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The housing problem and revealed preference theory: duality and an application

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  • Ivar Ekeland
  • Alfred Galichon

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Abstract

This paper exhibits a duality between the theory of revealed preference of Afriat and the housing allocation problem of Shapley and Scarf. In particular, it is shown that Afriat’s theorem can be interpreted as a second welfare theorem in the housing problem. Using this duality, the revealed preference problem is connected to an optimal assignment problem, and a geometrical characterization of the rationalizability of experiment data is given. This allows in turn to give new indices of rationalizability of the data and to define weaker notions of rationalizability, in the spirit of Afriat’s efficiency index. Copyright Springer-Verlag 2013

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 54 (2013)
Issue (Month): 3 (November)
Pages: 425-441

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Handle: RePEc:spr:joecth:v:54:y:2013:i:3:p:425-441

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Related research

Keywords: Revealed preferences; Afriat’s theorem; Optimal assignments; Indivisible allocations; Primary D11; Secondary C60; C78;

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References

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  1. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2007. "The Collective Model of Household Consumption: A nonparametric characterization," ULB Institutional Repository 2013/98559, ULB -- Universite Libre de Bruxelles.
  2. Ivar Ekeland & Alfred Galichon & Marc Henry, 2010. "Optimal transportation and the falsifiability of incompletely specified economic models," Economic Theory, Springer, vol. 42(2), pages 355-374, February.
  3. Gretsky, Neil E & Ostroy, Joseph M & Zame, William R, 1992. "The Nonatomic Assignment Model," Economic Theory, Springer, vol. 2(1), pages 103-27, January.
  4. Cherchye, L.J.H. & Rock, B. de & Vermeulen, F.M.P., 2008. "An Afriat Theorem for the Collective Model of Household Consumption," Discussion Paper 2008-72, Tilburg University, Center for Economic Research.
  5. Ivar Ekeland, 2010. "Notes on optimal transportation," Economic Theory, Springer, vol. 42(2), pages 437-459, February.
  6. A. Fostel & H. Scarf & M. Todd, 2004. "Two new proofs of Afriat’s theorem," Economic Theory, Springer, vol. 24(1), pages 211-219, 07.
  7. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-86, November.
  8. Francoise Forges & Enrico Minelli, 2006. "Afriat's Theorem for General Budget Sets," Working Papers ubs0609, University of Brescia, Department of Economics.
  9. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 419-25, July.
  10. Federico Echenique & Sangmok Lee & Matthew Shum & M. Bumin Yenmez, 2013. "The Revealed Preference Theory of Stable and Extremal Stable Matchings," Econometrica, Econometric Society, vol. 81(1), pages 153-171, 01.
  11. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  12. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  13. Federico Echenique & Sangmok Lee & Matthew Shum, 2011. "The Money Pump as a Measure of Revealed Preference Violations," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1201 - 1223.
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Cited by:
  1. Francoise Forges & Vincent Iehlé, 2013. "Afriat's Theorem for Indivisible Goods," CESifo Working Paper Series 4498, CESifo Group Munich.

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