 265–290.
Arrow, Kenneth J., and Michael D. Intriligator. 1982. Existence of Competitive Equilibrium. In Handbook of Mathematical Economics, eds. Kenneth J. Arrow and Michael D. Intriligator, Vol. 2: Mathematical Approaches to Microeconomic Theory, 677–743. Amsterdam, NY: Elsevier NorthHolland.
Debreu, Gerard. 1959. Separation Theorem for Convex Set. SIAM Review 1: 95–98.
Debreu, Gerard. 1959. The Theory of Value: An Axiomatic Analysis of Economic Equilibrium. New York: Wiley.
Debreu, Gerard. 1983. Mathematical Economics: Twenty Papers of Gerard Debreu. New York and Cambridge, U.K.: Cambridge University Press.
Debreu, Gerard. 1993. Random Walk and Life Philosophy. In Eminent Economists, Their Life Philosophies, ed. Michael Szenberg, 107–114. New York and Cambridge, U.K.: Cambridge University Press.
Ramrattan, Lall, and Michael Szenberg. 2005. Gerard Debreu: The General Equilibrium Model (19212005). The American Economist 49 (1): 3–14.
Lall Ramrattan
Michael Szenberg
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Debreu, Gerard
Gerard Debreu (dəbrōō´), 1921–2005, FrenchAmerican economist, b. Calais, France. He studied mathematics in France before coming to the United States in 1950, where he worked with the Chicagobased Cowles Foundation for Research in Economics. With such books as Theory of Value (1959), Debreu made mathematical advances in the theory of economic equilibrium, examining how supply and demand are balanced through prices. He taught economics and mathematics at the Univ. of California, Berkeley, from 1962 to 1991, and became an American citizen in 1975. Debreu was awarded the Nobel Memorial Prize in Economic Sciences in 1983.
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