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
calculus-based 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 fixed-point theorem that is based on the
Kakutani fixed-point 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 is known as the "
Arrow–Debreu security". In 1960–61, 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 sabbaticals in the late 1960s and 1970s, he visited universities in
Leiden,
Cambridge,
Bonn and
Paris. In 1987, he visited the
University of Canterbury as an Erskine Fellow, lecturing in economic theory. 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, he showed that economies have a finite number of price equilibria. In 1976, he received the French
Legion of Honour. 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, the
American Academy of Arts and Sciences, the United States
National Academy of Sciences, and the
American Philosophical Society. In 1990, he served as president of the
American Economic Association. ==Major publications==