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A Characterization of Rationalizable Consumer Behavior

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  • Philip J. Reny

    () (University of Chicago)

Abstract

For an arbitrary finite or infinite dataset D of prices and corresponding chosen bundles, it is shown that the following three conditions are equivalent. (i) D satisfies GARP; (ii) D can be rationalized by a utility function; (iii) D can be rationalized by a strictly increasing, quasiconcave utility function. Examples of infinite datasets satisfying GARP are provided for which every utility rationalization fails to be lower semicontinuous, upper semicontinuous, or concave. Thus condition (iii) cannot be substantively improved upon.

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  • Philip J. Reny, 2014. "A Characterization of Rationalizable Consumer Behavior," Working Papers 2014-004, Becker Friedman Institute for Research In Economics.
  • Handle: RePEc:bfi:wpaper:2014-004
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    1. repec:the:publsh:2733 is not listed on IDEAS
    2. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2018. "Transitivity of preferences: when does it matter?," Theoretical Economics, Econometric Society, vol. 13(3), September.
    3. Christopher P. Chambers & Federico Echenique & Nicolas S. Lambert, 2018. "Preference Identification," Papers 1807.11585, arXiv.org.
    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. Hiroki Nishimura & Efe A. Ok & John K.-H. Quah, 2017. "A Comprehensive Approach to Revealed Preference Theory," American Economic Review, American Economic Association, vol. 107(4), pages 1239-1263, April.

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