Welfare comparisons with bounded equivalence scales

The paper considers the problem of comparing income distributions for heterogeneous populations. The first contribution of this paper is a precise dominance criterion combined with a simple algorithm for implementing the criterion. This criterion is shown to be equivalent to unanimity among utilitarian social planners whose objectives are compatible with given intervals of equivalence scales. The second contribution of the paper is to show that this criterion is equivalent to dominance for two different families of social welfare functions, one inspired by Atkinson and Bourguignon (in: G.R. Feiwel (Ed.), Arrow and Foundation of the Theory of Economic Policy, Macmillan, London, 1987), in which household utility is a general function of income and needs, and a second family inspired by Ebert (Soc. Choice Welfare 16 (1999) 233), in which household utility is a function of equivalent incomes. Finally, we extend our results to the case where the distributions of needs differ between the two populations being compared.