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

This paper analyzes the redistributive effect of transformations of in comes when the same transformation is applied to all incomes. Followin g Marshall and Olkin (''Inequalities: A Theory of Majorization and its Applications,'' Academic Press, New York, 1979), we consider two comp eting families of nested inequality criteria, all of which are consist ent with the Lorenz ordering. Looking at the transformations that redu ce the inequality of incomes, we show that, within each family, all th e criteria generate exactly the same class of transformations. We next identify those transformations that preserve or convert a given inequ ality ranking into a finer ranking. We finally find necessary and suff icient conditions to be imposed on a pair of transformations for the i nequality ranking of distributions to be preserved. (C) 1994 Academic Press, Inc.