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Afriat's Theorem for Indivisible Goods

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  • Francoise Forges
  • Vincent Iehlé

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 CESifo Group Munich in its series CESifo Working Paper Series with number 4498.

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Date of creation: 2013
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Handle: RePEc:ces:ceswps:_4498

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

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  1. 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.
  2. Francoise Forges & Vincent Iehlé, 2013. "Essential Data, Budget Sets and Rationalization," Post-Print halshs-00727806, HAL.
  3. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  4. Matthew Polisson & John Quah, 2012. "Revealed Preference in a Discrete Consumption Space," Discussion Papers in Economics 12/02, Department of Economics, University of Leicester, revised Feb 2012.
  5. 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.
  6. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  7. Ivar Ekeland & Alfred Galichon, 2013. "The housing problem and revealed preference theory: duality and an application," Economic Theory, Springer, vol. 54(3), pages 425-441, November.
  8. Chambers, Christopher P. & Echenique, Federico, 2009. "Supermodularity and preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1004-1014, May.
  9. 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.
  10. Donald Brown & Caterina Calsamiglia, 2007. "The Nonparametric Approach to Applied Welfare Analysis," Economic Theory, Springer, vol. 31(1), pages 183-188, April.
  11. Francoise Forges & Enrico Minelli, 2006. "Afriat’s Theorem for General Budget Sets," CESifo Working Paper Series 1703, CESifo Group Munich.
  12. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
  13. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 419-25, July.
  14. Satoru Fujishige & Zaifu Yang, 2012. "On Revealed Preference and Indivisibilities," Discussion Papers 12/02, Department of Economics, University of York.
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