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Gérard Debreu

May 08, 2023

Gérard Debreu (French: [dəbʁø]; 4 July 1921 – 31 December 2004) was a French-born economist and mathematician. 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 Economic Sciences.[1]

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
InstitutionUniversity of California, Berkeley
FieldMathematical economics
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
integration of set-valued correspondences
AwardsNobel Memorial Prize in Economics (1983)
Information at IDEAS / RePEc

Biography

His father was the business partner of his maternal grandfather in lace manufacturing, a traditional industry in Calais. Debreu was orphaned at an early age, as his father committed suicide and his mother died of natural causes.[2] 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 Vichy France 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, the Normandy landings occurred and he, instead, enlisted in the French army. He was transferred for training to Algeria and then served in the occupying French 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 went to the United States on a Rockefeller Fellowship which allowed him to visit several American universities, as well as those in Uppsala and Oslo in 1949–50.[3] He received his Ph.D. from the University of Paris in 1956. In 1960 he became a professor at the University 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 on New Year's Eve, 2004.

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.[4] 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.[5]

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.[6][7][8]

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

Major publications

Books

  • Debreu, Gérard (1959). The theory of value: an axiomatic analysis of economic equilibrium (PDF). New York: Wiley. OCLC 270657.
  • Debreu, Gérard (1986). Mathematical economics: twenty papers of Gerard Debreu. Cambridge Cambridgeshire New York: Cambridge University Press. ISBN 9780521335614.
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 (by Gérard Debreu and Kenneth 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 (by Gérard Debreu and Herbert 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

  • Debreu, Gérard (1954), "Representation of a preference ordering by a numerical function", in Thrall, Robert M.; Coombs, Clyde H.; Raiffa, Howard (eds.), Decision processes, New York: Wiley, pp. 159–167, OCLC 639321.
  • Debreu, Gérard (1960), "Topological methods in cardinal utility theory", in Arrow, Kenneth J.; Karlin, Samuel; Suppes, Patrick (eds.), Mathematical models in the social sciences, 1959: Proceedings of the first Stanford symposium, Stanford mathematical studies in the social sciences, IV, Stanford, California: Stanford University Press, pp. 16–26, ISBN 9780804700214. Pdf.
  • Debreu, Gérard; Scarf, Herbert (1972), "A limit theorem on the core of an economy", in McGuire, C.B.; Radner, Roy (eds.), Decision and organization: a volume in honor of Jacob Marschak, Studies in Mathematical and Managerial Economics Series (volume 12), Amsterdam: North-Holland Pub. Co., pp. 283–297, ISBN 9780720433135.
  • Debreu, Gérard (1981), "Existence of competitive equilibrium", in Arrow, Kenneth J.; Intriligator, Michael D. (eds.), Handbook of mathematical economics, Handbook of Economics Series, Amsterdam New York, New York: Elsevier North-Holland, pp. 697–744, ISBN 9780444861269.

