Alternative ways of measuring and decomposing equivalent variation

Two different concepts of 'equivalent variation' have been used to measure the welfare effects of policy changes. One applies to uncompensated changes in which utility can vary, the other to compensated changes in which it is held constant. Harberger [J. Economic Lit. 9 (1971) 785-797] decomposed infinitesimally small changes in the uncompensated measure into components that measure the alleviation, or exacerbation, of existing distortions. We extend his methodology to obtain an exact decomposition of the compensated measure for finite changes, and show that no corresponding decomposition of the uncompensated measure is generally possible for finite changes, without introducing a residual or a scaling factor.