Compensated Variation in Random Utility Models

In this paper we introduce the notion of random expenditure function and derive the distribution of the expenditure function and corresponding compensated choice probabilities in the general case when the (random) utilities are nonlinear in income. We also derive formulae for expenditure and choice under price (policy) changes conditional on the initial utility level. This is of particular interest for welfare measurement because it enables the researcher to analyze the distribution of Compensating variation.