On the Structure of Additive Inequality Measures

This paper examines the properties of the family of additively separable inequality measures. In particular it investigates the possibility of decomposition of such a measure by population subgroups, and the scope for treating different groups in different ways within the overall measure. This differential treatment of subpopulations is potentially very important, as we shall see from a simplified example. Table I depicts an eight-" person " society arranged into two groups so that persons 5 to 8 (in group 2) have exactly twice the incomes of persons 1 to 4 (in group 1) respectively. Call the values of the inequality measure for group 1, for group 2 and for the whole population IP, j2 and I* respectively. If the inequality measure used is mean-independent and the same for either group and for the total, and if each income recipient is identical in every respect other than income, we expect Table I to yield I = 12 and I*> I. If the measure is decomposable then we can write I* = f(I', 12, PB) where jE is " between-group " inequality found by applying the measure to the vector of group average incomes ($2,500, $5,000). TABLE I