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On Revealed Preference and Indivisibilities

Author

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  • Satoru Fujishige
  • Zaifu Yang

Abstract

We consider a market model in which all commodities are inherently indivisible and thus are traded in integer quantities. We ask whether a finite set of price-quantity observations satisfying the Generalized Axiom of Revealed Preference (GARP) is consistent with utility maximization. Although familiar conditions such as non-satiation become meaningless in the current discrete model, by refining the standard notion of demand set we show that Afriat's celebrated theorem still holds true. Exploring network structure and a new and easy-to-use variant of GARP, we propose an elementary, simple, intuitive, combinatorial, and constructive proof for the result.

Suggested Citation

  • Satoru Fujishige & Zaifu Yang, 2012. "On Revealed Preference and Indivisibilities," Discussion Papers 12/02, Department of Economics, University of York.
  • Handle: RePEc:yor:yorken:12/02
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    File URL: https://www.york.ac.uk/media/economics/documents/discussionpapers/2012/1202.pdf
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    References listed on IDEAS

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    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.
    2. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2007. "The Collective Model of Household Consumption: A Nonparametric Characterization," Econometrica, Econometric Society, vol. 75(2), pages 553-574, March.
    3. Richard W. Blundell & Martin Browning & Ian A. Crawford, 2003. "Nonparametric Engel Curves and Revealed Preference," Econometrica, Econometric Society, vol. 71(1), pages 205-240, January.
    4. Frederic Vermeulen, 2012. "Foundations of Revealed Preference: Introduction," Economic Journal, Royal Economic Society, vol. 122(560), pages 287-294, May.
    5. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 419-425.
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    Citations

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    Cited by:

    1. Polisson, Matthew & Renou, Ludovic, 2016. "Afriat’s Theorem and Samuelson’s ‘Eternal Darkness’," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 36-40.
    2. Forges, Françoise & Iehlé, Vincent, 2014. "Afriat’s theorem for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 1-6.
    3. 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.
    4. Kohei Shiozawa, 2015. "Note on goodness-of-fit measures for the revealed preference test: The computational complexity of the minimum cost index," Economics Bulletin, AccessEcon, vol. 35(4), pages 2455-2461.
    5. repec:hal:wpaper:halshs-00870052 is not listed on IDEAS
    6. 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.

    More about this item

    Keywords

    Afriat's theorem; GARP; indivisibilities; revealed preference.;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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