Journal articles

  • Debreu, Gérard (July 1951). "The coefficient of resource utilization". Econometrica. 19 (3): 273–292. doi:10.2307/1906814. JSTOR 1906814. Pdf. 2016-03-07 at the Wayback Machine
  • Debreu, Gérard (April 1952). "Definite and semidefinite quadratic forms". Econometrica. 20 (2): 295–300. doi:10.2307/1907852. JSTOR 1907852.
  • Debreu, Gérard (October 1952). "A social equilibrium existence theorem". Proceedings of the National Academy of Sciences. 38 (10): 886–893. Bibcode:1952PNAS...38..886D. doi:10.1073/pnas.38.10.886. JSTOR 88720. PMC 1063675. PMID 16589195. Full text.
  • Debreu, Gérard; Herstein, Israel N. (October 1953). "Nonnegative square matrices". Econometrica. 21 (4): 597–607. doi:10.2307/1907925. JSTOR 1907925. Pdf.
  • Debreu, Gérard (January 1954). "A classical tax-subsidy problem". Econometrica. 22 (1): 14–22. doi:10.2307/1909828. JSTOR 1909828. Pdf.
  • Debreu, Gérard (June 1954). "Numerical representations of technological change". Metroeconomica. 6 (2): 45–54. doi:10.1111/j.1467-999X.1954.tb00485.x.
  • Debreu, Gérard (July 1954). "Valuation equilibrium and Pareto optimum". Proceedings of the National Academy of Sciences. 40 (7): 588–592. Bibcode:1954PNAS...40..588D. doi:10.1073/pnas.40.7.588. JSTOR 89325. PMC 528000. PMID 16589528. Pdf.
  • Debreu, Gérard; Arrow, Kenneth J. (July 1954). "Existence of an equilibrium for a competitive economy". Econometrica. 22 (3): 265–290. doi:10.2307/1907353. JSTOR 1907353. Pdf.
  • Debreu, Gérard (November 1956). "Market equilibrium". Proceedings of the National Academy of Sciences. 42 (11): 876–878. Bibcode:1956PNAS...42..876D. doi:10.1073/pnas.42.11.876. JSTOR 89463. PMC 528356. PMID 16589963. Pdf.
  • Debreu, Gérard (July 1958). "Stochastic choice and cardinal utility" (PDF). Econometrica. 26 (3): 440–444. doi:10.2307/1907622. JSTOR 1907622. Pdf.
  • Debreu, Gérard (June 1959). "Cardinal utility for even-chance mixtures of pairs of sure prospects" (PDF). The Review of Economic Studies. 26 (3): 174–177. doi:10.2307/2295745. JSTOR 2295745. Pdf.
  • Debreu, Gérard (1960). [Economics under uncertainty]. Économie Appliquée. 13 (1): 111–116. Archived from the original on 2016-06-02.
  • Debreu, Gérard (April 1960). "On 'an identity in arithmetic'". Proceedings of the American Mathematical Society. 11 (2): 220–221. doi:10.2307/2032959. JSTOR 2032959. Pdf.
  • Debreu, Gérard (September 1962). "New concepts and techniques for equilibrium analysis" (PDF). International Economic Review. 3 (3): 257–273. doi:10.2307/2525394. JSTOR 2525394.
  • Debreu, Gérard; Scarf, Herbert (September 1963). "A limit theorem on the core of an economy". International Economic Review. 4 (3): 235–246. doi:10.2307/2525306. JSTOR 2525306.
  • Debreu, Gérard (October 1963). "On a theorem of Scarf". The Review of Economic Studies. 30 (3): 177–180. doi:10.2307/2296318. JSTOR 2296318.
  • Debreu, Gérard (May 1964). "Nonnegative solutions of linear inequalities". International Economic Review. 5 (2): 178–184. doi:10.2307/2525561. JSTOR 2525561.
