Compensating and Equivalent Variations, and the Deadweight Loss of Taxation

Abstract

Using the expenditure function, Diamond and McFadden (1974) express the measures of deadweight loss of taxation of Hotelling (1938) and Harberger (1974) in terms of the compensating variation. Kay (1980) has criticized the Diamond-McFadden measure because the concept of tax revenue it implies is very different from the actual revenue that the system will bring in, and has proposed another measure based on the equivalent variation. This note, the purpose of which is largely clarificatory, shows that the deadweight loss of taxation can be consistently defined in terms of both compensating and equivalent variations, and that both measures follow very naturally from a common framework of analysis. The measure of loss based on the equivalent variation coincides with the measure proposed by Kay, but that based on the compensating variation differs from the Diamond-McFadden measure in that the resulting loss-compensating factor is the actual rather than the compensated level of tax revenue. The analysis also points out an asymmetry between these measures hitherto unnoticed-while the equivalent variation measure can be reduced (as in Harberger, 1974) to a triangular approximation, the compensating variation measure in general cannot. This, of course, does not imply that the former measure is superior to the latter; it only serves to illustrate the fact that there is nothing special about measures that can be reduced to triangular approximations.