Measuring consumer welfare with mean demands

The welfare change from a price increase-for example, the compensating variation (cv) - is often calculated using the expenditure function from an estimated demand. If there is unobserved preference heterogeneity, then the estimated demand is an average over households with different preferences. And the cv from the mean demand does not generally equal the mean cv. We give conditions ensuring that the cv from the mean demand equals the mean cv, is less than the mean cv, and approximates the mean cv better than the change in consumers' surplus. A necessary condition is that demands become more dispersed as income rises.