  • Debreu, Gérard (September 1964). "Contuinity properties of Paretian utility". International Economic Review. 5 (3): 285–293. doi:10.2307/2525513. JSTOR 2525513. Pdf. 2016-03-07 at the Wayback Machine
  • Debreu, Gérard (1967). "Integration of correspondences". Proceedings of Fifth Berkeley Symposium on Mathematical Statistics and Probability, Part 1. 2: 351–372. Pdf.
  • Debreu, Gérard (January 1967). "Preference functions on measure spaces of economic agents". Econometrica. 35 (1): 111–122. doi:10.2307/1909386. JSTOR 1909386.
  • Debreu, Gérard (1969). . La Décision. 171: 85–90. Archived from the original on 2016-02-21.
  • Debreu, Gérard (May 1970). "Economies with a finite set of equilibria". Econometrica. 38 (3): 387–392. doi:10.2307/1909545. JSTOR 1909545. Pdf. 2003-09-04 at the Wayback Machine
  • Debreu, Gérard (July 1972). "Smooth preferences". Econometrica. 40 (4): 603–615. doi:10.2307/1912956. JSTOR 1912956. Pdf.[permanent dead link]
  • Debreu, Gérard (1974). "Four aspects of the mathematical theory of economic equilibrium" (PDF). Proceedings of International Congress of Mathematicians: 65–77.
  • Debreu, Gérard (March 1974). "Excess demand functions". Journal of Mathematical Economics. 1 (1): 15–21. doi:10.1016/0304-4068(74)90032-9.
  • Debreu, Gérard (March 1975). "The rate of convergence of the core of an economy". Journal of Mathematical Economics. 2 (1): 1–7. doi:10.1016/0304-4068(75)90008-7.
  • Debreu, Gérard (May 1976). "The application to economics of differential topology and global analysis: regular differentiable economies". The American Economic Review: Papers and Proceedings. 66 (2): 280–287. JSTOR 1817234.
  • Debreu, Gérard (July 1976). "Least concave utility functions". Journal of Mathematical Economics. 3 (2): 121–129. doi:10.1016/0304-4068(76)90020-3.
  • Debreu, Gérard; Koopmans, Tjalling C. (December 1982). "Additively decomposed quasiconvex functions" (PDF). Mathematical Programming. 24 (1): 1–38. doi:10.1007/BF01585092. S2CID 206799604.
  • Debreu, Gérard (June 1984). "Economic theory in the mathematical mode". The American Economic Review. 74 (3): 267–278. JSTOR 1804007.
  • Debreu, Gérard (December 1984). "Economic theory in the mathematical mode". The Scandinavian Journal of Economics. 86 (4): 393–410. doi:10.2307/3439651. JSTOR 3439651.
  • Debreu, Gérard (November 1986). "Theoretic models: mathematical form and economic content". Econometrica. 54 (6): 1259–1270. doi:10.2307/1914299. JSTOR 1914299.
  • Debreu, Gérard (March 1991). "The mathematization of economic theory". The American Economic Review. 81 (1): 1–7. JSTOR 2006785. (Presidential address delivered at the 103rd meeting of the American Economic Association, 29 December 1990, Washington, DC.) Full text.
  • Debreu, Gérard (1994). "Innovation and research: an economist's viewpoint on uncertainty". Nobelists for the Future.
  • Debreu, Gérard; Buchanan, James M.; Klein, Lawrence R.; Friedman, Milton; Solow, Robert M. (Autumn 2001). "The most significant contributions to economics during the twentieth century: lists of the Nobel laureates". The European Journal of the History of Economic Thought. 8 (3): 289–297. doi:10.1080/09672560110062915. S2CID 154302343.

