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Afriat’s Theorem for General Budget Sets

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  • Francoise Forges
  • Enrico Minelli

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 CESifo Group Munich in its series CESifo Working Paper Series with number 1703.

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Date of creation: 2006
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Handle: RePEc:ces:ceswps:_1703

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Keywords: GARP; rational choice; revealed preferences; market games; SARP; WARP;

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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, University of Chicago Press, vol. 85(5), pages 937-68, October.
  2. Mas-Colell, Andreu, 1978. "On Revealed Preference Analysis," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 45(1), pages 121-31, February.
  3. Anna Fostel & Herbert E. Scarf & Michael J. Todd, 2003. "Two New Proofs of Afriat's Theorem," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1415, Cowles Foundation for Research in Economics, Yale University.
  4. 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.
  5. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 945-73, July.
  6. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 40(3), pages 419-25, July.
  7. Franco Spinelli & Carmine Trecroci, . "Le determinanti del tasso di sconto in Italia negli anni 1876-1913: un'analisi empirica e documentale," Working Papers, University of Brescia, Department of Economics ubs0405, University of Brescia, Department of Economics.
  8. Mas-Colell, Andreu, 1977. "The Recoverability of Consumers' Preferences from Market Demand Behavior," Econometrica, Econometric Society, Econometric Society, vol. 45(6), pages 1409-30, September.
  9. Chavas, Jean-Paul & Cox, Thomas L, 1993. "On Generalized Revealed Preference Analysis," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 108(2), pages 493-506, May.
  10. Raffaele Miniaci & Maria Laura Parisi, 2005. "Which Plans to Reduce the Digital Divide? Policy Evaluation and Social Interaction," Working Papers, University of Brescia, Department of Economics ubs0509, University of Brescia, Department of Economics.
  11. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, Elsevier, vol. 93(2), pages 205-232, August.
  12. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, Econometric Society, vol. 59(6), pages 1779-86, November.
  13. Chiara Dalla Nogare & Roberto Ricciuti, . "Chief Executives' Term Limits and Fiscal Policy Choices: International Evidence," Working Papers, University of Brescia, Department of Economics ubs0411, University of Brescia, Department of Economics.
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