Stochastic demand correspondences and their aggregation properties
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.
|Date of creation:||01 Sep 2003|
|Date of revision:||08 Jan 2005|
|Note:||Type of Document - Tex; prepared on IBM PC - PC-TEX; to print on HP; pages: 9 ; figures: none|
|Contact details of provider:|| Web page: http://econwpa.repec.org|
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- 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.
- E. Eisenberg, 1961. "Aggregation of Utility Functions," Management Science, INFORMS, vol. 7(4), pages 337-350, July.
- Shafer, Wayne J, 1977. "Revealed Preference and Aggregation," Econometrica, Econometric Society, vol. 45(5), pages 1173-82, July.
- 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.
- Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, vol. 8(1), pages 26-38, May.
- 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.
- 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 707-15, May.
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