It was conjectured by Pigou that an increase in real national income, as reckoned in the prices of either the initial or the terminal period, would always correctly indicate an improvement in national welfare provided the increase referred to the aggregate income of a given group of persons with fixed preferences and a fixed proportional distribution of income among them. We show that if the individual preferences are assumed to be homothetic, and if by a welfare improvement one means respectively a potential improvement (in which losers can be compensated by gainers) or an actual improvement (in which all are gainers), then on either of these respective criteria Pigou's conjecture holds true under these conditions if and only if individual preferences are identical.

The compensating variation was defined by J. R. Hicks (1942) as the amount one would have to deduct from a person's income to make him just as well off after a change in prices and income as he had been in the initial situation. If the compensating variation is positive, the individual is better off under the new situation. Since the compensating variation furnishes a uniquely defined numerical (cardinal) indicator of welfare improvement, it provides an implicit ranking of alternative prospective situations not only relative to the initial situation, but also relative to each other. In practice this appears to be how this and other tools of cost-benefit analysis are actually used: one is interested in knowing not only whether a particular bridge, or a particular excise tax, will lead to an improvement in welfare, but which out of a set of alternative bridges or alternative tax systems will improve welfare the most.1 In this paper we analyze conditions under which the compensating variation can be validly used in this generalized sense; these turn out to be precisely the same as conditions previously derived (see our 1976 paper) for the valid use of consumer' s surplus as a welfare measure. In our final section we analyze the problem of deriving the generalized equivalent and compensating variations (either exactly or approximately) from observable demand functions, by means of generalizations of, or alternatives to, consumer's surplus.

Journal Article Resource Allocation in a Non-convex Economy Get access James C. Moore, James C. Moore Purdue University Search for other works by this author on: Oxford Academic Google Scholar Andrew B. Whinston, Andrew B. Whinston Purdue University Search for other works by this author on: Oxford Academic Google Scholar Joseph S. Wu Joseph S. Wu Purdue University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 39, Issue 3, July 1972, Pages 303–323, https://doi.org/10.2307/2296361 Published: 01 July 1972 Article history Received: 01 April 1971 Revision received: 01 November 1971 Published: 01 July 1972