Source and Subgroup Decomposition Inequalities for the Lorenz Curve

In this note, the author derives inequalities on the Lorenz curve of an aggregate income distribution in terms of the Lorenz curves of its constituent parts. These parts are made up of different income sources in one case and different groups in another. These inequalities are applied to the class of linear inequality measures to derive a further set of inequalities. The method of proof for the Lorenz inequalities is based on statistical arguments involving the use of asymptotic theory. Copyright 1987 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.