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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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Postal: School of Economics University of Nottingham University Park Nottingham NG7 2RD
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Web page: http://www.nottingham.ac.uk/economics/
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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. WILLIAM J. McCAUSLAND, 2009. "Random Consumer Demand," Economica, London School of Economics and Political Science, vol. 76(301), pages 89-107, 02.
  2. John Quah, 2006. "Weak axiomatic demand theory," Economic Theory, Springer, vol. 29(3), pages 677-699, November.
  3. J. C. R. Alcantud, 2005. "Stochastic demand correspondences and their aggregation properties," Microeconomics 0501004, EconWPA.
  4. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  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. 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. 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.
  8. Indraneel Dasgupta, 2005. "Consistent firm choice and the theory of supply," Economic Theory, Springer, vol. 26(1), pages 167-175, 07.
  9. 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.
  10. 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.
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Cited by:
  1. Dasgupta, Indraneel, 2009. "Contraction Consistent Stochastic Choice Correspondence," IZA Discussion Papers 4596, Institute for the Study of Labor (IZA).

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