Gérard Debreu

Gérard Debreu

Walrasian economics
Born	July 4, 1921(1921-07-04) Calais
Died	December 31, 2004(2004-12-31) (aged 83) Paris
Nationality	French
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 set-valued correspondences
Awards	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.

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 so-called "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, D-Day 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 1949-50.

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 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 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 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 Semi-Definite 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 Tax-Subsidy 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 Even-Chance 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

1. ^ Debreu, Gérard (March 1991). "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. JSTOR 2006785. 

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

Persondata
Name	Debreu, Gerard
Alternative names
Short description
Date of birth	July 4, 1921
Place of birth	Calais
Date of death	December 31, 2004
Place of death	Paris