TEL  Vol.4 No.6 , June 2014
On Price and Income Effects in Discrete Choice Models
Abstract: We consider the classical micro-economic foundation of discrete choice, additive random utility models, with conditional utilities depending on expenditure on the numéraire. We show that signs of own- and cross-price effects are identified on the basis of the primal problem only, and Giffen behaviour is ruled out. For the translog specification, we prove that the alternative with highest price behaves as normal good, and the alternative with lowest price behaves as inferior good. We establish conditions for equivalence between the primal and the dual problem. We provide a discrete choice version of the Slutsky equation which, similarly to divisible goods, decomposes the own-price effect into a substitution and an income effect.
Cite this paper: Site, P. (2014) On Price and Income Effects in Discrete Choice Models. Theoretical Economics Letters, 4, 497-505. doi: 10.4236/tel.2014.46062.

[1]   Mas-Colell, A., Whinston, M.D. and Green, J.R. (1995) Microeconomic Theory. Oxford University Press, New York.

[2]   Luenberger, D.G. (1995) Microeconomic Theory. McGraw-Hill, New York.

[3]   McKenzie, L. (1957) Demand Theory without a Utility Index. The Review of Economic Studies, 24, 185-189.

[4]   Allen, R.G.D. (1950) The Substitution Effect in Value Theory. Economic Journal, 60, 675-685.

[5]   Hicks, J.R. (1956) A Revision of Demand Theory. Oxford University Press, Oxford.

[6]   McFadden, D. (1981) Econometric Models of Probabilistic Choice. In: Manski, C. and McFadden, D., Eds., Structural Analysis of Discrete Data with Econometric Applications, MIT Press, Cambridge, 198-272.

[7]   Dagsvik, J.K. and Karlstrom, A. (2005) Compensating Variation and Hicksian Choice Probabilities in Random Utility Models That Are Nonlinear in Income. Review of Economic Studies, 72, 57-76.

[8]   Delle Site, P. (2014) On the Expenditure Function and Welfare in Random Utility Models. Economics Bulletin, 34, 152-163.

[9]   Fosgerau, M., McFadden, D. and Bierlaire, M. (2013) Choice Probability Generating Functions. Journal of Choice Modelling, 8, 1-18.

[10]   Herriges, J.A. and Kling, C.L. (1999) Nonlinear Income Effects in Random Utility Models. The Review of Economics and Statistics, 81, 62-72.

[11]   Tra, C.I. (2013) Nonlinear Income Effects in Random Utility Models: Revisiting the Accuracy of the Representative Consumer Approximation. Applied Economics, 45, 55-63.

[12]   Beer, G. (1993) Topologies on Closed and Closed Convex Sets. Kluwer Academic Publishers, Dordrecht.

[13]   Williams, H.C.W.L. (1977) On the Formation of Travel Demand Models and Economic Evaluation Measures of User Benefit. Environment and Planning A, 9, 285-344.

[14]   Anderson, S.P., De Palma, A. and Thisse, J.-F. (1992) Discrete Choice Theory of Product Differentiation. MIT Press, Cambridge.

[15]   Boyd, S. and Vandenberghe, L. (2004) Convex Optimization. Cambridge University Press, Cambridge.

[16]   Sydsater, K., Strom, A. and Berck, P. (1998) Economists’ Mathematical Manual. Springer, Berlin.