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General Revealed Preferences

Author

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  • Cesar Martinelli

    () (Interdisciplinary Center for Economic Science and Department of Economics, George Mason University)

  • Mikhail Freer

    () (Interdisciplinary Center for Economic Science and Department of Economics, George Mason University)

Abstract

Following Richter (1966), we provide criteria under which a preference relation implied by a finite set of choice observations has a complete extension that can in turn be represented by a utility function. These criteria rely on a mapping over preference relations, the rational closure, which is a generalization of the transitive closure and is employed to construct the complete extension. We illustrate this approach by re- visiting the problem of rationalizing incomplete preferences revealed by a sequence of consumption decisions under different budget sets. Our result relaxes the usual assumptions about the consumption space and the structure of budgets generating the observed choices, and allows for a new interpretation of classical revealed preference axioms.Length: 20

Suggested Citation

  • Cesar Martinelli & Mikhail Freer, 2016. "General Revealed Preferences," Working Papers 1059, George Mason University, Interdisciplinary Center for Economic Science, revised Jun 2016.
  • Handle: RePEc:gms:wpaper:1059
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    File URL: http://www.gmu.edu/schools/chss/economics/icesworkingpapers.gmu.edu/pdf/1059.pdf
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    References listed on IDEAS

    as
    1. Matthew Polisson & John Quah & Ludovic Renou, 2015. "Revealed preferences over risk and uncertainty," IFS Working Papers W15/25, Institute for Fiscal Studies.
    2. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    3. Heufer, Jan, 2012. "Revealed Preference and Nonparametric Analysis – Continuous Extensions and Recoverability," Ruhr Economic Papers 324, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    4. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
    5. Diewert, W. E. & Parkan, C., 1985. "Tests for the consistency of consumer data," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 127-147.
    6. Bosi, G. & Mehta, G. B., 2002. "Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 311-328, November.
    7. Matzkin, Rosa L. & Richter, Marcel K., 1991. "Testing strictly concave rationality," Journal of Economic Theory, Elsevier, vol. 53(2), pages 287-303, April.
    8. Francoise Forges & Enrico Minelli, 2009. "Afriat's theorem for generalized budget sets," Post-Print hal-00360726, HAL.
    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. Ian Crawford, 2010. "Habits Revealed," Review of Economic Studies, Oxford University Press, vol. 77(4), pages 1382-1402.
    11. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    12. David M. Kreps, 2012. "Microeconomic Foundations I: Choice and Competitive Markets," Economics Books, Princeton University Press, edition 1, number 9890.
    13. Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
    14. Ghanshyam B. Mehta, 1997. "A remark on a utility representation theorem of Rader (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 367-370.
    15. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-1786, November.
    16. repec:dau:papers:123456789/4099 is not listed on IDEAS
    17. repec:zbw:rwirep:0324 is not listed on IDEAS
    18. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
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