 Gérard Debreu

Gérard Debreu Walrasian economics Born July 4, 1921
CalaisDied December 31, 2004 (aged 83)
ParisNationality French Institution University of California, Berkeley Field Mathematical economics Influences Léon Walras
Henri Cartan
Maurice AllaisInfluenced Jacques Drèze
Stephen SmaleContributions General equilibrium
utility theory
topological methods
integration of setvalued correspondencesAwards Nobel Memorial Prize in Economics (1983) Information at IDEAS/RePEc Gérard Debreu (July 4, 1921 – December 31, 2004) was a French economist and mathematician, who also came to have United States citizenship. Best known as a professor of economics at the University of California, Berkeley, where he began work in 1962, he won the 1983 Nobel Memorial Prize in Economics.
Contents
Biography
His father was the business partner of his maternal grandfather in lace manufacturing, a traditional industry in Calais. Prior to the start of World War II, he received his baccalauréat and went to Ambert to begin preparing for the entrance examination of a grande école. Later on, he moved from Ambert to Grenoble to complete his preparation, both places being in the socalled "Free Zone" during World War II. In 1941, he was admitted to the École Normale Supérieure in Paris, along with Marcel Boiteux. He was influenced by Henri Cartan and the Bourbaki writers. When he was about to take the final examinations in 1944, DDay arrived and he, instead, enlisted in the French army. He was transferred for training to Algeria and then served among the French occupational forces in Germany until July 1945. Debreu passed the Agrégation de Mathématiques exams at the end of 1945 and the beginning of 1946. By this time, he had become interested in economics, particularly in the general equilibrium theory of Léon Walras. From 1946 to 1948, he was an assistant in the Centre National de la Recherche Scientifique. During these two and a half years, he made the transition from mathematics to economics. In 1948, Debreu came to the USA on a Rockefeller Fellowship which allowed him to visit several American universities, as well as those in Uppsala and Oslo in 194950.
Debreu married Françoise Bled in 1946 and had two daughters, Chantal and Florence, born in 1946 and 1950 respectively.
Debreu died in Paris at the age of 83 of natural causes on New Year's Eve, 2004, and was interred in the Père Lachaise Cemetery.
Academic career
Debreu began working as a Research Associate and joined the Cowles Commission at the University of Chicago in the summer of 1950. He remained there for five years, returning to Paris periodically.
In 1954, he published a breakthrough paper, entitled Existence of an Equilibrium for a Competitive Economy, together with Kenneth Arrow, in which they provided a definitive mathematical proof of the existence of a general equilibrium, using topological rather than calculusbased methods.
In 1955, he moved to Yale University.
In 1959, he published his classical monograph, Theory of Value: An Axiomatic Analysis of Economic Equilibrium (Cowles Foundation Monographs Series), which is one of the most important works in mathematical economics. He also studied several problems in the theory of cardinal utility, in particular the additive decomposition of a utility function defined on a Cartesian product of sets.
In this monograph, Debreu set up an axiomatic foundation for competitive markets. He also established the existence of an equilibrium using a novel approach. The main idea of his argument is to show that there exists a price system for which the aggregate excess demand correspondence vanishes. He did so by proving a type of fixedpoint theorem that is based on the Kakutani FixedPoint Theorem. In Chapter 7, Debreu introduced the concept of uncertainty and showed how it could be incorporated into the deterministic model. Here, he introduced the notion of a contingent commodity, which is a promise to deliver a good should a certain state of nature be realized. This concept is very frequently used in financial economics, where it known as the "ArrowDebreu security".
In 196061, he worked at the Center for Advanced Study in the Behavioral Sciences at Stanford and devoted most of his time to the complex proof that appeared in 1962 of a general theorem on the existence of an economic equilibrium.
In January 1962, he started working at the University of California, Berkeley, where he held the titles of University Professor and Class of 1958 Professor of Economics and Mathematics Emeritus.
During his leaves in the late 1960s and 1970s, he visited universities in Leiden, Cambridge, Bonn and Paris.
His later studies centered mainly on the theory of differentiable economies, where he showed that, in general, aggregate excess demand functions vanish at a finite number of points  basically, he showed that economies have a finite number of price equilibria.
In 1976, he received the French Legion of Honor. He was awarded the 1983 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel, for having incorporated new analytical methods into economic theory and for his rigorous reformulation of general equilibrium theory. He was a member of the International Academy of Science.
In 1990, he served as President of the American Economic Association.^{[1]}
Major publications
 "The Coefficient of Resource Utilization", 1951, Econometrica.
 "A Social Equilibrium Existence Theorem", 1952, Proceedings of the National Academy of Sciences.
 "Definite and SemiDefinite Quadratic Forms", 1952, Econometrica
 "Nonnegative Square Matrices", with I.N. Herstein, 1953, Econometrica.
 "Valuation Equilibrium and Pareto Optimum", 1954, Proceedings of the National Academy of Sciences.
 "Existence of an Equilibrium for a Competitive Economy", with K.J.Arrow, 1954, Econometrica.
 "Representation of a Preference Ordering by a Numerical Function", 1954, in Thrall et al., editors, Decision Processes.
