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A Characterization of Rationalizable Consumer Behavior

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  • Philip J. Reny

Abstract

For an arbitrary data set D = {(p, x)} ⊆ (ℝ + -super-m∖ {0}) × ℝ + -super-m, finite or infinite, it is shown that the following three conditions are equivalent: (a) D satisfies GARP; (b) D can be rationalized by a utility function; (c) D can be rationalized by a utility function that is quasiconcave, nondecreasing, and that strictly increases when all its coordinates strictly increase. Examples of infinite data sets satisfying GARP are provided for which every utility rationalization fails to be lower semicontinuous, upper semicontinuous, or concave. Thus condition (c) cannot be substantively improved upon.

Suggested Citation

  • Philip J. Reny, 2015. "A Characterization of Rationalizable Consumer Behavior," Econometrica, Econometric Society, vol. 83, pages 175-192, January.
    • Handle: RePEc:wly:emetrp:v:83:y:2015:i::p:175-192
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    Cited by:

    1. Christopher P. Chambers & Federico Echenique & Nicolas S. Lambert, 2021. "Recovering Preferences From Finite Data," Econometrica, Econometric Society, vol. 89(4), pages 1633-1664, July.
    2. 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.
    3. Polisson, Matthew & Renou, Ludovic, 2016. "Afriat’s Theorem and Samuelson’s ‘Eternal Darkness’," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 36-40.
    4. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2018. "Transitivity of preferences: when does it matter?," Theoretical Economics, Econometric Society, vol. 13(3), September.
    5. Alvaro Sandroni & Leo Katz, 2024. "The leveling axiom," Theory and Decision, Springer, vol. 96(1), pages 135-152, February.
    6. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2018. "Transitivity of preferences: when does it matter?," Theoretical Economics, Econometric Society, vol. 13(3), September.
    7. Gorno, Leandro, 2019. "Revealed preference and identification," Journal of Economic Theory, Elsevier, vol. 183(C), pages 698-739.
    8. Heufer, Jan & van Bruggen, Paul & Yang, Jingni, 2020. "Giving According to Agreement," Discussion Paper 2020-035, Tilburg University, Center for Economic Research.
    9. Pawe{l} Dziewulski & Joshua Lanier & John K. -H. Quah, 2024. "Revealed preference and revealed preference cycles: a survey," Papers 2405.08459, arXiv.org.
    10. Freer, Mikhail & Martinelli, César, 2021. "A utility representation theorem for general revealed preference," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 68-76.
    11. Christopher P. Chambers & Federico Echenique & Nicolas S. Lambert, 2018. "Preference Identification," Papers 1807.11585, arXiv.org.
    12. Gonczarowski, Yannai A. & Kominers, Scott Duke & Shorrer, Ran I., 0. "To infinity and beyond: a general framework for scaling economic theories," Theoretical Economics, Econometric Society.

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