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Stochastic demand correspondences and their aggregation properties

Author

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  • J. C. R. Alcantud

    (Universidad de Salamanca, Spain)

Abstract
Bandyopadhyay, Dasgupta and Pattanaik [JET, 2002] have presented a construction that aggregates standard demand functions by a stochastic demand function, in such way that the latter satisfies the weak axiom of stochastic revealed preference when the former fulfil Samuelson's weak axiom of revealed preference. We introduce a concept of stochastic demand correspondences and generalize WASRP to this new setting. Also, we propose a procedure to aggregate stochastic demand correspondences that (a) includes the previous one by those authors, (b) aggregates the weak axiom of stochastic revealed preference (and thus stochastic substitutability when we started with tight stochastic demand functions), and (c) produces a stochastically rational stochastic demand correspondence when the primitive ones are stochastically rational. Interpretations of the model are provided too. An analogous to the result that rationalizability of stochastic demand functions by stochastic orderings implies WASRP holds for the correspondence setting. We also discuss the convenience of adopting a formal variation of the notion of being stochastically rational that was proposed in the literature.

Suggested Citation

  • J. C. R. Alcantud, 2003. "Stochastic demand correspondences and their aggregation properties," Microeconomics 0309001, University Library of Munich, Germany, revised 08 Jan 2005.
    • Handle: RePEc:wpa:wuwpmi:0309001
    Note: Type of Document - Tex; prepared on IBM PC - PC-TEX; to print on HP; pages: 9 ; figures: none
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/mic/papers/0309/0309001.pdf
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    References listed on IDEAS

    as
    1. E. Eisenberg, 1961. "Aggregation of Utility Functions," Management Science, INFORMS, vol. 7(4), pages 337-350, July.
    2. Shafer, Wayne J, 1977. "Revealed Preference and Aggregation," Econometrica, Econometric Society, vol. 45(5), pages 1173-1182, July.
    3. Barbera, Salvador & Pattanaik, Prasanta K, 1986. "Falmagne and the Rationalizability of Stochastic Choices in Terms of Random Orderings," Econometrica, Econometric Society, vol. 54(3), pages 707-715, May.
    4. 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.
    5. 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.
    6. Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, vol. 8(1), pages 26-38, May.
    7. 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.
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    Cited by:

    1. Dasgupta Indraneel & Pattanaik P. K, 2010. "Revealed Preference with Stochastic Demand Correspondence," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, August.

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    More about this item

    Keywords

    Weak Axiom of Stochastic Revealed Preference; Weak Axiom of Revealed Preference; representative consumer; stochastic demand aggregation.;
    All these keywords.

    JEL classification:

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

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