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Gerard Debreu (July 4, 1921 – December 31, 2004) is a French economist and mathematician (In July 1975, he became a naturalized citizen of the United States). He won the 1983 Nobel Memorial Prize in Economics.
He was born in Calais. His father was the business partner of his maternal grandfather in lace manufacturing, a traditional industry in Calais.
Just prior to the start of World War II he finished college, but instead of preparing for the university he studied at an improvised math curriculum in Ambert. Later on he moved to Grenoble, both being in the so-called "Free Zone" during World War II.
In 1941 he was admitted to the École Normale Supérieure with Marcel Boiteux, which he was about to graduate from in 1944 when the D-Day made him enlist in the Allies army. He was transferred for training to Algeria and then served in French occupational forces in Germany until July 1945.
Debreu took the Agrégation de Mathématiques at the end of 1945, and eventually he graduated at the beginning of 1946 and later became interested in economics, particularly the general equilibrium theory of Leon Walras. From 1946 to 1948, he was an assistant in the Centre National de la Recherche Scientifique. These two and a half years is the time 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 1949-50. Debreu began working as a Research Association and joined the Cowles Commissionat at the University of Chicago in the summer of 1950.
There he remained for five years, returning to Paris periodically. In 1954 he published a breakthrough paper titled Existence of an Equilibrium for a Competitive Economy (together with Kenneth Arrow), in which they provided a definitive mathematical proof of the existence of general equilibrium, using topological rather than calculus 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 perhaps the most important work in mathematical economics. He also studied several problems in the theory of cardinal utility, the additive decomposition of a utility function defined on a Cartesian product of sets.
In this monograph, Debreu sets up an axiomatic foundation for competitive markets. He establishes the existence of equilibrium using a novel approach. The main idea is to show that there exists a price system for which the aggregate excess demand correspondence vanishes. He does so by proving a fixed point like theorem based on Kakutani's fixed-point theorem. In Chapter 7 of the book Debreu introduces uncertainty and shows how it can be incorporated into the deterministic model. Here he introduces the notion of a contingent commodity, which is a promise to deliver a good should a state of nature realize. This notion is very used in financial economics as Arrow Debreu security.
In 1960-61, he worked at the Center for Advanced Study in the Behavioral Sciences at Stanford and devoted mostly to the complex proof that appeared in 1962 of a general theorem on the existence of an economic equilibrium.
In January of 1962, he started worked at the University of California, Berkeley where he held the title University Professor and Class of 1958 Professor of Economics and Mathematics Emeritus. During his leaves in late sixties and seventies he visited universities in Leiden, Cambridge, Bonn, and Paris.
His later studies centred 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, showing 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.
In 1990, he served as President of the American Economic Association.
Debreu married Françoise Bled in 1946 and had two daughters, Chantal and Florence, born in 1946 and 1950 respectively.
Debreu died in Paris on New Year's Eve, 2004, of natural causes, aged 83.
External Links
- The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel 1983
- Existence of an Equilibrium for a Competitive Economy
- Debreu page at Berkeley
- Obituary for Debreu
