Inequality and isoelastic equivalence scales: restrictions and implications

Comparisons of well-being across heterogenous households necessitate that households’ incomes are adjusted for differences in size and composition: equivalence scales are commonly 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., Buhmann et al., Equivalence scales, well-being, inequality and poverty: sensitivity estimates across ten countries using the Luxembourg Income Study (LIS) database. Rev Income Wealth 34:115–142, 1988) 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 Cobb–Douglas type.