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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

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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  1. Mas-Colell, Andreu, 1978. "On Revealed Preference Analysis," Review of Economic Studies, Wiley Blackwell, vol. 45(1), pages 121-31, February.
  2. 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.
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  8. Anna Fostel & Herbert E. Scarf & Michael J. Todd, 2003. "Two New Proofs of Afriat's Theorem," Cowles Foundation Discussion Papers 1415, Cowles Foundation for Research in Economics, Yale University.
  9. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 419-25, July.
  10. Mas-Colell, Andreu, 1977. "The Recoverability of Consumers' Preferences from Market Demand Behavior," Econometrica, Econometric Society, vol. 45(6), pages 1409-30, September.
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