Gerard Debreu
Encyclopedia
Gérard Debreu 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.
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.
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 axiom
atic 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
.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
economist
Economist
An economist is a professional in the social science discipline of economics. The individual may also study, develop, and apply theories and concepts from economics and write about economic policy...
and mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, who also came to have United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
citizenship
Naturalization
Naturalization is the acquisition of citizenship and nationality by somebody who was not a citizen of that country at the time of birth....
. Best known as a professor of economics at the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
, 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 laceLace
Lace is an openwork fabric, patterned with open holes in the work, made by machine or by hand. The holes can be formed via removal of threads or cloth from a previously woven fabric, but more often open spaces are created as part of the lace fabric. Lace-making is an ancient craft. True lace was...
manufacturing, a traditional industry in Calais
Calais
Calais is a town in Northern France in the department of Pas-de-Calais, of which it is a sub-prefecture. Although Calais is by far the largest city in Pas-de-Calais, the department's capital is its third-largest city of Arras....
. Prior to the start of World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, he received his baccalauréat
Baccalauréat
The baccalauréat , often known in France colloquially as le bac, is an academic qualification which French and international students take at the end of the lycée . It was introduced by Napoleon I in 1808. It is the main diploma required to pursue university studies...
and went to Ambert
Ambert
-Places of interest:Ambert is famous for its fourme-d'Ambert cheese, its paper mills and its circular town hall ....
to begin preparing for the entrance examination of a grande école. Later on, he moved from Ambert
Ambert
-Places of interest:Ambert is famous for its fourme-d'Ambert cheese, its paper mills and its circular town hall ....
to Grenoble
Grenoble
Grenoble is a city in southeastern France, at the foot of the French Alps where the river Drac joins the Isère. Located in the Rhône-Alpes region, Grenoble is the capital of the department of Isère...
to complete his preparation, both places being in the so-called "Free Zone" during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
. In 1941, he was admitted to the École Normale Supérieure
École Normale Supérieure
The École normale supérieure is one of the most prestigious French grandes écoles...
in Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
, along with Marcel Boiteux. He was influenced by Henri Cartan
Henri Cartan
Henri Paul Cartan was a French mathematician with substantial contributions in algebraic topology. He was the son of the French mathematician Élie Cartan.-Life:...
and the Bourbaki writers. When he was about to take the final examinations in 1944, D-Day
D-Day
D-Day is a term often used in military parlance to denote the day on which a combat attack or operation is to be initiated. "D-Day" often represents a variable, designating the day upon which some significant event will occur or has occurred; see Military designation of days and hours for similar...
arrived and he, instead, enlisted in the French army. He was transferred for training to Algeria
Algeria
Algeria , officially the People's Democratic Republic of Algeria , also formally referred to as the Democratic and Popular Republic of Algeria, is a country in the Maghreb region of Northwest Africa with Algiers as its capital.In terms of land area, it is the largest country in Africa and the Arab...
and then served among the French occupational forces in Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
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
Léon Walras
Marie-Esprit-Léon Walras was a French mathematical economist associated with the creation of the general equilibrium theory.-Life and career:...
. From 1946 to 1948, he was an assistant in the Centre National de la Recherche Scientifique
Centre national de la recherche scientifique
The National Center of Scientific Research is the largest governmental research organization in France and the largest fundamental science agency in Europe....
. 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
Uppsala University
Uppsala University is a research university in Uppsala, Sweden, and is the oldest university in Scandinavia, founded in 1477. It consistently ranks among the best universities in Northern Europe in international rankings and is generally considered one of the most prestigious institutions of...
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
New Year's Eve
New Year's Eve is observed annually on December 31, the final day of any given year in the Gregorian calendar. In modern societies, New Year's Eve is often celebrated at social gatherings, during which participants dance, eat, consume alcoholic beverages, and watch or light fireworks to mark the...
, 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 ChicagoUniversity of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
in the summer of 1950. He remained there for five years, returning to Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
periodically.
