Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-19T14:50:04.213Z Has data issue: false hasContentIssue false
  • English
  • Français

WHAT A DIFFERENCE A SUM (∑) MAKES: SUCCESS AND FAILURE IN THE RATIONALIZATION OF DEMAND

Published online by Cambridge University Press:  13 August 2012

D. WADE HANDS
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper discusses the Sonnenschein–Mantel–Debreu (SMD) theorems in general equilibrium theory. It argues that the SMD results were related to the previous literature on the integrability of demand. The integrability question involved rationalizing individual demand functions, and the SMD theorems asked the same question about aggregate (market) excess demand functions. The paper’s two goals are to demonstrate how the SMD results followed naturally from the earlier work on integrability, and to point out that the profession’s reception was quite different; the integrability results were considered a success story, while the SMD results were quite negative.

Type
Research Articles
Information
Journal of the History of Economic Thought , Volume 34 , Issue 3 , September 2012 , pp. 379 - 396
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

Aloqeili, Marwan. 2005. “On the Characterization of Excess Demand Functions.” Economic Theory 26: 217–225.CrossRefGoogle Scholar
Antonelli, Giovani Battista. 1886. “On the Mathematical Theory of Political Economy.” Sulla teoria mathematical della Economia politica. Translated by J.S. Chipman and A.P. Kirman, and edited and annotated by J.S. Chipman. In Chipman, John S., Hurwicz, Leonid, Richter, Marcel, and Sonnenschein, Hugo F., eds., Preferences, Utility, and Demand. New York: Harcourt Brace Jovanovich, 1971, 333–363.Google Scholar
Arrow, Kenneth J., and Hahn, Frank H.. 1971. General Competitive Analysis. San Francisco: Holden-Day.Google Scholar
Bloor, David 1991. Knowledge and Social Imagery. Second edition. Chicago: University of Chicago Press.Google Scholar
Breslau, Daniel, and Yonay, Yoval. 1999. “Beyond Metaphor: Mathematical Models in Economics as Empirical Research.” Science in Context 12: 317–332.CrossRefGoogle Scholar
Brown, Donald J., and Matzkin, Rosa L.. 1996. “Testable Restrictions on the Equilibrium Manifold.” Econometrica 64: 1249–1262.CrossRefGoogle Scholar
Brown, Donald J, and Shannon, Chris. 2000. “Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets.” Econometrica 68: 1529–1539.CrossRefGoogle Scholar
Chiappori, Pierre-Andre, and Ekeland, Ivar. 2004. “Individual Excess Demands.” Journal of Mathematical Economics 40: 41–57.CrossRefGoogle Scholar
Chipman, John S. 1982. “Samuelson and Consumption Theory.” In Feiwel, G.R., ed., Samuelson and Neoclassical Economics. Boston: Kluwer Nijhoff, 31–71.CrossRefGoogle Scholar
Chipman, John S, Hurwicz, Leonid, Richter, Marcel, and Sonnenschein, Hugo F., eds. 1971. Preferences, Utility, and Demand: A Minnesota Symposium. New York: Harcourt Brace Jovanovich.Google Scholar
Colander, David. 2000. “The Death of Neoclassical Economics,” Journal of the History of Economic Thought 22: 127–143.CrossRefGoogle Scholar
Davis, John B. 1998. “New Economics and Its History: A Pickeringian View.” In Davis, J.B., ed., New Economics and Its Writing. Annual supplement to Volume 29 of History of Political Economy. Durham, NC: Duke University Press, 285–304.Google Scholar
Davis, John B. 2006. “The Turn in Economics: Neoclassical Dominance to Mainstream Pluralism.” Journal of Institutional Economics 2: 1–20.CrossRefGoogle Scholar
Debreu, Gerard. 1959. Theory of Value. New Haven, CT: Yale University Press.Google Scholar
Debreu, Gerard. 1974. “Excess Demand Functions.” Journal of Mathematical Economics 1: 15–21.CrossRefGoogle Scholar
Evans, Griffith C. 1930. Mathematical Introduction to Economics. New York: McGraw-Hill.Google Scholar
Hands, D. Wade. 1993. “More Light on Integrability, Symmetry, and Utility as Potential Energy in Mirowski’s Critical History.” In De Marchi, N., ed., Non-Natural Social Science: Reflecting on the Enterprise of ‘More Heat Than Light .’ Annual supplement to Volume 25 of History of Political Economy. Durham, NC: Duke University Press, 118–130.Google Scholar
