Inequality of Living Standards and Isoelastic Equivalence Scales

Comparisons of well-being across heterogenous households necessitate that households' incomes are adjusted for differences in size and composition: equivalence scales arecommonly used to achieve this objective.Equivalence scales with constant elasticity with respect to family size have been argued to provide a good approximation to a large variety of scales (see, e.g., B. Buhmann, L. Rainwater, G. Schmaus, and T.M. Smeeding, Review of Income and Wealth (1988), 115--142) and they therefore play a prominent role in empirical work. Focusing on inequality of well-being, we first show that, if one requires that the index of inequality is -in addition to standard properties – invariant to modifications of the relative (marginal) distributions of needs and income across households, then the equivalence scales must be isoelastic. In addition, if all households' members have the same preferences and if households maximise the sum of their members' utilities, then the only preferences consistent with isoelastic scales are of the CobbDouglas type.