Marginal compensated effects and the slutsky equation for discrete choice models

In many instances the consumer faces choice settings where the alternatives are discrete. Examples include choice between variants of differentiated products, urban transportation modes, residential locations, types of education, etc. So far, a Slutsky equation for discrete choice models has not been derived. In this paper an aggregate Slutsky equation for the discrete case is obtained, which differs in important ways from the corresponding equation in the standard theory of consumer demand. A remarkable feature of the compensated marginal effects in the discrete case is that they are usually not symmetric, as the marginal compensated effects with respect to a price increase versus a price decrease may be different. The description of the analytic formulas is accompanied by several examples of their use: for example, in travel demand and labor supply.