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Gérard Debreu

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Gérard Debreu
Debreu in 1977
Born(1921-07-04)4 July 1921
Calais,France
Died31 December 2004(2004-12-31)(aged 83)
Paris,France
NationalityFrench
Academic career
FieldMathematical economics
InstitutionUniversity of California, Berkeley
University of Chicago
School or
tradition		Walrasian economics
Alma materÉcole Normale Supérieure
University of Paris
Doctoral
students		Graciela Chichilnisky
Beth E. Allen
Xavier Vives
Ishac Diwan
InfluencesLéon Walras
Henri Cartan
Maurice Allais
Bourbaki
ContributionsGeneral equilibrium
utility theory
topological methods
integrationof set-valued correspondences
AwardsNobel Memorial Prize in Economics(1983)
InformationatIDEAS / RePEc

Gérard Debreu(French:[dəbʁø];4 July 1921 – 31 December 2004) was a French-borneconomistandmathematician.Best known as a professor ofeconomicsat theUniversity of California, Berkeley,where he began work in 1962, he won the 1983Nobel Memorial Prize in Economic Sciences.[1]

Biography

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His father was the business partner of his maternal grandfather inlacemanufacturing, 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 hisbaccalauréatand went toAmbertto begin preparing for the entrance examination of agrande école.Later on, he moved fromAmberttoGrenobleto complete his preparation, both places being inVichy Franceduring World War II. In 1941, he was admitted to theÉcole Normale Supérieurein Paris, along withMarcel Boiteux.He was influenced byHenri Cartanand theBourbakiwriters. When he was about to take the final examinations in 1944, theNormandy landingsoccurred and he, instead, enlisted in the French army. He was transferred for training toAlgeriaand then served in the occupyingFrench Forces in Germanyuntil July 1945. Debreu passed theAgrégation de Mathématiquesexams at the end of 1945 and the beginning of 1946. By this time, he had become interested in economics, particularly in thegeneral equilibrium theoryofLéon 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 Fellowshipwhich allowed him to visit several American universities, as well as those inUppsalaandOsloin 1949–50.[3]He received his Ph.D. from theUniversity of Parisin 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.

Academic career

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Debreu began working as a Research Associate and joined theCowles Commissionat theUniversity of Chicagoin 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,usingtopologicalrather thancalculus-based methods.

In 1955, he moved toYale 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 inmathematical economics.[4]He also studied several problems in the theory ofcardinal utility,in particular the additivedecompositionof autility functiondefined on aCartesian productof sets.

In this monograph, Debreu set up anaxiomaticfoundation 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 theaggregateexcess 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 ofuncertaintyand 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 atStanfordand 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,BonnandParis.In 1987, he visited theUniversity of Canterburyas an Erskine Fellow, lecturing in economic theory.[5]

His later studies centred mainly on the theory ofdifferentiableeconomies, where he showed that, in general, aggregateexcess demand functionsvanish at a finite number of points – basically, he showed that economies have a finite number of price equilibria.

In 1976, he received the FrenchLegion of Honour.He was awarded the 1983 Bank of Sweden Prize in Economic Sciences in Memory ofAlfred Nobel,for having incorporated new analytical methods into economic theory and for his rigorous reformulation ofgeneral equilibrium theory.He was a member of the International Academy of Science, theAmerican Academy of Arts and Sciences,the United StatesNational Academy of Sciences,and theAmerican Philosophical Society.[6][7][8]

In 1990, he served as president of theAmerican Economic Association.[9]

Major publications

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Books

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  • Debreu, Gérard (1959).The theory of value: an axiomatic analysis of economic equilibrium(PDF).New York:Wiley.OCLC270657.
  • Debreu, Gérard (1986).Mathematical economics: twenty papers of Gerard Debreu.Cambridge Cambridgeshire New York: Cambridge University Press.ISBN9780521335614.
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 DebreuandKenneth 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 DebreuandHerbert 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

Book chapters

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Journal articles

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References

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  1. ^Atlas, Riva D. (6 January 2005)."Gerard Debreu, 83, Dies; Won Nobel in Economics".The New York Times.
  2. ^Düppe, Till (Fall 2012). "Gerard Debreu's secrecy: his life in order and silence".History of Political Economy.44(3): 413–449.doi:10.1215/00182702-1717239.
  3. ^ab"The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1983".NobelPrize.org.Retrieved2023-01-01.
  4. ^Debreu, Gérard (1959).The theory of value: an axiomatic analysis of economic equilibrium(PDF).New York:Wiley.OCLC270657.
  5. ^Archived atGhostarchiveand theWayback Machine:"Gerard Debreu: Lecture 2 on Economic Theory (1987)".YouTube.21 September 2008.
  6. ^"Gerard Debreu".American Academy of Arts & Sciences.Retrieved2022-05-23.
  7. ^"Gerard Debreu".nasonline.org.Retrieved2022-05-23.
  8. ^"APS Member History".search.amphilsoc.org.Retrieved2022-05-23.
  9. ^Debreu, Gérard (March 1991). "The mathematization of economic theory".The American Economic Review.81(1): 1–7.JSTOR2006785.Full text.
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Awards
Preceded by Laureate of the Nobel Memorial Prize in Economics
1983 		Succeeded by
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