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Afriat's theorem for general budget sets

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  • Forges, Françoise
  • Minelli, Enrico

Abstract

Afriat proved the equivalence of a variant of the strong axiom of revealed preference and the existence of a solution to a set of linear inequalities. From this solution he constructed a utility function rationalizing the choices of a competitive consumer. We extend Afriat's theorem to a class of nonlinear, nonconvex budget sets. We thereby obtain testable implications of rational behavior for a wide class of economic environments, and a constructive method to derive individual preferences from observed choices. We also show that by increasing in a regular way the number of observed choices from our class of budget sets one can fully identify the underlying preference relation.

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Bibliographic Info

Paper provided by Université Paris-Dauphine in its series Open Access publications from Université Paris-Dauphine with number urn:hdl:123456789/4099.

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Date of creation: Jan 2009
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Publication status: Published in Journal of Economic Theory (2009-01) v.144, p.135-145
Handle: RePEc:ner:dauphi:urn:hdl:123456789/4099

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Related research

Keywords: GARP; Rational choice; Revealed preferences; SARP; WARP;

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  1. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  2. Herbert E. Scarf & Ana Fostel & Michael J. Todd, 2004. "Two New Proofs of Afriat's Theorem," Yale School of Management Working Papers ysm377, Yale School of Management.
  3. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 419-25, July.
  4. Mas-Colell, Andreu, 1977. "The Recoverability of Consumers' Preferences from Market Demand Behavior," Econometrica, Econometric Society, vol. 45(6), pages 1409-30, September.
  5. Michele Polo & Carlo Scarpa, 2003. "Entry Without Competition," Working Papers 245, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
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  7. Mas-Colell, Andreu, 1978. "On Revealed Preference Analysis," Review of Economic Studies, Wiley Blackwell, vol. 45(1), pages 121-31, February.
  8. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August.
  9. Franco Spinelli & Carmine Trecroci, . "Le determinanti del tasso di sconto in Italia negli anni 1876-1913: un'analisi empirica e documentale," Working Papers ubs0405, University of Brescia, Department of Economics.
  10. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-86, November.
  11. Chiara Dalla Nogare & Roberto Ricciuti, . "Chief Executives' Term Limits and Fiscal Policy Choices: International Evidence," Working Papers ubs0411, University of Brescia, Department of Economics.
  12. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-68, October.
  13. Dubey, Pradeep & Sahi, Siddhartha, 2003. "Price-mediated trade with quantity signals: an axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 377-389, July.
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