Gerard Debreu (b. 1921)

Gerard Debreu was born in Calais, France in 1921. He studied at the École Normal Supérieure, Paris in the early 1940s and obtained his degree in mathematics from the University of Paris in 1946. From 1946 to 1948 he was a research associate at the Centre National de la Recherche Scientifique in Paris. In receipt of a Rockefeller Foundation Scholarship (1948–50), he spent time in the United States (where he visited Harvard University, the University of California, Berkeley, the University of Chicago and Columbia University), Sweden (where he visited the University of Uppsala) and Norway (where he visited the University of Oslo). From 1950 to 1955, he was a research associate at the Cowles Commission for Research in Economics at the University of Chicago. In 1956 he obtained his doctorate in mathematics from the University of Paris. He moved from Chicago to New Haven, Connecticut in 1955 when the Cowles Commission moved from the University of Chicago to Yale University. He was associate professor at the renamed Cowles Foundation until 1961. In 1962 he joined the faculty of the University of California, Berkeley as Professor of Economics, and in 1975 was appointed Professor of Mathematics, the same year he became a US citizen. Since 1986, Debreu has been Professor of Economics and Mathematics, Emeritus, at Berkeley.

Debreu’s many offices and honours include the presidencies of the Econometric Society in 1971 and the American Economic Association in 1990; in 1976 was made a Chevalier of the French Legion of Honour. In 1983, Debreu was awarded the Nobel Memorial Prize in Economics ‘for having incorporated new analytical methods into economic theory and for his rigorous reformulation of the theory of general equilibrium’ (Nobel Foundation, 2004).

Debreu is best known for his pioneering contributions in two main areas: the theory of general equilibrium and mathematical economics. In order to place his work in perspective we need to mention some insights of two eminent past economists. Writing in the eighteenth century, the Scottish economist and philosopher Adam Smith (1723–90) argued that, in a market economy, the decisions of ‘self-interested’ agents are coordinated through the ‘invisible hand’ of the price system. Later in the nineteenth century, the French economist Léon Walras (1834–1910) presented a mathematical formulation of Smith’s ideas in which equilibrium in all markets in an economy is simultaneously determined. Although this work was important to the development of the theory of general equilibrium, without the necessary mathematical tools Walras was not able to prove that there exists a set of prices that equilibrates all markets simultaneously. It was not until the mid-1950s that Debreu, working in collaboration with Kenneth Arrow (the 1972 Nobel Memorial Laureate), provided a rigorous and definitive mathematical proof of the existence of general equilibrium in a model of a market economy (Arrow and Debreu, 1954). Their seminal article, ‘Existence of an Equilibrium for a Competitive Economy’, has come to be known as the Arrow–Debreu model. Given certain assumptions, Arrow and Debreu were able to prove the existence of equilibrium prices using complex mathematical techniques (set theory and topology) not previously used in economics.

Equally famous is Debreu’s classic book, Theory of Value (Debreu, 1959), in which he put forward what he termed ‘an axiomatic analysis of economic equilibrium’. The book, which presents a rigorous yet succinct exposition of the theory of general economic equilibrium, follows a logical and structured direction. Having outlined in the opening chapter the mathematical concepts and results used in the rest of the book, Debreu then discusses the concepts of a commodity and prices, producer behaviour, consumer behaviour, equilibrium, the relationship between equilibrium and Pareto optimality,and uncertainty. Much of Debreu’s later work, which is highly technical in nature, has been devoted to an analysis of the uniqueness of an equilibrium (for example, Debreu, 1970), the stability of equilibrium (for example, Debreu and Scarf, 1963), the rate of convergence to a set of equilibria (for example, Debreu, 1975), and an examination of the conditions which ensure that the price system brings about an efficient allocation of resources. For those readers not trained in mathematical economics, more accessible discussions of ‘economic theory in a mathematical mode’ and the ‘mathematization of economic theory’ can be found in Debreu (1984 – his Nobel Memorial Lecture); and Debreu (1991 – his presidential address to the American Economic Association).

Compared to the large number of books and articles written by many of the Nobel Memorial Laureates outlined in this volume, Debreu’s published works are relatively few in number. His main contributions to economics can be found in his short book Theory of Value (Debreu, 1959), which is just over 100 pages in length, and the 20 papers he selected for inclusion in his book Mathematical Economics (Debreu, 1983) – a volume which contains an introduction by Werner Hildenbrand assessing Debreu’s contributions and the part played by the selected papers in the development of mathematical economics. Despite the relative paucity of his published works Debreu’s influence on the form and direction that economic theory has taken since the mid-1950s, most notably the mathematisation of economic theory, has been profound. His pioneering research in the field of general equilibrium theory has made a lasting impression on the (axiomatic) methods and techniques used in numerous fields of study, including the theory of international trade, capital theory and macroeconomic theory. Those readers interested in general equilibrium theory should consult the three-volume set (Debreu, 1996) which gathers together many of the most important articles that have played an influential role in the development of this central field of study.

Main Published Works
(1954), ‘Existence of an Equilibrium for a Competitive Economy’ (with K.J. Arrow),
Econometrica, 22, July, pp. 265–90.

(1959), Theory of Value: An Axiomatic Analysis of Economic Equilibrium, New York: John Wiley
& Sons; New Haven, CT: Yale University Press, 1971.

(1963), ‘A Limit Theorem on the Core of an Economy’ (with H. Scarf), International Economic
Review, 4, September, pp. 235–46.

(1970), ‘Economies with a Finite Set of Equilibria’, Econometrica, 38, May, pp. 387–92.
(1975), ‘The Rate of Convergence of the Core of an Economy’, Journal of Mathematical Economics, 2, pp. 1–7.
(1983), Mathematical Economics: Twenty Papers of Gerard Debreu, Cambridge: Cambridge University Press.
(1984), ‘Economic Theory in the Mathematical Mode’, American Economic Review, 74, June, pp. 267–78.
(1991), ‘The Mathematization of Economic Theory’, American Economic Review, 81, March, pp. 1–7.
(1996), General Equilibrium Theory, 3 vols (ed.), Cheltenham, UK and Brookfield, USA: Edward Elgar.