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Revealed Preference with Stochastic Demand Correspondence

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  • Indraneel Dasgupta

Abstract

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.

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Paper provided by University of Nottingham, School of Economics in its series Discussion Papers with number 07/06.

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Handle: RePEc:not:notecp:07/06

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

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  1. J. C. R. Alcantud, 2005. "Stochastic demand correspondences and their aggregation properties," Microeconomics 0501004, EconWPA.
  2. Quah, J.K.-H., 2000. "Weak Axiomatic Demand Theory," Economics Papers 2000-w12, Economics Group, Nuffield College, University of Oxford.
  3. Chiappori, Pierre-Andre & Rochet, Jean-Charles, 1987. "Revealed Preferences and Differentiable Demand: Notes and Comments," Econometrica, Econometric Society, vol. 55(3), pages 687-91, May.
  4. Indraneel Dasgupta & Prasanta Pattanaik, 2007. "‘Regular’ choice and the weak axiom of stochastic revealed preference," Economic Theory, Springer, vol. 31(1), pages 35-50, April.
  5. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer, vol. 26(2), pages 245-264, 08.
  6. 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.
  7. Indraneel Dasgupta, 2005. "Consistent firm choice and the theory of supply," Economic Theory, Springer, vol. 26(1), pages 167-175, 07.
  8. Eddie Dekel, 1997. "A Unique Subjective State Space for Unforeseen Contingencies," Discussion Papers 1202, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Dasgupta Indraneel, 2009. "Supply Theory sans Profit Maximization," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-16, July.
  10. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
  11. 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.
  12. Taradas Bandyopadhyay & Indraneel Dasgupta & Prasanta Pattanaik, 2004. "A general revealed preference theorem for stochastic demand behavior," Economic Theory, Springer, vol. 23(3), pages 589-599, March.
  13. 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.
  14. WILLIAM J. McCAUSLAND, 2009. "Random Consumer Demand," Economica, London School of Economics and Political Science, vol. 76(301), pages 89-107, 02.
  15. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, September.
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Cited by:
  1. Indraneel Dasgupta, . "Contraction consistent stochastic choice correspondence," Discussion Papers 08/04, University of Nottingham, School of Economics.

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