Skip to main content
×
Home
    • Aa
    • Aa

ARROW AND DEBREU DE-HOMOGENIZED

Abstract

To this day, the so-called Arrow–Debreu model represents a trademark of rigorous economic research—be it as a benchmark for extending the model, for weakening its assumptions, for structuring data sets, or for providing alternative models. But who should earn the credit? Arrow or Debreu? This essay presents “the making of” Arrow’s and Debreu’s joint article of 1954 as documented in their extensive letter exchange between their first contact in February 1952 and submission in May 1953. I show, pivotally, that Arrow and Debreu did not share the same interest in their work, that they played different roles, and drew different lessons from it. Moreover, neither Arrow nor Debreu can be identified with the way the profession would later refer to the Arrow–Debreu model. To the contrary, both, in their own ways, sought to counter what others perceived as limitations when placing their hopes in the model.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

Kenneth Arrow , and Gerard Debreu . 1954. “Existence of an Equilibrium for a Competitive Economy.” Econometrica 22 (3): 265290.

Kenneth Arrow , and Leonid Hurwicz . 1958. “On the Stability of Competitive Equilibrium I.” Econometrica 26: 522552.

Kenneth Arrow , H. D. Block , and Leonid Hurwicz . 1959. “On the Stability of the Competitive Equilibrium, II.” Econometrica 27 (1): 82109.

Edward G Begle . 1950. “A Fixed Point Theorem.” The Annals of Mathematics 51 (3): 544550.

Gerard Debreu . 1951a. “The Coefficient of Resource Utilization.” Econometrica 19 (3): 273292.

Gerard Debreu . 1952b. “A Social Equilibrium Existence Theorem.” Proceedings of the National Academy of Sciences 38 (8): 886893.

Gerard Debreu . 1956. “Market Equilibrium.” Proceedings of the National Academy of Sciences 42 (11): 876878.

Gerard Debreu , and Israel N. Herstein . 1953. “Nonnegative Square Matrices.” Econometrica 21 (4): 597607.

Till Düppe . 2012. “Gerard Debreu’s Secrecy: His Life in Order and Silence.” History of Political Economy 44 (3): 413449.

Samuel Eilenberg , and Deane Montgomery . 1946. “Fixed Point Theorems for Multi-Valued Transformations.” American Journal of Mathematics 68 (2): 214222.

R. Feiwel George , ed. 1987. Arrow and the Ascent of Modern Economic Theory. New York: New York University Press.

David Gale . 1963. “A Note on Global Instability of Competitive Equilibrium.” Naval Research Logistics Quarterly 10: 8187.

Israel N. Herstein , and John Milnor . 1953. “An Axiomatic Approach to Measurable Utility.” Econometrica 21 (2): 291297.

Harold Hotelling . 1938. “The General Welfare in Relation to Problems of Taxation and of Railway and Utility Rates.” Econometrica 6 (3): 242269.

William Jaffe . 1967. “Walras Theory of Tâtonnement: Critique of Recent Interpretations.” Journal of Political Economy 75 (1): 119.

Shizuo Kakutani . 1951. “A Generalization of Brouwer’s Fixed Point Theorem.” Duke Mathematical Journal 8 (3): 457459.

Oscar Lange . 1942. “The Foundations of Welfare Economics.” Econometrica 10 (3/4): 215228.

Robert Leonard . 2010. Von Neumann, Morgenstern, and the Creation of Game Theory: From Chess to Social Science, 1900–1960. Cambridge: Cambridge University Press.

Lionel McKenzie . 1954. “On Equilibrium in Graham’s Model of World Trade and Other Competitive Systems.” Econometrica 22: 147161.

Lionel McKenzie . 1960. “Stability of Equilibrium and the Value of Positive Excess Demand.” Econometrica 28 (3): 606617.

John F Nash . 1950. “Equilibrium Points in N-person Games.” Proceedings of the National Academy of Sciences 36: 4849.

John von Neumann . 1928. „Zur Theorie der Gesellschaftspiele.” Mathematische Annalen 100: 295320. Translated 1959, “On the Theory of Games of Strategy.” In Luce and Tucker, eds., Contributions to the Theory of Games, IV. Princeton: Princeton University Press, pp. 13–42.

Hukukane Nikaido . 1956. “On the Classical Multilateral Exchange Problem.” Metroeconomica 8: 135145.

K. Oehler 1990. “Speaking Axiomatically: Citation Patterns to Early Articles in General Equilibrium Theory.” History of Political Economy 22 (1): 101112.

Herbert Scarf . 1960. “Some Examples of Global Instability of Competitive Equilibrium.” International Economic Review 1 (3): 157172.

Martin Shubik . 1961. “Review of Theory of Value.” The Canadian Journal of Economics and Political Science 27 (1): 133.

Martin Shubik . [1972] 1977. “Competitive and Controlled Price Economies: The Arrow–Debreu Model Revisited.” In G. Schwodiauer , ed., Equilibrium and Disequilibrium in Economic Theory. Dordrecht: D. Reidel, pp. 213224.

Abraham Wald . [1936] 1951. “On Some Systems of Equations of Mathematical Economics.” Econometrica 19 (4): 368403. Translated from “Über einige Gleichungssysteme der mathematischen Ökonomie.” Zeitschrift für Nationalökonomie 7 (5): 637–670.

E. Roy. Weintraub 2002. How Economics Became a Mathematical Science. Durham and London: Duke University Press.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the History of Economic Thought
  • ISSN: 1053-8372
  • EISSN: 1469-9656
  • URL: /core/journals/journal-of-the-history-of-economic-thought
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×