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Revealed Preference in a Discrete Consumption Space

Author

Listed:
  • Matthew Polisson
  • John K.-H. Quah

Abstract

We show that an agent maximizing some utility function on a discrete (as opposed to continuous) consumption space will obey the generalized axiom of revealed preference (GARP), so long as the agent obeys cost efficiency. Cost efficiency will hold if there is some good, outside the set of goods being studied by the modeler, that can be consumed by the agent in continuous quantities. An application of Afriat's Theorem then guarantees that there is a strictly increasing utility function on the discrete consumption space that rationalizes price and demand observations. (JEL D11)

Suggested Citation

  • 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.
  • Handle: RePEc:aea:aejmic:v:5:y:2013:i:1:p:28-34
    Note: DOI: 10.1257/mic.5.1.28
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    References listed on IDEAS

    as
    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. A. Fostel & H. Scarf & M. Todd, 2004. "Two new proofs of Afriat’s theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(1), pages 211-219, July.
    3. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 419-425.
    4. Donald Brown & Caterina Calsamiglia, 2007. "The Nonparametric Approach to Applied Welfare Analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 183-188, April.
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    Citations

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    Cited by:

    1. Sam Cosaert & Thomas Demuynck, 2015. "Revealed preference theory for finite choice sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 169-200, May.
    2. Yuichi Kitamura & Jorg Stoye, 2016. "Nonparametric Analysis of Random Utility Models," Papers 1606.04819, arXiv.org, revised Dec 2017.
    3. John Quah & Hiroki Nishimura & Efe A. Ok, 2013. "A Unified Approach to Revealed Preference Theory: The Case of Rational Choice," Economics Series Working Papers 686, University of Oxford, Department of Economics.
    4. Ian Crawford & Bram De Rock, 2014. "Empirical Revealed Preference," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 503-524, August.
    5. Sabrina Bruyneel & Laurens Cherchye & Sam Cosaert & Bram De Rock & Siegfried Dewitte, 2012. "Are the Smart Kids More Rational ?," Working Papers ECARES ECARES 2012-050, ULB -- Universite Libre de Bruxelles.
    6. Thomas Demuynck & Christian Seel, 2018. "Revealed Preference with Limited Consideration," American Economic Journal: Microeconomics, American Economic Association, vol. 10(1), pages 102-131, February.
    7. Kohei Shiozawa, 2015. "Revealed Preference Test and Shortest Path Problem; Graph Theoretic Structure of the Rationalizability Test," Discussion Papers in Economics and Business 15-17-Rev.2, Osaka University, Graduate School of Economics and Osaka School of International Public Policy (OSIPP), revised Aug 2016.
    8. Matthew Polisson, 2011. "Goods Versus Characteristics: Revealed Preference Procedures for Nested Models," Economics Series Working Papers 531, University of Oxford, Department of Economics.
    9. Polisson, Matthew & Renou, Ludovic, 2016. "Afriat’s Theorem and Samuelson’s ‘Eternal Darkness’," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 36-40.
    10. Shiozawa, Kohei, 2016. "Revealed preference test and shortest path problem; graph theoretic structure of the rationalizability test," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 38-48.
    11. Ian Crawford & Matthew Polisson, 2015. "Demand Analysis with Partially Observed Prices," Discussion Papers in Economics 15/12, Department of Economics, University of Leicester, revised Dec 2016.
    12. Forges, Françoise & Iehlé, Vincent, 2014. "Afriat’s theorem for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 1-6.
    13. Kohei Shiozawa, 2015. "Revealed Preference Test and Shortest Path Problem; Graph Theoretic Structure of the Rationalizability Test," Discussion Papers in Economics and Business 15-17-Rev., Osaka University, Graduate School of Economics and Osaka School of International Public Policy (OSIPP), revised Jul 2015.
    14. repec:spr:etbull:v:3:y:2015:i:2:d:10.1007_s40505-014-0061-5 is not listed on IDEAS
    15. repec:hal:wpaper:halshs-00870052 is not listed on IDEAS

    More about this item

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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