On the Measurement of Welfare Cost under Uncertainty

Abstract

Welfare cost measurement under various sorts of uncertainty (essentially all welfare cost measurement) has proceeded with ad hoc and unsatisfactory methods. Generally, either uncertainty is suppressed entirely, with social surplus computed at the point of mean values of the random variables, or expected social surplus is used. While a natural evolution from the certainty case, neither procedure has a justification except as an approximation to some undefined true measure, and either can lead to gross miscalculations of benefit. This paper offers a rigorous and operational alternative by defining an appropriate concept of compensation under uncertainty and developing an approximation to it. Most dead weight loss analysis of tax changes involves pure planner uncertainty about preferences and thus about the price and income changes due to the tax changes. Each consumer is assumed to know his own tastes with certainty, but planners know them only probabilistically. This creates a forecast problem for prices and incomes. The universal procedure is to suppress randomness entirely and use mean values of demand slopes, intercepts, and induced price and income changes as if they were certain. With price and income uncertainty for both consumers and planners the focus, a number of authors have studied the effects of price stabilization using expected social surplus. Brown, [2], Hueth and Schmitz, [4], and others have followed the lead of Waugh, [11], and Oi, [8], in this procedure. AndersonRiley, [1], criticize expected social surplus for ignoring the variation in the marginal utility of income which lies at the heart of welfare issues under uncertainty.' In fact, it is shown that when prices are stabilized at the mean, the signs of expected welfare change and expected social surplus can differ.