Expected Consumer's Surplus as an Approximate Welfare Measure

Willig (1976) argues that the change in consumerís surplus is often a good approximation to the willingness to pay for a price change: if the income elasticity of demand is small, or the price change is small, then the percentage error from using consumerís surplus is small. If the price of a good is random, then the change in (ECS) equals a consumerís willingness to pay for a change in its distribution if and only if its demand is independent of income and the consumer is risk neutral over income gambles. We ask how well the change in ECS approximates the willingness to pay if these conditions fail. We show that the di§erence between the change in ECS and willingness to pay is of higher order than the L1 distance between the distributions if and only if the indirect utility function is additively separable in the price and income. If, however, this knife-edge condition fails, then the percentage error from using ECS can be arbitrarily large for small changes in the price distribution. Moreover, we show that the percentage error can be large even if risk aversion, the goodís income elasticity of demand and its budget share are all small. Thus, the widespread use of expected consumerís surplus as a welfare measure under uncertainty cannot be justified by approximation arguments inspired by those formulated for nonrandom prices.