Hands, D. Wade. 1994. “Restabilizing Dynamics.” Economics and Philosophy 10: 243–283.CrossRefGoogle Scholar
Hands, D. Wade. 2006. “Integrability, Rationalizability, and Path-Dependency in the History of Demand Theory.” In Mirowski, P. and Hands, D.W., eds., Agreement on Demand: Consumer Choice Theory in the Twentieth Century. Annual supplement to Volume 38 of History of Political Economy. Durham, NC: Duke University Press, 153–185.Google Scholar
Hands, D. Wade. 2009. “Stabilizing Consumer Choice: The Role of ‘True Dynamic Stability and Related Concepts in the History of Consumer Choice Theory.” The European Journal of the History of Economic Thought 17: 313–43.CrossRefGoogle Scholar
Hands, D. Wade. 2011. “Back to the Ordinalist Revolution: Behavioral Economic Concerns in Early Twentieth Century Consumer Choice Theory.” Metroeconomica 62: 386–410.CrossRefGoogle Scholar
Hands, D. Wade, and Mirowski, Philip. 1998. “Harold Hotelling and the Neoclassical Dream.” In Backhouse, R., Hausman, D., Mäki, U., and Salanti, A., eds., Economics and Methodology: Crossing Boundaries. London: Macmillan, 322–397.Google Scholar
Hicks, John R. 1939. Value and Capital. Oxford: Clarendon Press.Google Scholar
Hicks, John R, and Allen, R.G.D.. 1934. “A Reconsideration of the Theory of Value, Parts I and II.” Economica 2, 52–76, 196–219.CrossRefGoogle Scholar
Hurwicz, Leonid. 1971. “On the Problem of Integrability in Economics.” In Chipman, J.S., Hurwicz, L., Richter, M.K., and Sonnenschein, H.F., eds., Preferences, Utility, and Demand. New York: Harcourt Brace Jovanovich, 174–213.Google Scholar
Hurwicz, Leonid, and Richter, Marcel K.. 1979a. “An Integrability Condition with Applications to Utility Theory and Thermodynamics.” Journal of Mathematical Economics 6: 7–14.CrossRefGoogle Scholar
Hurwicz, Leonid. 1979b. “Ville Axioms and Consumer Theory.” Econometrica 47: 603–620.CrossRefGoogle Scholar
Hurwicz, Leonid, and Uzawa, Hirofumi. 1971. “On the Integrability of Demand Functions.” In Chipman, J.S., Hurwicz, L., Richter, M.K., and Sonnenschein, H.F., eds., Preferences, Utility, and Demand. New York: Harcourt Brace Jovanovich, 114–147.Google Scholar
Ingrao, Bruna, and Israel, Giorgio. 1990. The Invisible Hand: Economic Theory in the History of Science. Cambridge, MA: MIT Press.Google Scholar
Katzner, Donald W. 1970. Static Demand Theory. London: Macmillan.Google Scholar
Kirman, Alan. 1989 “The Intrinsic Limits of Modern Economic Theory: The Emperor Has No Clothes.” The Economic Journal 99: 126–139.CrossRefGoogle Scholar
Kirman, Alan. 1992. “Whom or What Does the Representative Individual Represent?” Journal of Economic Perspectives 6: 117–136.CrossRefGoogle Scholar
Kirman, Alan. 2006. “Demand Theory and General Equilibrium: From Explanation to Introspection, a Journey Down the Wrong Road.” In Mirowski, P. and Hands, D.W., eds., Agreement on Demand: Consumer Theory in the Twentieth Century. Annual supplement to Volume 38 of History of Political Economy. Durham, NC: Duke University Press, 246–280.Google Scholar
Knight, Frank H. 1944. “Realism and Relevance in the Theory of Demand.” Journal of Political Economy 52: 289–318.CrossRefGoogle Scholar
Mantel, Rolf R. 1974. “On the Characterization of Aggregate Excess Demand.” Journal of Economic Theory 7: 348–353.CrossRefGoogle Scholar
Mantel, Rolf R. 1977. “Implications of Microeconomic Theory for Community Excess Demand Functions.” In Intriligator, M.D., ed., Frontiers in Quantitative Economic IIIA. Amsterdam: North-Holland, 111–126.Google Scholar
Mas-Colell, Andreu, Whinston, Michael D., and Green, Jerry R.. 1995. Microeconomic Theory. New York: Oxford University Press.Google Scholar
McCauley, Joseph L. 2004. Dynamics of Markets: Econophysics and Finance. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