 "A Classical TaxSubsidy Problem", 1954, Econometrica.
 "Numerical Representations of Technological Change", 1954, Metroeconomica
 "Market Equilibrium", 1956, Proceedings of the NAS.
 "Stochastic Choice and Cardinal Utility", 1958, Econometrica
 "Cardinal Utility for EvenChance Mixtures of Pairs of Sure Prospects", 1959, RES
 The Theory of Value: An axiomatic analysis of economic equilibrium, 1959
 "Topological Methods in Cardinal Utility Theory", 1960, in Arrow, Karlin and Suppes, editors, Mathematical Methods in the Social Sciences.
 "On 'An Identity in Arithmetic'", 1960, Proceedings of AMS
 "Economics Under Uncertainty", 1960, Économie Appliquée.
 "New Concepts and Techniques for Equilibrium Analysis", 1962, IER
 "On a Theorem by Scarf", 1963, RES.
 "A Limit Theorem on the Core of an Economy", with H.Scarf, 1964, IER.
 "Contuinity Properties of Paretian Utility", 1964, IER
 "Integration of Correspondences", 1967, Proceedings of Fifth Berkeley Symposium.
 "Preference Functions of Measure Spaces of Economic Agents", 1967, Econometrica.
 "Neighboring Economic Agents", 1969, La Décision.
 "Economies with a Finite Set of Equilibria", 1970, Econometrica.
 "Smooth Preferences", 1972, Econometrica.
 "The Limit of the Core of an Economy", with H. Scarf, 1972, in McGuire and Radner, editors, Decision and Organization
 "Excess Demand Functions", 1974, JMathE
 "Four Aspects of the Mathematical Theory of Economic Equilibrium", 1974, Proceedings of Int'l Congress of Mathematicians.
 "The Rate of Convergence of the Core of an Economy", 1975, JMathE.
 "The Application to Economics of Differential Topology and Global Analysis: Regular differentiable economies", 1976, AER.
 "Least Concave Utility Functions", 1976, JMathE.
 "Additively Decomposed Quasiconcave Functions", with T.C.Koopmans, 1982, Mathematical Programming.
 "Existence of Competitive Equilibrium", 1982, in Arrow and Intriligator, Handbook of Mathematical Economics
 Mathematical Economics: Twenty papers of Gerard Debreu, 1983.
 "Economic Theory in a Mathematical Mode: the Nobel lecture", 1984, AER.
 "Theoretic Models: Mathematical form and economic content", 1986, Econometrica.
 "The Mathematization of economic theory". The American Economic Review 81 (Presidential address delivered at the 103rd meeting of the American Economic Association, 29 December 1990, Washington, DC): 1–7. March 1991. JSTOR 2006785.
 "Innovation and Research: An Economist's Viewpoint on Uncertainty", 1994, Nobelists for the Future
References
External links
 The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel 1983
 Existence of an Equilibrium for a Competitive Economy
 Obituary for Debreu
 Guide to the Gerard Debreu Papers at The Bancroft Library
 IDEAS/RePEc
 Theory of Value. An Axiomatic Analysis of Economic Equilibrium
Neoclassical economists William Stanley Jevons · Francis Ysidro Edgeworth · Alfred Marshall · John Bates Clark · Irving Fisher · Kenneth Arrow · Hal Varian · Hirofumi Uzawa · Axel Leijonhufvud · Martin Feldstein · Fumio Hayashi
Walrasian economics Maurice Allais · Gérard Debreu · Edmond Malinvaud · Jacques Drèze · JeanMichel Grandmont · Guy Laroque · JeanPascal Benassy · Yves YounesNew classical macroeconomics Robert Lucas, Jr. · Neil Wallace · Robert Barro · Edward C. Prescott · Finn E. Kydland · Bennett McCallumNobel Memorial Laureates in Economics (1976–2000) Milton Friedman (1976) · Bertil Ohlin / James Meade (1977) · Herbert Simon (1978) · Theodore Schultz / Arthur Lewis (1979) · Lawrence Klein (1980) · James Tobin (1981) · George Stigler (1982) · Gérard Debreu (1983) · Richard Stone (1984) · Franco Modigliani (1985) · James M. Buchanan (1986) · Robert Solow (1987) · Maurice Allais (1988) · Trygve Haavelmo (1989) · Harry Markowitz / Merton Miller / William Forsyth Sharpe (1990) · Ronald Coase (1991) · Gary Becker (1992) · Robert Fogel / Douglass North (1993) · John Harsanyi / John Forbes Nash, Jr. / Reinhard Selten (1994) · Robert Lucas, Jr. (1995) · James Mirrlees / William Vickrey (1996) · Robert C. Merton / Myron Scholes (1997) · Amartya Sen (1998) · Robert Mundell (1999) · James Heckman / Daniel McFadden (2000)
Complete list · (1969–1975) · (1976–2000) · (2001–2025) Categories: 1921 births
 2004 deaths
 Burials at Père Lachaise Cemetery
 French emigrants to the United States
 French economists
 Nobel laureates in Economics
 Mathematical economists
 French Nobel laureates
 American Nobel laureates
 General equilibrium theorists
 Members of the French Academy of Sciences
 University of California, Berkeley faculty
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