References

  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. ^ a b "The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1983". NobelPrize.org. Retrieved 2023-01-01.
  4. ^ Debreu, Gérard (1959). The theory of value: an axiomatic analysis of economic equilibrium (PDF). New York: Wiley. OCLC 270657.
  5. ^ Archived at Ghostarchive and the : "Gerard Debreu: Lecture 2 on Economic Theory (1987)". YouTube.
  6. ^ "Gerard Debreu". American Academy of Arts & Sciences. Retrieved 2022-05-23.
  7. ^ "Gerard Debreu". www.nasonline.org. Retrieved 2022-05-23.
  8. ^ "APS Member History". search.amphilsoc.org. Retrieved 2022-05-23.
  9. ^ Debreu, Gérard (March 1991). "The mathematization of economic theory". The American Economic Review. 81 (1): 1–7. JSTOR 2006785. Full text.

External links

 
Wikiquote has quotations related to Gérard Debreu.
 
Wikimedia Commons has media related to Gérard Debreu.

May 08, 2023
gérard, debreu, french, dəbʁø, july, 1921, december, 2004, french, born, economist, mathematician, best, known, professor, economics, university, california, berkeley, where, began, work, 1962, 1983, nobel, memorial, prize, economic, sciences, debreu, 1977born. Gerard Debreu French debʁo 4 July 1921 31 December 2004 was a French born economist and mathematician 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 Economic Sciences 1 Gerard DebreuDebreu in 1977Born 1921 07 04 4 July 1921Calais FranceDied31 December 2004 2004 12 31 aged 83 Paris FranceNationalityFrenchInstitutionUniversity of California BerkeleyFieldMathematical economicsSchool ortraditionWalrasian economicsAlma materEcole Normale SuperieureUniversity of ParisDoctoralstudentsGraciela ChichilniskyBeth E AllenXavier VivesIshac DiwanInfluencesLeon Walras Henri Cartan Maurice Allais BourbakiContributionsGeneral equilibrium utility theory topological methods integration of set valued correspondencesAwardsNobel Memorial Prize in Economics 1983 Information at IDEAS RePEc Contents 1 Biography 2 Academic career 3 Major publications 3 1 Books 3 2 Book chapters 3 3 Journal articles 4 References 5 External linksBiography EditHis father was the business partner of his maternal grandfather in lace manufacturing a traditional industry in Calais Debreu was orphaned at an early age as his father committed suicide and his mother died of natural causes 2 Prior to the start of World War II he received his baccalaureat and went to Ambert to begin preparing for the entrance examination of a grande ecole Later on he moved from Ambert to Grenoble to complete his preparation both places being in Vichy France during World War II In 1941 he was admitted to the Ecole Normale Superieure 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 the Normandy landings occurred and he instead enlisted in the French army He was transferred for training to Algeria and then served in the occupying French Forces in Germany until July 1945 Debreu passed the Agregation de Mathematiques 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 Leon 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 went to the United States on a Rockefeller Fellowship which allowed him to visit several American universities as well as those in Uppsala and Oslo in 1949 50 3 He received his Ph D from the University of Paris in 1956 In 1960 he became a professor at the University of California where he taught until 1991 3 Debreu married Francoise 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 on New Year s Eve 2004 Academic career EditDebreu 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 4 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 5 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 6 7 8 In 1990 he served as president of the American Economic Association 9 Major publications EditBooks Edit Debreu Gerard 1959 The theory of value an axiomatic analysis of economic equilibrium PDF New York Wiley OCLC 270657 Debreu Gerard 1986 Mathematical economics twenty papers of Gerard Debreu Cambridge Cambridgeshire New York Cambridge University Press ISBN 9780521335614 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 by Gerard Debreu and Kenneth 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 by Gerard Debreu and Herbert 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 dd Debreu Gerard Arrow