Inequality of well-being and isoelastic equivalence scales

Equivalence scales are typically designed for adjusting households' incomes for differences in size and composition. On the one hand, there is evidence that the way differences in needs across households are taken into account has a significant impact on the assessment of inequality in the society. On the other hand, equivalence scales with constant elasticity with respect to family size have been shown to provide a good approximation to a large variety of scales used in empirical work. We first show that, if one requires that the (multidimensional) inequality index 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. Assuming that all individuals have the same preferences and that households maximise the sum of their members' utilities, we also prove that the only preferences consistent with isoelastic scales are of the Cobb-Douglas type.