A Note on Decomposable Inequality Measures - Russell, R. Robert (Review of Economic Studies, 1985)
Cowell has shown that if an inequality measure satisfies (1) additivity, (2) decomposability (among population groups), (3) additivitiy of the group inequality measures, (4) symmetry within groups, and (5) twice differentiability, it can be written as an additive function of group measures belonging to the CES class or of the form ∑i, si, ln si, where si is the i-th person's share. Using a result from the theory of functional equations, I prove that the first two conditions, often imposed for analytical convenience, alone imply Cowell's structure. Symmetry, or other ethical postulates, can then be represented by simple parametric restrictions.