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Afriat's theorem for indivisible goods

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  • Francoise Forges

    ()
    (LEDa - Laboratoire d'Economie de Dauphine - Université Paris IX - Paris Dauphine, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris IX - Paris Dauphine)

  • Vincent Iehlé

    ()
    (LEDa - Laboratoire d'Economie de Dauphine - Université Paris IX - Paris Dauphine, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris IX - Paris Dauphine)

Abstract

We identify a natural counterpart of the standard GARP for demand data in which goods are all indivisible. We show that the new axiom (DARP, for "discrete axiom of revealed preference") is necessary and sufficient for the rationalization of the data by a well-behaved utility function. Our results complement the main finding of Polisson and Quah, Am. Econ. J.: Micro. 5(1) p.28-34 (2013), who rather minimally modify the original consumer problem with indivisible goods so that the standard GARP still applies.

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Paper provided by HAL in its series Working Papers with number halshs-00870052.

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Date of creation: 16 May 2014
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Handle: RePEc:hal:wpaper:halshs-00870052

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Keywords: Afriat's theorem; GARP; indivisible goods; rationalization; revealed preference;

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  1. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
  2. Francoise Forges & Vincent Iehlé, 2013. "Essential Data, Budget Sets and Rationalization," Post-Print halshs-00727806, HAL.
  3. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 419-25, July.
  4. A. Fostel & H. Scarf & M. Todd, 2004. "Two new proofs of Afriat’s theorem," Economic Theory, Springer, vol. 24(1), pages 211-219, 07.
  5. Chambers, Christopher P. & Echenique, Federico, 2009. "Supermodularity and preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1004-1014, May.
  6. Donald Brown & Caterina Calsamiglia, 2007. "The Nonparametric Approach to Applied Welfare Analysis," Economic Theory, Springer, vol. 31(1), pages 183-188, April.
  7. Ivar Ekeland & Alfred Galichon, 2013. "The Housing Problem and Revealed Preference Theory: Duality and an application," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
  8. Satoru Fujishige & Zaifu Yang, 2012. "On Revealed Preference and Indivisibilities," Discussion Papers 12/02, Department of Economics, University of York.
  9. Matthew Polisson & John K.-H. Quah, 2013. "Revealed Preference in a Discrete Consumption Space," American Economic Journal: Microeconomics, American Economic Association, vol. 5(1), pages 28-34, February.
  10. Sam COSAERT & Thomas DEMUYNCK, 2013. "Revealed preference theory for finite choice sets," Center for Economic Studies - Discussion papers ces13.08, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  11. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
  12. 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.
  13. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, October.
  14. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
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