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On Duality In Random Utility Models


  • Paolo Delle Site

    (DICEA Dept. of Civil Architectural and Environmental Engineering, CTL Centre of Research on Transport and Logistics, University of Rome La Sapienza)


We provide the discrete choice, random utility counterparts of some basic results of consumer theory. For the primal problem and related Marshallian probabilities, we provide a new, simpler proof of Roy's identity at aggregate level and investigate price and income effects. For the dual problem and related Hicksian probabilities, we extend Shepard's lemma at aggregate level to unbound expenditure and investigate compensated price effects. We establish a primal-dual equivalence result and provide the counterpart of the Slutsky equation.

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  • Paolo Delle Site, 2013. "On Duality In Random Utility Models," Working Papers 0513, CREI Università degli Studi Roma Tre, revised 2013.
  • Handle: RePEc:rcr:wpaper:05_13

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    References listed on IDEAS

    1. Lionel McKenzie, 1957. "Demand Theory Without a Utility Index," Review of Economic Studies, Oxford University Press, vol. 24(3), pages 185-189.
    2. Viton, Philip A., 1985. "On the interpretation of income variables in discrete-choice models," Economics Letters, Elsevier, vol. 17(3), pages 203-206.
    3. John K. Dagsvik & Anders Karlström, 2005. "Compensating Variation and Hicksian Choice Probabilities in Random Utility Models that are Nonlinear in Income," Review of Economic Studies, Oxford University Press, vol. 72(1), pages 57-76.
    4. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, June.
    5. Diewert, W E, 1981. "The Measurement of Deadweight Loss Revisited," Econometrica, Econometric Society, vol. 49(5), pages 1225-1244, September.
    6. Delle Site, Paolo, 2013. "Integration of choice probabilities in logit," Economics Letters, Elsevier, vol. 120(1), pages 57-60.
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