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Revealed preference analysis for convex rationalizations on nonlinear budget sets

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  • Laurens CHERCHYE
  • Thomas DEMUYNCK
  • Bram DE ROCK

Abstract

We present necessary and sufficient revealed preference conditions to verify whether a finite data set on nonlinear budget sets is consistent with the maximization of a quasi–concave utility function. Our results can be used to test for convexity of the underlying preference relation. We also show that in many settings, our conditions are easy to use in practical applications.

Suggested Citation

  • Laurens CHERCHYE & Thomas DEMUYNCK & Bram DE ROCK, 2012. "Revealed preference analysis for convex rationalizations on nonlinear budget sets," Working Papers Department of Economics ces12.15, KU Leuven, Faculty of Economics and Business, Department of Economics.
  • Handle: RePEc:ete:ceswps:ces12.15
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    References listed on IDEAS

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    1. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    2. 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.
    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. Yatchew, Adonis John, 1985. "A note on non-parametric tests of consumer behaviour," Economics Letters, Elsevier, vol. 18(1), pages 45-48.
    5. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2014. "Revealed preference analysis for convex rationalizations on nonlinear budget sets," Journal of Economic Theory, Elsevier, vol. 152(C), pages 224-236.
    6. Matzkin, Rosa L. & Richter, Marcel K., 1991. "Testing strictly concave rationality," Journal of Economic Theory, Elsevier, vol. 53(2), pages 287-303, April.
    7. Francoise Forges & Enrico Minelli, 2009. "Afriat's theorem for generalized budget sets," Post-Print hal-00360726, HAL.
    8. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762, May.
    9. Demuynck, Thomas, 2009. "A general extension result with applications to convexity, homotheticity and monotonicity," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 96-109, January.
    10. Charles F. Manski, 2014. "Identification of income–leisure preferences and evaluation of income tax policy," Quantitative Economics, Econometric Society, vol. 5, pages 145-174, March.
    11. Richter, Marcel K. & Wong, K.-C.Kam-Chau, 2004. "Concave utility on finite sets," Journal of Economic Theory, Elsevier, vol. 115(2), pages 341-357, April.
    12. W. Erwin Diewert, 2012. "Afriat's Theorem and some Extensions to Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 122(560), pages 305-331, May.
    13. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-1786, November.
    14. repec:ecj:econjl:v:122:y:2012:i::p:305-331 is not listed on IDEAS
    15. repec:dau:papers:123456789/4099 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Ian Crawford & Bram De Rock, 2014. "Empirical Revealed Preference," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 503-524, August.
    2. Polisson, Matthew & Renou, Ludovic, 2016. "Afriat’s Theorem and Samuelson’s ‘Eternal Darkness’," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 36-40.
    3. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2014. "Revealed preference analysis for convex rationalizations on nonlinear budget sets," Journal of Economic Theory, Elsevier, vol. 152(C), pages 224-236.
    4. 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.

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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