Ranking Distributions with Generalized Lorenz Curves

Abstract

Recently Shorrocks [29] and Kakwani [18] have extended Atkinson's [1] theorem on Lorenz dominance and social welfare to allow social welfare evaluations of income distributions with unequal mean incomes.' Shorrocks and Kakwani independently develop the Lorenz curve as a device for simultaneously taking account of differences in mean incomes and the degree of income inequality. The generalized Lorenz curve is . . constructed by scaling up the Lorenz curve by the mean of the distribution [29, 6]. Thus, the height of the generalized Lorenz curve reflects the level of incomes, while the convexity of the generalized Lorenz curve reflects degree of income inequality. Shorrocks and Kakwani both show that, regardless of mean incomes, generalized Lorenz dominance is equivalent to preference by all increasing, S-concave social welfare functions.2