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Afriat's theorem for general budget sets

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Forges, Françoise
Minelli, Enrico

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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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Publisher Info
Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 1 (January)
Pages: 135-145
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Handle: RePEc:eee:jetheo:v:144:y:2009:i:1:p:135-145

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: GARP Rational choice Revealed preferences SARP WARP;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July. [Downloadable!] (restricted)
  3. Chavas, Jean-Paul & Cox, Thomas L, 1993. "On Generalized Revealed Preference Analysis," The Quarterly Journal of Economics, MIT Press, vol. 108(2), pages 493-506, May. [Downloadable!] (restricted)
  4. 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. [Downloadable!]
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  5. 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. [Downloadable!] (restricted)
  6. Mas-Colell, Andreu, 1978. "On Revealed Preference Analysis," Review of Economic Studies, Blackwell Publishing, vol. 45(1), pages 121-31, February. [Downloadable!] (restricted)
  7. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Blackwell Publishing, vol. 40(3), pages 419-25, July. [Downloadable!] (restricted)
  8. Mas-Colell, Andreu, 1977. "The Recoverability of Consumers' Preferences from Market Demand Behavior," Econometrica, Econometric Society, vol. 45(6), pages 1409-30, September. [Downloadable!] (restricted)
  9. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August. [Downloadable!] (restricted)
  10. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-86, November. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Tasos Kalandrakis, 2008. "Rationalizable Voting," Wallis Working Papers WP51, University of Rochester - Wallis Institute of Political Economy. [Downloadable!]
  2. Amedeo Fossati & Rosella Levaggi, 2008. "Delay is not the answer: waiting time in health care & income redistribution," Working Papers 0801, University of Brescia, Department of Economics. [Downloadable!]
  3. Deb, Rahul & Fenske, James, 2009. "A Nonparametric Test of Strategic Behavior in the Cournot Model," MPRA Paper 16560, University Library of Munich, Germany. [Downloadable!]
  4. Chambers, Christopher P. & Echenique, Federico & Shmaya, Eran, 2007. "On behavioral complementarity and its implications," Working Papers 1270, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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