Characterizations of Lorenz curves and income distributions

The purpose of this paper is to propose and justify the use of a few measur es of inequality for summarizing the basic information provided by the Lore nz curve. By exploiting the fact that the Lorenz curve can be considered an alogous to a cumulative distribution function it is demonstrated that the m oments of the Lorenz curve generate a convenient family of inequality measu res, called the Lorenz family of inequality measures. In particular, the fi rst few moments, which often capture the essential features of a distributi on function, are proposed as the primary quantities for summarizing the inf ormation content of the Lorenz curve. Employed together these measures, whi ch include the Gini coefficient, also provide essential information on the shape of the income distribution. Relying on the principle of diminishing t ransfers it is shown that the Lorenz measures, as opposed to the Atkinson m easures, have transfer-sensitivity properties that depend on the shape of t he income distribution.