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Revealed Preference with Stochastic Demand Correspondence


  • Indraneel Dasgupta


We unify and expand the theory of consumer’s behavior, based on Samuelson’s Weak Axiom of Revealed Preference, to permit simultaneously both random choice and non-singleton choice sets. We provide a consistency postulate for demand behavior when such behavior is represented in terms of a stochastic demand correspondence. When the consumer spends her entire wealth, our rationality postulate is equivalent to a condition we term stochastic substitutability. This equivalence generates: (i) Samuelson’s Substitution Theorem, (ii) the central result in Bandyopadhyay, Dasgupta and Pattanaik (2004) and (iii) a version pertinent to deterministic demand correspondences (which independently yields Samuelson’s Substitution Theorem), as alternative special cases. Relevant versions of the non-positivity of the own substitution effect, the demand theorem and homogeneity of degree zero in prices and wealth for the consumer’s demand behavior, also follow as corollaries in every case.

Suggested Citation

  • Indraneel Dasgupta, "undated". "Revealed Preference with Stochastic Demand Correspondence," Discussion Papers 07/06, University of Nottingham, School of Economics.
  • Handle: RePEc:not:notecp:07/06

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    References listed on IDEAS

    1. Chiappori, Pierre-Andre & Rochet, Jean-Charles, 1987. "Revealed Preferences and Differentiable Demand: Notes and Comments," Econometrica, Econometric Society, vol. 55(3), pages 687-691, May.
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    5. Bandyopadhyay, Taradas & Bandyopadhyay, Bandyopadhyay & Pattanaik, Prasanta K., 2002. "Demand Aggregation and the Weak Axiom of Stochastic Revealed Preference," Journal of Economic Theory, Elsevier, vol. 107(2), pages 483-489, December.
    6. Dasgupta Indraneel, 2009. "Supply Theory sans Profit Maximization," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-16, July.
    7. J. C. R. Alcantud, 2003. "Stochastic demand correspondences and their aggregation properties," Microeconomics 0309001, EconWPA, revised 08 Jan 2005.
    8. Dekel, Eddie & Lipman, Barton L & Rustichini, Aldo, 2001. "Representing Preferences with a Unique Subjective State Space," Econometrica, Econometric Society, vol. 69(4), pages 891-934, July.
    9. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Oxford University Press, vol. 38(3), pages 307-317.
    10. Indraneel Dasgupta & Prasanta Pattanaik, 2007. "‘Regular’ choice and the weak axiom of stochastic revealed preference," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 35-50, April.
    11. Indraneel Dasgupta, 2005. "Consistent firm choice and the theory of supply," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 167-175, July.
    12. Bandyopadhyay, Taradas & Dasgupta, Indraneel & Pattanaik, Prasanta K., 1999. "Stochastic Revealed Preference and the Theory of Demand," Journal of Economic Theory, Elsevier, vol. 84(1), pages 95-110, January.
    13. WILLIAM J. McCAUSLAND, 2009. "Random Consumer Demand," Economica, London School of Economics and Political Science, vol. 76(301), pages 89-107, February.
    14. Taradas Bandyopadhyay & Indraneel Dasgupta & Prasanta Pattanaik, 2004. "A general revealed preference theorem for stochastic demand behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(3), pages 589-599, March.
    15. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 245-264, August.
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    Cited by:

    1. Indraneel Dasgupta, 2011. "Contraction consistent stochastic choice correspondence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 643-658, October.

    More about this item


    Stochastic demand correspondence; weak axiom of revealed preference; weak axiom of stochastic revealed preference; general substitution theorem; demand theorem.;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory


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