Measuring Consumer Welfare with Mean Demands

32 Pages Posted: 8 Aug 2005

Date Written: July 2005

Abstract

Measures of welfare changes - either the equivalent or compensating variation of a price increase for a good - are often calculated using the expenditure function from an estimated demand. If the regression errors are due to unobserved preference heterogeneity, then then the estimated demand is really an average taken over households with different preferences. And the welfare change calculated from the expenditure function for the mean demand does not generally equal the mean welfare change. We give conditions ensuring that the compensating variation calculated from the mean demand i) equals the mean compensating variation; ii) is less than the mean compensating variation for a price increase; iii) is closer to the mean compensating variation than the change in consumers' surplus. A necessary condition for ii) is that demands become more dispersed as income rises (for each cell of households with the same demographic characteristics and income). This plausible necessary condition is not sufficient for either ii) or iii). If however we can write the indirect utility functions for households as additively separable in income and the preference type, then increasing dispersion is equivalent to ii) and implies iii) if the single good whose price has risen is normal.

If households are uncertain of their preferences for goods at the time of the policy change, then the indirect (von Neumann-Morgenstern) utility function must be additively separable in income and the preference type if the compensating variation from the mean demand is even a first-order approximation to the ex ante compensating variation; the change in consumers' surplus can easily be a better approximation when additive separability fails.

Keywords: Welfare, Preference Heterogeneity, Aggregation, Representative Household, Consumers' Surplus, Estimation

JEL Classification: D1, D61, C43, C13

Suggested Citation

Schlee, Edward E., Measuring Consumer Welfare with Mean Demands (July 2005). Available at SSRN: https://ssrn.com/abstract=771164 or http://dx.doi.org/10.2139/ssrn.771164

Edward E. Schlee (Contact Author)

Arizona State University ( email )

Box 873806
Tempe, AZ 85287-3806
United States
480-965-5745 (Phone)
480-965-0748 (Fax)

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