Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-12T17:00:57.696Z Has data issue: false hasContentIssue false
  • English
  • Français

ARROW AND DEBREU DE-HOMOGENIZED

Published online by Cambridge University Press:  14 November 2012

TILL DÜPPE
Get access Rights & Permissions [Opens in a new window]

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.

Type
Articles
Information
Journal of the History of Economic Thought , Volume 34 , Issue 4 , December 2012 , pp. 491 - 514
Copyright
Copyright © The History of Economics Society 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Arrow, Kenneth J. 1951a. “Alternative Proof of the Substitution Theorem of Leontief Models in the General Case.” In Koopmans, T., ed., Activity Analysis of Production and Allocation. New York: John Wiley, pp. 155–164.Google Scholar
Arrow, Kenneth J. 1951b. Social Choice and Individual Values. New York: John Wiley.Google Scholar
Arrow, Kenneth J. 1951c. “An Extension of the Basic Theorems of Classical Welfare Economics.” In Neyman, J., ed., Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. Berkeley and Los Angeles: University of California Press, pp. 507–532.Google Scholar
Arrow, Kenneth J. 1952. “Le role des valeurs boursières pour la répartition la meilleure des risques.” International Colloquium on Econometrics. Paris: CNRS, pp. 1–8.Google Scholar
Arrow, Kenneth, and Debreu, Gerard. 1954. “Existence of an Equilibrium for a Competitive Economy.” Econometrica 22 (3): 265–290.CrossRefGoogle Scholar
Arrow, Kenneth, and Debreu, Gerard, eds. 2001. Companion to General Equilibrium. Landmark Papers in General Equilibrium Theory, Social Choice and Welfare. Cheltenham: Edward Elgar.Google Scholar
Arrow, Kenneth, and Enthoven, Alain. 1956. “A Theorem on Expectations and the Stability of Equilibrium.” Econometrica 24 (3): 288–293.Google Scholar
Arrow, Kenneth, and Hurwicz, Leonid. 1958. “On the Stability of Competitive Equilibrium I.” Econometrica 26: 522–552.CrossRefGoogle Scholar
Arrow, Kenneth, Block, H. D., and Hurwicz, Leonid. 1959. “On the Stability of the Competitive Equilibrium, II.” Econometrica 27 (1): 82–109.CrossRefGoogle Scholar
Arrow, Kenneth, and Hahn, Frank. 1971. General Competitive Analysis. Amsterdam: Elsevier.Google Scholar
Begle, Edward G. 1950. “A Fixed Point Theorem.” The Annals of Mathematics 51 (3): 544–550.CrossRefGoogle Scholar
Debreu, Gerard. Gerard Debreu Papers [DP], Carton 1–14, additional carton 1–4, BANC MSS 2006/218. The Bancroft Library, University of California, Berkeley.Google Scholar
Debreu, Gerard. 1951a. “The Coefficient of Resource Utilization.” Econometrica 19 (3): 273–292.CrossRefGoogle Scholar
Debreu, Gerard. 1951b. “Saddle Point Existence Theorems.” CCDP Mathematics 412.Google Scholar
Debreu, Gerard. 1952a. “An Economic Equilibrium Existence Theorem.” CCDP Economics 2032.Google Scholar
Debreu, Gerard. 1952b. “A Social Equilibrium Existence Theorem.” Proceedings of the National Academy of Sciences 38 (8): 886–893.CrossRefGoogle ScholarPubMed
Debreu, Gerard. 1953. “The Continuity of Multivalued Functions.” CCDP Economics 2079.Google Scholar
Debreu, Gerard. 1956. “Market Equilibrium.” Proceedings of the National Academy of Sciences 42 (11): 876–878.CrossRefGoogle ScholarPubMed
Debreu, Gerard. 1959. Theory of Value: An Axiomatic Analysis of Economic Equilibrium. New York: Wiley.Google Scholar
Debreu, Gerard. 1983. “Autobiography.” In Odelberg, Wilhelm, ed., Les Prix Nobel: The Nobel Prizes 1983. Nobel Foundation: Stockholm.Google Scholar
Debreu, Gerard. 1984. “Economic Theory in the Mathematical Mode.” The American Economic Review 74 (3): 267–278.Google Scholar
Debreu, Gerard. 1998. “Foreword: Economics in a Mathematics Colloquium.” In Dierker, E., Siegmund, K., and Menger, K., eds., Ergebnisse eines Mathematischen Kolloquiums. Wien: Springer, pp. 1–4.Google Scholar
Debreu, Gerard, and Herstein, Israel N.. 1953. “Nonnegative Square Matrices.” Econometrica 21 (4): 597–607.CrossRefGoogle Scholar
Düppe, Till. 2012. “Gerard Debreu’s Secrecy: His Life in Order and Silence.” History of Political Economy 44 (3): 413–449.CrossRefGoogle Scholar
Düppe, Till, and Weintraub, E. Roy. Forthcoming. Finding Equilibrium. Princeton: Princeton University Press.Google Scholar
Eilenberg, Samuel, and Montgomery, Deane. 1946. “Fixed Point Theorems for Multi-Valued Transformations.” American Journal of Mathematics 68 (2): 214–222.CrossRefGoogle Scholar
Feiwel George, R., ed. 1987. Arrow and the Ascent of Modern Economic Theory. New York: New York University Press.CrossRefGoogle Scholar
Gale, David. 1955. “The Law of Supply and Demand.” Mathematica Scandinavica 3: 33–44.CrossRefGoogle Scholar
