Comment on “The Relative Deprivation Curve and Its Applications”

Abstract

The article by Kakwani (1984) introduced a measure of inequality that is weighted to take account of a sense of deprivation an individual may feel on seeing others who are better off. In the second part of the article, Kakwani presented estimates of deprivation using Australian data. I would like, first, to comment on the welfare implications of the measure of relative deprivation proposed in the article and, second, to point out some crucial assumptions underlying the use of household incomes in the empirical work. The measure of relative deprivation is based on a utility function for the representative individual of the form w = u (y, x), with uy x, uy = 0 for y O, where x is own income and y denotes the incomes of other individuals. The condition uy x is interpreted as the deprivation an individual suffers with an increment in the income of any individual who is better off. The conditions on uy introduce a crucial asymmetry in the individual's utility function: the individual suffers deprivation on observing incomes above x but derives no sense of satisfaction from observing individuals on incomes below x. Under this condition, a social welfare function of the form w = U(w), U,, > O, does not necessarily satisfy the Pareto criterion. It may be possible to increase social welfare by making some people worse off without making anyone better off. In particular, it may be possible to increase social welfare by reducing incomes of individuals just above x, who may be relatively poor if x is sufficiently low. Clearly this is the case when the utility function is specified as