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.
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