Hicksian Surplus Measures of Individual Welfare Change When There is Price and Income Uncertainty

This article considers measures of individual welfare change for projects that change the state distribution of prices and incomes. For a consumer whose preferences satisfy the expected utility hypothesis, we investigate whether there is an increasing function of the state-contingent compensating variations that is positive valued if and only if a project makes the consumer better off ex ante when income and some or all prices are permitted to vary across states. We show that any such measure of individual welfare change must rank projects by their expected compensating variation. Furthermore, the indirect utility function that the consumer uses to evaluate prices and income in each state and that is used to compute expected utilities must be affine in income with the origin term independent of all prices and the weight on income independent of those prices that are uncertain. These restrictions imply that preferences are homothetic. If all prices are uncertain, these conditions are inconsistent with the homogeneity properties of an indirect utility function and, hence, we obtain an impossibility result.