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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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    Cited by:

    1. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    2. 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.
    3. Victor H. Aguiar & Nail Kashaev, 2025. "Identification and Estimation of Discrete Choice Models with Unobserved Choice Sets," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 43(1), pages 204-215, January.
    4. Polisson, Matthew & Renou, Ludovic, 2016. "Afriat’s Theorem and Samuelson’s ‘Eternal Darkness’," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 36-40.
    5. 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.
    6. Demuynck, Thomas & Hjertstrand, Per, 2019. "Samuelson's Approach to Revealed Preference Theory: Some Recent Advances," Working Paper Series 1274, Research Institute of Industrial Economics.
    7. Mingshi Chen & Tracy Xiao Liu & You Shan & Shu Wang & Songfa Zhong & Yanju Zhou, 2025. "How General Are Measures of Choice Consistency? Evidence from Experimental and Scanner Data," Papers 2505.05275, arXiv.org, revised Sep 2025.
    8. Ian Crawford & Matthew Polisson, 2015. "Demand Analysis with Partially Observed Prices," Discussion Papers in Economics 15/12, Division of Economics, School of Business, University of Leicester, revised Dec 2016.
    9. Rahul Deb & Yuichi Kitamura & John K H Quah & Jörg Stoye, 2023. "Revealed Price Preference: Theory and Empirical Analysis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(2), pages 707-743.
    10. 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.
    11. 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.
    12. Tipoe, Eileen, 2021. "Price inattention: A revealed preference characterisation," European Economic Review, Elsevier, vol. 134(C).
    13. Matthew Polisson & John K. -H. Quah, 2024. "Rationalizability, Cost-Rationalizability, and Afriat's Efficiency Index," Papers 2406.10136, arXiv.org, revised Jul 2024.
    14. Forges, Françoise & Iehlé, Vincent, 2014. "Afriat’s theorem for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 1-6.
    15. 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, revised Jul 2015.
    16. Grech, Philip D. & Nax, Heinrich H., 2020. "Rational altruism? On preference estimation and dictator game experiments," Games and Economic Behavior, Elsevier, vol. 119(C), pages 309-338.
    17. Stefan Hoderlein & Jörg Stoye, 2015. "Testing stochastic rationality and predicting stochastic demand: the case of two goods," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 313-328, October.
    18. Thomas Demuynck & Christian Seel, 2018. "Revealed Preference with Limited Consideration," American Economic Journal: Microeconomics, American Economic Association, vol. 10(1), pages 102-131, February.
    19. Smeulders, Bart & Crama, Yves & Spieksma, Frits C.R., 2019. "Revealed preference theory: An algorithmic outlook," European Journal of Operational Research, Elsevier, vol. 272(3), pages 803-815.
    20. 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, revised Aug 2016.
    21. Matthew Polisson, 2011. "Goods Versus Characteristics: Revealed Preference Procedures for Nested Models," Economics Series Working Papers 531, University of Oxford, Department of Economics.
    22. Ian Crawford & Bram De Rock, 2014. "Empirical Revealed Preference," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 503-524, August.
    23. repec:hal:wpaper:halshs-00870052 is not listed on IDEAS
    24. Dziewulski, Paweł & Lanier, Joshua & Quah, John K.-H., 2024. "Revealed preference and revealed preference cycles: A survey," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    25. Matthew Polisson, 2012. "Goods versus characteristics: dimension reduction and revealed preference," IFS Working Papers W12/02, Institute for Fiscal Studies.

    More about this item

    JEL classification:

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

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