FAO.org

This analytical tool illustrates how Crossing Generalised Lorenz (GL) curves can be used to identify the best income distribution on social welfare grounds within a set of alternative income distributions generated by different policy options.

It starts by illustrating two alternative income distributions resulting from policy changes that lead to income increases for some individuals and decreases for others. GL curves are then calculated for the alternative distributions to rank them on welfare grounds on the basis of Shorrocks’ Theorem. After observing that Shorrocks’ Theorem is not applicable, because GL curves cross once, necessary additional conditions, such as restrictions on the features of the Social Welfare Function (SWF) and the shape of income distributions, are set and discussed. Subsequently, a step-by-step procedure to use GL curves to infer welfare judgments when GL cross once, is provided and illustrated with some simple numerical examples.

For more information, see also:

• Charting Income Inequality. The Lorenz Curve. EASYPol Series 000
• Social Welfare Analysis of Income Distributions: Ranking Income Distributions with Lorenz Curves. EASYPol Series 001
• Social Welfare Analysis of Income Distributions: Ranking Income Distributions with Generalised Lorenz Curves. EASYPol Series 002

This paper is part of a FAO Policy series: EASYPol-Resources for policy making (in agriculture, rural development and food security). To find other EASYPol series' resources, go to the Policy Support and Governance website>Resources and type "EASYPol" in the free text search.