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Afriat's Theorem for General Budget Sets

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Author Info
Francoise Forges
Enrico Minelli

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Abstract

Afriat (1967) showed the equivalence 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 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. In an application to market games, we identify a set of observable restrictions characterizing Nash equilibrium outcomes.

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Paper provided by University of Brescia, Department of Economics in its series Working Papers with number ubs0609.

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Date of creation: 2006
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Handle: RePEc:ubs:wpaper:ubs0609

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  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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  1. Deb, Rahul & Fenske, James, 2009. "A Nonparametric Test of Strategic Behavior in the Cournot Model," MPRA Paper 16560, University Library of Munich, Germany. [Downloadable!]
  2. Tasos Kalandrakis, 2008. "Rationalizable Voting," Wallis Working Papers WP51, University of Rochester - Wallis Institute of Political Economy. [Downloadable!]
  3. 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!]
  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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