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Revealed preference in a discrete consumption space

Author

Listed:
  • Matthew Polisson

    (Institute for Fiscal Studies and University of Bristol)

  • John Quah

    (Institute for Fiscal Studies)

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 in that space.

Suggested Citation

  • Matthew Polisson & John Quah, 2012. "Revealed preference in a discrete consumption space," IFS Working Papers W12/03, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:ifsewp:12/03
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    File URL: http://www.ifs.org.uk/wps/wp1203.pdf
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    References listed on IDEAS

    as
    1. 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.
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    3. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    4. William T. Harbaugh & Kate Krause & Timothy R. Berry, 2001. "GARP for Kids: On the Development of Rational Choice Behavior," American Economic Review, American Economic Association, vol. 91(5), pages 1539-1545, December.
    5. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 419-425.
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    Citations

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    Cited by:

    1. 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.
    2. Ian Crawford & Bram De Rock, 2014. "Empirical Revealed Preference," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 503-524, August.
    3. 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.
    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. Forges, Françoise & Iehlé, Vincent, 2014. "Afriat’s theorem for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 1-6.
    6. Tipoe, Eileen, 2021. "Price inattention: A revealed preference characterisation," European Economic Review, Elsevier, vol. 134(C).
    7. Matthew Polisson, 2011. "Goods Versus Characteristics: Dimension Reduction and Revealed Preference," Discussion Papers in Economics 11/44, Division of Economics, School of Business, University of Leicester, revised Dec 2011.
    8. 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.
    9. 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.
    10. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    11. 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.
    12. Matthew Polisson & John Quah, 2022. "Rationalizability, Cost-Rationalizability, and Afriat's Efficiency Index," Bristol Economics Discussion Papers 22/754, School of Economics, University of Bristol, UK.
    13. Thomas Demuynck & Christian Seel, 2018. "Revealed Preference with Limited Consideration," American Economic Journal: Microeconomics, American Economic Association, vol. 10(1), pages 102-131, February.
    14. Victor H. Aguiar & Nail Kashaev, 2019. "Identification and Estimation of Discrete Choice Models with Unobserved Choice Sets," Papers 1907.04853, arXiv.org, revised Jun 2021.
    15. 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.
    16. 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.
    17. 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.
    18. Matthew Polisson, 2011. "Goods Versus Characteristics: Dimension Reduction and Revealed Preference," Discussion Papers in Economics 11/44, Division of Economics, School of Business, University of Leicester, revised Dec 2011.
    19. Demuynck, Thomas & Hjertstrand, Per, 2019. "Samuelson's Approach to Revealed Preference Theory: Some Recent Advances," Working Paper Series 1274, Research Institute of Industrial Economics.
    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., Osaka University, Graduate School of Economics, revised Jul 2015.
    21. repec:hal:wpaper:halshs-00870052 is not listed on IDEAS
    22. 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.
    23. 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.

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    More about this item

    JEL classification:

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

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