The Measurement of Welfare

Abstract:     
Harberger (1971) proposes that the consumer surplus should be used to measure the individual utility and the social welfare. "Since Harberger's paper, the limitation and pitfall of consumer's surplus have been demonstrated systematically and definitively by Chipman and Moore among many others" [Slesnick (1998), p. 2159]. As pointed out by Chipman and Moore (1976, p. 70), "consumer's surplus is not intended to measure a consumer's utility at all; but what is supposed to measure we are not told". Despite the serious conceptual problems, however, "consumer's surplus is the overwhelming choice as a welfare indicator" [Slesnick (1998), p. 2110]. "It is easy to use, the intuition underlying its interpretation as a welfare measure is transparent, and the data requirements for implementation are minimal" [Slesnick (1998), p. 2159].

Using aggregate data to directly measure aggregate behavior, an "aggregate to aggregate" approach is developed in this paper to measure welfare in a world of many goods with many consumers. The purpose of this paper is to show that there exist some welfare functions such that the change in welfare resulting from changes of prices is equal to the sum of the Marshallian surplus of aggregate demands, the surplus of aggregate supplies, and the changes in government revenue. Therefore, a theoretical ground is built for using Marshallian consumer surplus as a welfare indicator.

It is well known that Marshallian consumer surplus does not measure the consumer's utility in the case of a single consumer. How can the Marshallian surplus be an indicator for social welfare? The consumer's utility maximization problem gives that marginal utility equals market price times the marginal utility of income (MUI). The market price would measure the marginal utility if the MUI were constant. Unfortunately, the constancy of MUI has proved to be impossible [Samuelson (1942)]. Therefore, the Marshallian surplus does not measure the individual utility.

However, It is also well known that the market price measures the marginal social value of a good. As pointed out in Varian's textbook [Varian (1992), p. 334], "we see that the competitive prices measure the (marginal) social value of a good: how much welfare would increase if we had a small additional amount of the good." Therefore, it is intuitive that Marshallian consumer surplus could measure welfare, at least in the case of one good.

In the case of many goods, the problem preventing consumer surplus to be a good welfare indicator is known as the path dependency problem. To solve this problem, we decompose the change in welfare into two parts. The first part is the change in welfare due to income change, maintaining prices constant, which is shown to be path independent and equal to the sum of the surplus of aggregate supplies and the change in government revenue. The second part is the change in welfare due to price changes, maintaining income constant, which is shown to be path independent and equal to the Marshallian consumer surplus of aggregate demands.

Keywords: aggregation, consumer surplus, composite goods, producer surplus, welfare

JEL Classifications: C43, D6

Working Paper Series