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Afriat's Theorem for Indivisible Goods

  • Francoise Forges
  • Vincent Iehlé

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
Date of revision:
Handle: RePEc:ces:ceswps:_4498
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  1. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 419-25, July.
  2. Francoise Forges & Vincent Iehlé, 2013. "Essential Data, Budget Sets and Rationalization," Post-Print halshs-00727806, HAL.
  3. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc0o6ctj2 is not listed on IDEAS
  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. Mattei, Aurelio, 2000. "Full-scale real tests of consumer behavior using experimental data," Journal of Economic Behavior & Organization, Elsevier, vol. 43(4), pages 487-497, December.
  6. Donald Brown & Caterina Calsamiglia, 2007. "The Nonparametric Approach to Applied Welfare Analysis," Economic Theory, Springer, vol. 31(1), pages 183-188, April.
  7. Philippe Fevrier & Michael Visser, 2000. "A Study of Consumer Behavior Using Laboratory Data," Econometric Society World Congress 2000 Contributed Papers 1095, Econometric Society.
  8. M.J. Todd & A. Fostel & H.E. Scarf, 2004. "Two New Proofs of Afriat's Theorem," Econometric Society 2004 North American Summer Meetings 632, Econometric Society.
  9. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  10. Francoise Forges & Enrico Minelli, 2006. "Afriat’s Theorem for General Budget Sets," CESifo Working Paper Series 1703, CESifo Group Munich.
  11. 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.
  12. Chambers, Christopher P. & Echenique, Federico, 2009. "Supermodularity and preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1004-1014, May.
  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.
  14. 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.
  15. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
  16. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  17. Satoru Fujishige & Zaifu Yang, 2012. "On Revealed Preference and Indivisibilities," Discussion Papers 12/02, Department of Economics, University of York.
  18. Hammond, Peter & Traub, Stefan, 2012. "A Three-Stage Experimental Test of Revealed Preference," CAGE Online Working Paper Series 72, Competitive Advantage in the Global Economy (CAGE).
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