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

This paper analyzes the effects of population growth and other demographic changes on the distribution of income by examining Lorenz curves and generalized Lorenz curves produced from combinations of income distributions. The paper shows that when subpopulations 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 subpopulations. These conditions become less regular when the subpopulations 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. The results are illustrated by comparing income distributions across generations in Brazil.