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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.

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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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  1. 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.
  2. J. C. R. Alcantud, 2003. "Stochastic demand correspondences and their aggregation properties," Microeconomics 0309001, EconWPA, revised 08 Jan 2005.
  3. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, March.
  4. 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.
  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," IZA Discussion Papers 4018, Institute for the Study of Labor (IZA).
  7. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
  8. 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.
  9. John Quah, 2000. "Weak Axiomatic Demand Theory," Economics Series Working Papers 2000-W12, University of Oxford, Department of Economics.
  10. Indraneel Dasgupta, 2005. "Consistent firm choice and the theory of supply," Economic Theory, Springer, vol. 26(1), pages 167-175, 07.
  11. 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.
  12. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer, vol. 26(2), pages 245-264, 08.
  13. 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.
  14. 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.
  15. WILLIAM J. McCAUSLAND, 2009. "Random Consumer Demand," Economica, London School of Economics and Political Science, vol. 76(301), pages 89-107, 02.
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