McFadden, Daniel, Mas-Colell, Andreu, Mantel, Rolf, and Richter, Marcel K.. 1974. “A Characterization of Community Excess Demand Functions.” Journal of Economic Theory 9: 361–374.CrossRefGoogle Scholar
Mirowski, Philip. 1989. More Heat Than Light: Economics as Social Physics, Physics as Nature’s Economics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Pareto, Vilfredo. 1971. Manual of Political Economy. Translated from the 1927 French edition by Schwier, Ann S.. New York: Augustus M. Kelley.Google Scholar
Pickering, Andrew. 1995. The Mangle of Practice: Time, Agency, and Science. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Pickering, Andrew, and Stephanides, Adam. 1992. “Constructing Quaternions: On the Analysis of Conceptual Practice.” In Pickering, A., ed., Science as Practice and Culture. Chicago: University of Chicago Press, 139–167.CrossRefGoogle Scholar
Rizvi, S. Abu Turab. 1994. “The Microfoundations Project in General Equilibrium Theory.” Cambridge Journal of Economics 18: 357–377.CrossRefGoogle Scholar
Rizvi, S. Abu Turab. 1998. “Responses to Arbitrariness in Contemporary Economics.” In Davis, John B., ed., New Economics and Its History. Annual supplement to Volume 29 of History of Political Economy. Durham, NC: Duke University Press, 275–288.Google Scholar
Rizvi, S. Abu Turab. 2003. “The Stabilization of Price Theory, 1920–1955.” In Samuels, W.J., Biddle, J.E., and Davis, J.B., eds., A Companion to the History of Economic Thought. Oxford: Wiley-Blackwell, 372–394.Google Scholar
Rizvi, S. Abu Turab. 2006. “The Sonnenschein-Mantel-Debreu Results after Thirty Years.” In Mirowski, P. and Hands, D.W., eds., Agreement on Demand: Consumer Theory in the Twentieth Century. Annual supplement to Volume 38 of History of Political Economy. Durham, NC: Duke University Press, 228–245.Google Scholar
Samuelson, Paul A. 1938. “A Note on the Pure Theory of Consumer’s Behaviour.” Economica 5: 61–71.CrossRefGoogle Scholar
Samuelson, Paul A. 1947. Foundations of Economic Analysis. Cambridge, MA: Harvard University Press.Google Scholar
Samuelson, Paul A. 1948. “Consumption Theory in Terms of Revealed Preference.” Economica 15: 243–253.CrossRefGoogle Scholar
Samuelson, Paul A. 1950. “The Problem of Integrability in Utility Theory.” Economica 17: 355–385.CrossRefGoogle Scholar
Scarf, Herbert. 1981. “Comment on: ‘On the Stability of Competitive Equilibrium and the Patterns of Initial Holdings: An Example.’” International Economic Review 22: 469–470.CrossRefGoogle Scholar
Shafer, Wayne, and Sonnenschein, Hugo. 1982. “Market Excess Demand Functions.” In Arrow, K.J. and Intriligator, M.D., eds., Handbook of Mathematical Economics. Volume II. Amsterdam: North-Holland, 671–693.Google Scholar
Slutsky, E.E. 1915 “Sulla Teoria del Bilancio del Consonatore.” Giornale degli Economisti 51: 1–26. Translated in G.J. Stigler and K.E. Boulding, eds., Readings in Price Theory. Homewood, IL: Richard D. Irwin, 1952, 27–56.Google Scholar
Sonnenschein, Hugo. 1972. “Market Excess Demand Functions.” Econometrica 40: 549–563.CrossRefGoogle Scholar
Sonnenschein, Hugo. 1973. “Do Walras’ Identity and Continuity Characterize the Class of Community Excess Demand Functions?” Journal of Economic Theory 6: 345–354.CrossRefGoogle Scholar
Sonnenschein, Hugo. 1974. “The Utility Hypothesis and Market Demand Theory.” Western Economic Journal 11: 404–410.Google Scholar
Thomé, Fernando. 2006. “Rolf Mantel and the Computability of General Equilibria: On the Origins of the Sonnenschein-Mantel-Debreu Theorem.” In Mirowski, P. and Hands, D.W., eds., Agreement on Demand: Consumer Choice Theory in the Twentieth Century. Annual supplement to Volume 38 of History of Political Economy. Durham, NC: Duke University Press, 213–227.Google Scholar
Uzawa, Hirofumi. 1960 “Preferences and Rational Choice in the Theory of Consumption.” In Arrow, K.J., Karlin, S., and Suppes, P., eds., Proceedings of the First Stanford Symposium on Mathematical Methods in the Social Sciences. Stanford, CA: Stanford University Press, 129–148.Google Scholar