Discontinuous transformations, Lorenz curves and transfer policies

Abstract

This article reconsiders the effect of variable transformations on the redistribution of income. If the theorems hold for all income distributions, previously given conditions are both necessary and sufficient. Different versions of the conditions are compared and their equivalence are stated. It is proved that the continuity of the transformations can be implicitly included in the necessary and sufficient conditions. In general, continuity is a realistic restriction when the theory is applied to transfer problems. The effect of dropping the explicit continuity restriction on the transformations is analysed, since situations in which discontinuity can be assumed are also considered. The analyses have yielded the fundamental result that continuity is a necessary condition if income inequality persists or is reduced.