Gale, David. 1963. “A Note on Global Instability of Competitive Equilibrium.” Naval Research Logistics Quarterly 10: 81–87.CrossRefGoogle Scholar
Gallagher, Noel. 2005. “Gerard Debreu Dies at 83: First of Four Berkeley Economists to Win Nobel Prize over 18-Year Span.” UC Berkeley Public Affairs.Google Scholar
Herstein, Israel N., and Milnor, John. 1953. “An Axiomatic Approach to Measurable Utility.” Econometrica 21 (2): 291–297.CrossRefGoogle Scholar
Hotelling, Harold. 1938. “The General Welfare in Relation to Problems of Taxation and of Railway and Utility Rates.” Econometrica 6 (3): 242–269.CrossRefGoogle Scholar
Hurwicz, Leonid. 1961. “Review of Theory of Value.” American Economic Review 51 (3): 414–417.Google Scholar
Jaffe, William. 1967. “Walras Theory of Tâtonnement: Critique of Recent Interpretations.” Journal of Political Economy 75 (1): 1–19.CrossRefGoogle Scholar
Kakutani, Shizuo. 1951. “A Generalization of Brouwer’s Fixed Point Theorem.” Duke Mathematical Journal 8 (3): 457–459.Google Scholar
Koopmans, Tjalling, ed. 1951. Activity Analysis of Production and Allocation. Cowles Commission Monograph 13. New York: John Wiley.Google Scholar
Lange, Oscar. 1942. “The Foundations of Welfare Economics.” Econometrica 10 (3/4): 215–228.CrossRefGoogle Scholar
Leonard, R. 1992. Interview with Gerard Debreu, April 15, Evans Hall, Berkeley. Debreu Papers, Carton 4.Google Scholar
Leonard, Robert. 2010. Von Neumann, Morgenstern, and the Creation of Game Theory: From Chess to Social Science, 1900–1960. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
McKenzie, Lionel. 1954. “On Equilibrium in Graham’s Model of World Trade and Other Competitive Systems.” Econometrica 22: 147–161.CrossRefGoogle Scholar
McKenzie, Lionel. 1960. “Stability of Equilibrium and the Value of Positive Excess Demand.” Econometrica 28 (3): 606–617.CrossRefGoogle Scholar
Mirowski, Philip. 2002. Machine Dreams: Economics Becomes a Cyborg Science. Cambridge: Cambridge University Press.Google Scholar
Nash, John F. 1950. “Equilibrium Points in N-person Games.” Proceedings of the National Academy of Sciences 36: 48–49.CrossRefGoogle ScholarPubMed
Neumann, John von. 1928. „Zur Theorie der Gesellschaftspiele.” Mathematische Annalen 100: 295–320. 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.CrossRefGoogle Scholar
Neumann, John von. 1936.“Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes.” In Menger, Karl, ed., Ergebnisse eines Mathematischen Kolloquiums 8: 73–83. Translated 1945–46, “A Model of General Economic Equilibrium.” Review of Economic Studies 13: 1–9.Google Scholar
Neumann, John von, and Morgenstern, Oskar. [1944] 1953. Theory of Games and Economic Behavior. Princeton: Princeton University Press.Google Scholar
Nikaido, Hukukane. 1956. “On the Classical Multilateral Exchange Problem.” Metroeconomica 8: 135–145.CrossRefGoogle Scholar
Oehler, K. 1990. “Speaking Axiomatically: Citation Patterns to Early Articles in General Equilibrium Theory.” History of Political Economy 22 (1): 101–112.CrossRefGoogle Scholar
Punzo, Lionello. 1991. “The School of Mathematical Formalism and the Viennese Circle of Mathematical Economics.” Journal of the History of Economic Thought 13: 1–18.CrossRefGoogle Scholar
Scarf, Herbert. 1960. “Some Examples of Global Instability of Competitive Equilibrium.” International Economic Review 1 (3): 157–172.CrossRefGoogle Scholar
Shubik, Martin. 1961. “Review of Theory of Value.” The Canadian Journal of Economics and Political Science 27 (1): 133.CrossRefGoogle Scholar
Shubik, Martin. [1972] 1977. “Competitive and Controlled Price Economies: The Arrow–Debreu Model Revisited.” In Schwodiauer, G., ed., Equilibrium and Disequilibrium in Economic Theory. Dordrecht: D. Reidel, pp. 213–224.CrossRefGoogle Scholar
Slater, Morton L. 1950. “Lagrange Multipliers Revisited.” CCDP Mathematics 403.Google Scholar
Wald, Abraham. [1936] 1951. “On Some Systems of Equations of Mathematical Economics.” Econometrica 19 (4): 368–403. Translated from “Über einige Gleichungssysteme der mathematischen Ökonomie.” Zeitschrift für Nationalökonomie 7 (5): 637–670.CrossRefGoogle Scholar
Weintraub, E. Roy. 2002. How Economics Became a Mathematical Science. Durham and London: Duke University Press.Google Scholar
Weintraub, E. Roy, and Gayer, Ted. 2001. “Equilibrium Proofmaking.” Journal of the History of Economic Thought 23 (4): 421–442.CrossRefGoogle Scholar

Interviews

Goldman, Steve. Monday, September 14, 2009. UC Berkeley.Google Scholar
Hildenbrand, Werner. Tuesday, March 23, 2010. University of Bonn.Google Scholar