The Potential Dependence of Equivalence Scales on Income

Abstract

In the framework of (neoclassical) demand analysis, the equivalence scale of household type k relative to household type r is that ratio of cost functions \( \frac{{c(u_k ,p_k ,s_k )}} {{c(u_r ,p_r ,s_r )}} \) which equalises the utility of both households. If the utility functions lack interpersonal comparability then any kind of equivalence scales may emerge from analysing household demands. This establishes an identification problem. IB and ESE avoid but do not solve the identification problem: relative income needs of different household types are simply assumed to be invariant to the households' utility or income levels at which they are compared. This necessitates a specific form of cost functions, viz. c(ur, pr, sk) = σ(pr, sk) * c(ur, pr)}. Other authors like Ray (1983) and Jorgenson and Slesnick (1987) implicitly assume in their empirical estimations that the equivalence scales are invariant with respect to income or utility. Thus, given a price vector, equivalence scales in both cases only depend on the demography of the households. Some authors like Lewbel (1989) try to make the constancy property the central point in equivalence scale measurement, yet not all authors agree with this idea. According to Conniffe (1992, p. 429) this “practice should be changed”, justifying his demand by means of an example: “[…] if a child is taken as equivalent to 0.5 of an adult and living standards of a “two adult-four children” household are comparable with a “two adult” household the income of the former would be first divided by two. This implies that the “cost” of a child is £1,250 per annum if that household has an income of £10, 000 per annum and £125, 000 per annum if the household has an income of £lm.”