Kenneth J 2001 Landmark papers in general equilibrium theory social choice and welfare Cheltenham UK Northampton Massachusetts USA Edward Elgar Publishing ISBN 9781840645699 Book chapters Edit Debreu Gerard 1954 Representation of a preference ordering by a numerical function in Thrall Robert M Coombs Clyde H Raiffa Howard eds Decision processes New York Wiley pp 159 167 OCLC 639321 Pdf Debreu Gerard 1960 Topological methods in cardinal utility theory in Arrow Kenneth J Karlin Samuel Suppes Patrick eds Mathematical models in the social sciences 1959 Proceedings of the first Stanford symposium Stanford mathematical studies in the social sciences IV Stanford California Stanford University Press pp 16 26 ISBN 9780804700214 Pdf Debreu Gerard Scarf Herbert 1972 A limit theorem on the core of an economy in McGuire C B Radner Roy eds Decision and organization a volume in honor of Jacob Marschak Studies in Mathematical and Managerial Economics Series volume 12 Amsterdam North Holland Pub Co pp 283 297 ISBN 9780720433135 Debreu Gerard 1981 Existence of competitive equilibrium in Arrow Kenneth J Intriligator Michael D eds Handbook of mathematical economics Handbook of Economics Series Amsterdam New York New York Elsevier North Holland pp 697 744 ISBN 9780444861269 Journal articles Edit Debreu Gerard July 1951 The coefficient of resource utilization Econometrica 19 3 273 292 doi 10 2307 1906814 JSTOR 1906814 Pdf Archived 2016 03 07 at the Wayback Machine Debreu Gerard April 1952 Definite and semidefinite quadratic forms Econometrica 20 2 295 300 doi 10 2307 1907852 JSTOR 1907852 Debreu Gerard October 1952 A social equilibrium existence theorem Proceedings of the National Academy of Sciences 38 10 886 893 Bibcode 1952PNAS 38 886D doi 10 1073 pnas 38 10 886 JSTOR 88720 PMC 1063675 PMID 16589195 Full text Debreu Gerard Herstein Israel N October 1953 Nonnegative square matrices Econometrica 21 4 597 607 doi 10 2307 1907925 JSTOR 1907925 Pdf Debreu Gerard January 1954 A classical tax subsidy problem Econometrica 22 1 14 22 doi 10 2307 1909828 JSTOR 1909828 Pdf Debreu Gerard June 1954 Numerical representations of technological change Metroeconomica 6 2 45 54 doi 10 1111 j 1467 999X 1954 tb00485 x Debreu Gerard July 1954 Valuation equilibrium and Pareto optimum Proceedings of the National Academy of Sciences 40 7 588 592 Bibcode 1954PNAS 40 588D doi 10 1073 pnas 40 7 588 JSTOR 89325 PMC 528000 PMID 16589528 Pdf Debreu Gerard Arrow Kenneth J July 1954 Existence of an equilibrium for a competitive economy Econometrica 22 3 265 290 doi 10 2307 1907353 JSTOR 1907353 Pdf Debreu Gerard November 1956 Market equilibrium Proceedings of the National Academy of Sciences 42 11 876 878 Bibcode 1956PNAS 42 876D doi 10 1073 pnas 42 11 876 JSTOR 89463 PMC 528356 PMID 16589963 Pdf Debreu Gerard July 1958 Stochastic choice and cardinal utility PDF Econometrica 26 3 440 444 doi 10 2307 1907622 JSTOR 1907622 Pdf Debreu Gerard June 1959 Cardinal utility for even chance mixtures of pairs of sure prospects PDF The Review of Economic Studies 26 3 174 177 doi 10 2307 2295745 JSTOR 2295745 Pdf Debreu Gerard 1960 Une economique de l incertain Economics under uncertainty Economie Appliquee 13 1 111 116 Archived from the original on 2016 06 02 Debreu Gerard April 1960 On an identity in arithmetic Proceedings of the American Mathematical Society 11 2 220 221 doi 10 2307 2032959 JSTOR 2032959 Pdf Debreu Gerard September 1962 New concepts and techniques for equilibrium analysis PDF International Economic Review 3 3 257 273 doi 10 2307 2525394 JSTOR 2525394 Pdf Debreu Gerard Scarf Herbert September 1963 A limit theorem on the core of an economy International Economic Review 4 3 235 246 doi 10 2307 2525306 JSTOR 2525306 Pdf Debreu Gerard October 1963 On a theorem of Scarf The Review of Economic Studies 30 3 177 180 doi 10 2307 2296318 JSTOR 2296318 Debreu Gerard May 1964 Nonnegative solutions of linear inequalities International Economic Review 5 2 178 184 doi 10 2307 2525561 JSTOR 2525561 Debreu Gerard September 1964 Contuinity properties of Paretian utility International Economic Review 5 3 285 293 doi 10 2307 2525513 JSTOR 2525513 Pdf Archived 2016 03 07 at the Wayback Machine Debreu Gerard 1967 Integration of correspondences Proceedings of Fifth Berkeley Symposium on Mathematical