INEQUALITY REDUCING AND INEQUALITY PRESERVING TRANSFORMATIONS OF INCOMES - SYMMETRICAL AND INDIVIDUALISTIC TRANSFORMATIONS

This paper analyzes the redistributive effect of transformations of incomes when the same transformation is applied to all incomes. Following Marshall and Olkin (''Inequalities: A Theory of Majorization and its Applications,'' Academic Press, New York, 1979), we consider two competing families of nested inequality criteria, all of which are consistent with the Lorenz ordering. Looking at the transformations that reduce the inequality of incomes, we show that, within each family, all the criteria generate exactly the same class of transformations. We next identify those transformations that preserve or convert a given inequality ranking into a finer ranking. We finally find necessary and sufficient conditions to be imposed on a pair of transformations for the inequality ranking of distributions to be preserved. (C) 1994 Academic Press, Inc.