Some classes of functions that preserve the inequality and welfare orderings of income distributions

Abstract

We identify in the paper those classes of functions that preserve the ranking of distributions according to three welfare criteria introduced recently by A. F. Shorrocks (Economica 50 (1983), 3–17). We prove that a necessary and sufficient condition for a function to preserve the generalized Lorenz ordering of distributions is that it be increasing and concave. Requiring welfare improvements to be compatible with more equality, we obtain linear [resp. affine] functions when emphasis is placed on relative [resp. absolute] income differentials.