Statistics and Probability Part 1 2 351 372 Pdf Debreu Gerard January 1967 Preference functions on measure spaces of economic agents Econometrica 35 1 111 122 doi 10 2307 1909386 JSTOR 1909386 Debreu Gerard 1969 Neighboring economic agents La Decision 171 85 90 Archived from the original on 2016 02 21 Debreu Gerard May 1970 Economies with a finite set of equilibria Econometrica 38 3 387 392 doi 10 2307 1909545 JSTOR 1909545 Pdf Archived 2003 09 04 at the Wayback Machine Debreu Gerard July 1972 Smooth preferences Econometrica 40 4 603 615 doi 10 2307 1912956 JSTOR 1912956 Pdf permanent dead link Debreu Gerard 1974 Four aspects of the mathematical theory of economic equilibrium PDF Proceedings of International Congress of Mathematicians 65 77 Debreu Gerard March 1974 Excess demand functions Journal of Mathematical Economics 1 1 15 21 doi 10 1016 0304 4068 74 90032 9 Debreu Gerard March 1975 The rate of convergence of the core of an economy Journal of Mathematical Economics 2 1 1 7 doi 10 1016 0304 4068 75 90008 7 Debreu Gerard May 1976 The application to economics of differential topology and global analysis regular differentiable economies The American Economic Review Papers and Proceedings 66 2 280 287 JSTOR 1817234 Debreu Gerard July 1976 Least concave utility functions Journal of Mathematical Economics 3 2 121 129 doi 10 1016 0304 4068 76 90020 3 Debreu Gerard Koopmans Tjalling C December 1982 Additively decomposed quasiconvex functions PDF Mathematical Programming 24 1 1 38 doi 10 1007 BF01585092 S2CID 206799604 Debreu Gerard June 1984 Economic theory in the mathematical mode The American Economic Review 74 3 267 278 JSTOR 1804007 Pdf Debreu Gerard December 1984 Economic theory in the mathematical mode The Scandinavian Journal of Economics 86 4 393 410 doi 10 2307 3439651 JSTOR 3439651 Pdf Debreu Gerard November 1986 Theoretic models mathematical form and economic content Econometrica 54 6 1259 1270 doi 10 2307 1914299 JSTOR 1914299 Debreu Gerard March 1991 The mathematization of economic theory The American Economic Review 81 1 1 7 JSTOR 2006785 Presidential address delivered at the 103rd meeting of the American Economic Association 29 December 1990 Washington DC Full text Debreu Gerard 1994 Innovation and research an economist s viewpoint on uncertainty Nobelists for the Future Debreu Gerard Buchanan James M Klein Lawrence R Friedman Milton Solow Robert M Autumn 2001 The most significant contributions to economics during the twentieth century lists of the Nobel laureates The European Journal of the History of Economic Thought 8 3 289 297 doi 10 1080 09672560110062915 S2CID 154302343 References Edit Atlas Riva D 6 January 2005 Gerard Debreu 83 Dies Won Nobel in Economics The New York Times Duppe 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 a b The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1983 NobelPrize org Retrieved 2023 01 01 Debreu Gerard 1959 The theory of value an axiomatic analysis of economic equilibrium PDF New York Wiley OCLC 270657 Archived at Ghostarchive and the Wayback Machine Gerard Debreu Lecture 2 on Economic Theory 1987 YouTube Gerard Debreu American Academy of Arts amp Sciences Retrieved 2022 05 23 Gerard Debreu www nasonline org Retrieved 2022 05 23 APS Member History search amphilsoc org Retrieved 2022 05 23 Debreu Gerard March 1991 The mathematization of economic theory The American Economic Review 81 1 1 7 JSTOR 2006785 Full text External links Edit Wikiquote has quotations related to Gerard Debreu Wikimedia Commons has media related to Gerard Debreu Gerard Debreu on Nobelprize org including the Nobel Lecture December 8 1983 Economic Theory in the Mathematical Mode Obituary for Debreu Guide to the Gerard Debreu Papers at The Bancroft Library Lectures on Mathematical Economics from 1987 at University of Canterbury via YouTube Duppe 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 Gerard Debreu 1921 2004 The Concise Encyclopedia of Economics Library of Economics and Liberty 2nd ed Liberty Fund 2008 AwardsPreceded byGeorge Stigler Laureate of the Nobel Memorial Prize in Economics1983 Succeeded byRichard Stone Retrieved from https en wikipedia org w index php title Gerard Debreu amp oldid 1142046173, wikipedia, wiki, book, books, 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