# How do we measure inequality?

Different tools have been created to measure inequality:

The Lorenz curve and the Gini coefficient

The Lorenz curve is a graphical representation of the distribution of wealth in a society. The further away from the bisector the curve is, the greater the inequality. The Gini coefficient, derived from the Lorenz curve, is the most widely used measure of income inequality in a society. Its value varies between 0 and 1, with 0 corresponding to a perfectly egalitarian distribution of total income, i.e. each individual has the same income, and 1 corresponding to a perfectly unequal distribution of total income, i.e. only one individual would have all the income. Thus, the higher the index, the greater the income inequality.

Theil's index

The Theil index measures the difference between the weight of an individual (or group) in the population and the weight of his or her income in the total income. An index of 0 indicates absolute equality, an index of 0.5 indicates inequality represented by a society where 74% of individuals have 26% of resources and 26% of individuals have 74% of resources, an index of 1 indicates inequality represented by a society where 82.4% of individuals have 17.6% of resources and 17.6% of individuals have 82.4% of resources. Less commonly used than the Gini index, the Theil index nevertheless has undeniable practical advantages. Its main advantage is that it can be decomposed ad infinitum by partitioning the population and then decomposing each group into different subgroups, in order to analyse the evolution of inequalities within and between different subpopulations.

The Atkinson Index

Like the Gini index, the Atkinson index varies between 0 and 1, with 0 representing perfect equality and 1 representing perfect inequality. The Atkinson index answers the following question: "If society could move towards a perfectly egalitarian distribution of income, what fraction of income would it be willing to give up to do so? This fraction is the Atkinson index. In other words, an Atkinson index of x% means that people would be willing to give up x% of their current income to make the distribution more equal.

Dispersion ratio by deciles: the Palma Ratio

The Palma index is a member of the family of inter-deciles ratios, the best known of which is the D90/D10 ratio. The Palma index is the sum of the income earned by households in the top decile (the top 10%) divided by the sum of the income earned by the 40% most vulnerable households. This indicator is based on the assumption that inequality is largely due to economic dynamics at the extreme ends of the resource distribution (earned income, accumulated savings) or, in other words, at the "tails" of the distribution. It provides a clear, synthetic measure of the extent to which higher tax rates paid by the rich and transfer payments received by the poor actually reduce income inequality in societies with progressive tax systems. Unlike the Gini coefficient, the index excludes from the calculation the middle class, located between the 40th and 90th percentiles, which account for about 50% to 60% of market income in empirical studies in different developed societies. The Palma thus measures inequality between the extremes of the distribution, i.e. between households at the top and the bottom.