A Social Welfare View of the Measurement of Income Equality

Economists' use of the term "equality" in reference to a distribution of incomes has historically been in the sense of a consensus for some statistical characteristic(s) of the distribution rather than a firm concept of equality. Of course such a concept rests on appropriate welfme assumptions about income and its distribution, assumptions which, for the most part, have been left implicit (and unknown) in discussions of income equality in the literature. Our purpose in this paper is dual: first, we wish to discover an unambiguous, welfare-related e q u a l i ~ measure. This we accomplish through suitable assumptions on a social welfare function. What is produced is an "index" of equality which describes the performance of a given distribution relative to the maximum welfare derivable from the total income it represents. The measure thus depends functionally on the welfare attributes of income, something which in reality we know little about. This impmse leads ur to inquire into the sensitivity of the index over specifications of the welfare function, which is done by comparing equality ranks for the states of the United States for 1960 under various functional forms and among curves within a given form. As an interesting secondary issue, the performance of traditional equality measures is tested relative to the welfareoriented index to discover implications about their welfare content. It is found that the equality index is, in certain ranges for the welfare function, insensitive to its specification. The findings lead directly to conclusions concerning traditional equality memures, their usefulness in correctly accounting for equality diflerences among alternative income distributions and, concomitantly, their implicit welfare inputs.