In 1954, he published a breakthrough paper, entitled Existence of an Equilibrium for a Competitive Economy, together with Kenneth Arrow
Kenneth Arrow
Kenneth Joseph Arrow is an American economist and joint winner of the Nobel Memorial Prize in Economics with John Hicks in 1972. To date, he is the youngest person to have received this award, at 51....
, in which they provided a definitive mathematical proof of the existence of a general equilibrium
General equilibrium
General equilibrium theory is a branch of theoretical economics. It seeks to explain the behavior of supply, demand and prices in a whole economy with several or many interacting markets, by seeking to prove that a set of prices exists that will result in an overall equilibrium, hence general...
, using topological
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
rather than calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
-based methods.
In 1955, he moved to Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
.
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
Mathematical economics
Mathematical economics is the application of mathematical methods to represent economic theories and analyze problems posed in economics. It allows formulation and derivation of key relationships in a theory with clarity, generality, rigor, and simplicity...
. He also studied several problems in the theory of cardinal utility
Cardinal utility
In economics, cardinal utility refers to a property of mathematical indices that preserve preference orderings uniquely up to positive linear transformations...
, in particular the additive decomposition
Decomposition
Decomposition is the process by which organic material is broken down into simpler forms of matter. The process is essential for recycling the finite matter that occupies physical space in the biome. Bodies of living organisms begin to decompose shortly after death...
of a utility function defined on a Cartesian product
Cartesian product
In mathematics, a Cartesian product is a construction to build a new set out of a number of given sets. Each member of the Cartesian product corresponds to the selection of one element each in every one of those sets...
of sets.
In this monograph, Debreu set up an axiom
Axiom
In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...
atic 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
Aggregate demand
In macroeconomics, aggregate demand is the total demand for final goods and services in the economy at a given time and price level. It is the amount of goods and services in the economy that will be purchased at all possible price levels. This is the demand for the gross domestic product of a...
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
Uncertainty
Uncertainty is a term used in subtly different ways in a number of fields, including physics, philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and information science...
and showed how it could be incorporated into the deterministic model. Here, he introduced the notion of a contingent commodity
Commodity
In economics, a commodity is the generic term for any marketable item produced to satisfy wants or needs. Economic commodities comprise goods and services....
, 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
Financial economics
Financial Economics is the branch of economics concerned with "the allocation and deployment of economic resources, both spatially and across time, in an uncertain environment"....
, 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
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
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
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
, 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
Leiden University
Leiden University , located in the city of Leiden, is the oldest university in the Netherlands. The university was founded in 1575 by William, Prince of Orange, leader of the Dutch Revolt in the Eighty Years' War. The royal Dutch House of Orange-Nassau and Leiden University still have a close...
, Cambridge, Bonn
University of Bonn
The University of Bonn is a public research university located in Bonn, Germany. Founded in its present form in 1818, as the linear successor of earlier academic institutions, the University of Bonn is today one of the leading universities in Germany. The University of Bonn offers a large number...
and Paris
University of Paris
The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...
.
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
Alfred Nobel
Alfred Bernhard Nobel was a Swedish chemist, engineer, innovator, and armaments manufacturer. He is the inventor of dynamite. Nobel also owned Bofors, which he had redirected from its previous role as primarily an iron and steel producer to a major manufacturer of cannon and other armaments...
, 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
American Economic Association
The American Economic Association, or AEA, is a learned society in the field of economics, headquartered in Nashville, Tennessee. It publishes one of the most prestigious academic journals in economics: the American Economic Review...
.
Major publications
- "The Coefficient of Resource Utilization", 1951, Econometrica.
- "A Social Equilibrium Existence Theorem", 1952, Proceedings of the National Academy of SciencesProceedings of the National Academy of SciencesThe Proceedings of the National Academy of Sciences of the United States of America, usually referred to as PNAS, is the official journal of the United States 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 SciencesProceedings of the National Academy of SciencesThe Proceedings of the National Academy of Sciences of the United States of America, usually referred to as PNAS, is the official journal of the United States 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.
- "Innovation and Research: An Economist's Viewpoint on Uncertainty", 1994, Nobelists for the Future
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
- Lectures on Mathematical Economics from 1987 at University of Canterbury