Abstract
The concept of “compensating variation” introduced by Hicks (1939), and developed by Henderson (1941) and Hicks (1942, 1956), remains along with its sister concept of “consumer’s surplus” the principal tool of analysis underlying present-day “cost- benefit analysis” and “applied welfare economics” (cf. Mishan, 1971; Harberger, 1964, 1971). In two previous papers (Chipman & Moore, 1976, 1980) we have respectively analyzed the consumer’s surplus and the compensating and equivalent variations in the context of single-valued, differentiable demand functions. In the present paper we extend the analysis of the latter two concepts to the context of demand correspondences. Since the alternative specifications of homothetic and parallel1 prefences turn out to be of particular importance in providing a rigorous justification for certain uses of the compensating variation as a welfare measure, we include a detailed development of the principal properties of demand correspondences and indirect preferences under these two specifications-particularly that of “parallel” preferences in Appendix B. Our main results (Theorems 1 and 3) establishing necessary conditions for the extended applicability of the compensating variation both make use of a basic duality theorem concerning the relationship between indirect preferences and demand correspondences proved in Appendix A (Theorem 6).
Research for this paper on the part of both authors was supported by National Science Foundation grant SOC77-27257.
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Chipman, J.S., Moore, J.C. (1992). Compensating Variation as a Measure of Welfare Change. In: Neuefeind, W., Riezman, R.G. (eds) Economic Theory and International Trade. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77671-7_5
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