Walrasian economics  

Birth  July 4, 1921 Calais 
Death  December 31, 2004 (aged 83) Paris 
Nationality  France 
Institution  University of California, Berkeley 
Field  Mathematical economics 
Influences  Léon Walras Henri Cartan Maurice Allais 
Influenced  Jacques Drèze Stephen Smale 
Contributions  General
equilibrium utility theory topological methods integration of setvalued correspondences 
Awards  Nobel Memorial Prize in Economics (1983) 
Information at IDEAS/RePEc 
Gérard Debreu (July 4, 1921 – December 31, 2004) was a Frenchborn economist and mathematician. In July 1975, he became a naturalized citizen of the United States. 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.
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 Leon 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 began working as a Research Associate and joined the Cowles Commission 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 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, 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 established the existence of an 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 did so by proving a type of fixedpoint theorem based on the Kakutani fixed point theorem. In Chapter 7 of the book, 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 state of nature be realized. This concept is very frequently used in financial economics as the socalled Arrow Debreu security.
In 196061, he worked at the Center for Advanced Study in the Behavioral Sciences at Stanford and devoted his time mostly 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 title of University Professor and Class of 1958 Professor of Economics and Mathematics Emeritus. During his leaves in the late 60's and 70's, 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. He was a member of the International Academy of Science.
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 at the age of 83 of natural causes on New Year's Eve, 2004, and was interred in the Père Lachaise Cemetery.


