His father was the business partner of his maternal grandfather inlace manufacturing, a traditional industry inCalais. Debreu was orphaned at an early age, as his father committed suicide and his mother died of natural causes.[2] Prior to the start ofWorld War II, he received hisbaccalauréat and went toAmbert to begin preparing for the entrance examination of agrande école. Later on, he moved fromAmbert toGrenoble to complete his preparation, both places being inVichy France during World War II. In 1941, he was admitted to theÉcole Normale Supérieure in Paris, along withMarcel Boiteux. He was influenced byHenri Cartan and theBourbaki writers. When he was about to take the final examinations in 1944, theNormandy landings occurred and he, instead, enlisted in the French army. He was transferred for training toAlgeria and then served in the occupyingFrench Forces in Germany until July 1945.Debreu passed theAgrégation de Mathématiques exams at the end of 1945 and the beginning of 1946. By this time, he had become interested in economics, particularly in thegeneral equilibrium theory ofLéon Walras. From 1946 to 1948, he was an assistant in theCentre National de la Recherche Scientifique. During these two and a half years, he made the transition from mathematics to economics. In 1948, Debreu went to the United States on aRockefeller Fellowship which allowed him to visit several American universities, as well as those inUppsala andOslo in 1949–50.[3] He received his Ph.D. from theUniversity of Paris in 1956. In 1960 he became a professor at theUniversity of California, where he taught until 1991.[3]
Debreu married Françoise Bled in 1946 and they had two daughters, Chantal and Florence, born in 1946 and 1950 respectively.
Debreu died in Paris at the age of 83 of natural causes onNew Year's Eve, 2004.[1]
Debreu began working as a Research Associate and joined theCowles Commission at theUniversity of Chicago in the summer of 1950. He remained there for five years, returning to Paris periodically.
In 1954, he published a breakthrough paper, entitledExistence of an Equilibrium for a Competitive Economy, together withKenneth Arrow, in which they provided a definitive mathematical proof of the existence of ageneral equilibrium, usingtopological rather thancalculus-based methods.
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 inmathematical economics.[4] He also studied several problems in the theory ofcardinal utility, in particular the additivedecomposition of autility function defined on aCartesian product of sets.
In this monograph, Debreu set up anaxiomatic 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 theaggregate excess demand correspondence vanishes. He did so by proving a type of fixed-point theorem that is based on theKakutani fixed-point theorem. In Chapter 7, Debreu introduced the concept ofuncertainty and showed how it could be incorporated into thedeterministicmodel. Here, he introduced the notion of acontingentcommodity, which is a promise to deliver a good should a certain state of nature be realized. This concept is very frequently used infinancial economics, where it is known as the "Arrow–Debreu security".
In 1960–61, he worked at the Center for Advanced Study in the Behavioral Sciences atStanford 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 theUniversity of California, Berkeley, where he held the titles of University Professor and Class of 1958 Professor of Economics and Mathematics Emeritus.
During his sabbaticals in the late 1960s and 1970s, he visited universities inLeiden,Cambridge,Bonn andParis. In 1987, he visited theUniversity of Canterbury as an Erskine Fellow, lecturing in economic theory.[5]
His later studies centred mainly on the theory ofdifferentiable economies, where he showed that, in general, aggregateexcess demand functions vanish at a finite number of points – basically, he showed that economies have a finite number of price equilibria.
Debreu, Gérard (1986).Mathematical economics: twenty papers of Gerard Debreu. Cambridgeshire & New York: Cambridge University Press.ISBN978-0521335614.
The twenty papers: The coefficient of resource utilization · A social equilibrium existence theorem · A classical tax-subsidy problem · Existence of an equilibrium for a competitive economy (byGérard Debreu andKenneth J. Arrow) · Valuation equilibrium and Pareto optimum · Representation of a preference ordering by a numerical function · Market equilibrium · Economics under uncertainty · Topological methods in cardinal utility theory · New concepts and techniques for equilibrium analysis · A limit theorem on the core of an economy (byGérard Debreu andHerbert Scarf) · Contuinity properties of Paretian utility · Neighboring economic agents · Economies with a finite set of equilibria · Smooth preferences · Excess demand functions · The rate of convergence of the core of an economy · Four aspects of the mathematical theory of economic equilibrium · The application to economics of differential topology and global analysis: differentiable economies · Least concave utility functions
Debreu, Gérard (1954), "Representation of a preference ordering by a numerical function", in Thrall, Robert M.;Coombs, Clyde H.;Raiffa, Howard (eds.),Decision processes, New York: Wiley, pp. 159–167,OCLC639321.Pdf.
Debreu, Gérard (1967)."Integration of correspondences".Proceedings of Fifth Berkeley Symposium on Mathematical Statistics and Probability, Part 1.2:351–372.Pdf.
Debreu, Gérard (May 1976). "The application to economics of differential topology and global analysis: regular differentiable economies".The American Economic Review: Papers and Proceedings.66 (2):280–287.JSTOR1817234.
Debreu, Gérard (March 1991). "The mathematization of economic theory".The American Economic Review.81 (1):1–7.JSTOR2006785. (Presidential address delivered at the 103rd meeting of the American Economic Association, 29 December 1990, Washington, DC.)Full text.
Debreu, Gérard (1994). "Innovation and research: an economist's viewpoint on uncertainty".Nobelists for the Future.
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including the Nobel Lecture December 8, 1983Economic Theory in the Mathematical Mode