Lorenz Curves, Inequality, and Social Welfare Under Changing Population Composition

Abstract

This paper analyzes the properties of Lorenz curves and generalized Lorenz curves produced from combinations of income distributions. The paper shows that when sub-populations have equal means, a number of simple conditions govern the position of the Lorenz curve for the combined population relative to the Lorenz curves for the sub-populations. These conditions become less regular when the sub-populations have different means, and suggest that a combined distribution will almost never Lorenz dominate an original distribution. Implications of the results for intertemporal comparisons of social welfare and inequality are discussed, and are illustrated by comparing income distributions across generations in Brazil