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Afriat’s theorem for indivisible goods

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  • Forges, Françoise
  • Iehlé, Vincent

Abstract

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 (2013), who rather minimally modify the original consumer problem with indivisible goods so that the standard GARP still applies.

Suggested Citation

  • Forges, Françoise & Iehlé, Vincent, 2014. "Afriat’s theorem for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 1-6.
  • Handle: RePEc:eee:mateco:v:54:y:2014:i:c:p:1-6
    DOI: 10.1016/j.jmateco.2014.08.001
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    References listed on IDEAS

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    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.
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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. 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.
    3. 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.
    4. 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; Indivisible goods; Rationalization; Revealed preference;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access

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