Karim Kilani

Invariance of conditional maximum utility

Abstract The consumer benefit in a discrete choice model is often measured by maximum utility. We characterize the conditional (on the chosen alternative) and the unconditional distribution of maximum utility. We show that among a wide class of distributions (independent with convex supports) of error terms, the Type I extreme-value distribution is the unique distribution which ensures that all the conditional distributions of maximum utility coincide. Moreover, we show that for i.i.d. (with convex support) error terms, the invariance of conditional expected maximum utility characterizes the multinomial logit model.

Un)Conditional Distribution of Compensating Variation in Discrete Choice Models

For a large class of additive random utility discrete choice models with income effects, we compute the probability distribution of the compensating variation. We show that the cumulative distribution function only depends on the choice probabilities. Our results are used to compute the distribution of equivalent variation. The moments of the compensating variation are a onedimensional integral of the choice probabilities. Using the expected compensating variation, we extend Shephards Lemma to the probabilistic demand systems. Both conditional and unconditional (on the individual choice) distributions of compensating variation are considered.