The social welfare bases of Gini and other income inequality measures

Abstract

In 1920, Dalton introduces the important issue of the social welfare bases of income nequality measures. Fifty years later, Atkinson takes up this issue and passing from Dalton utility space to the income space, provides new insight and further development to the measurement and interpretation of income inequality. These two contributions led Atkinson and several other authors to argue in favour of the income inequality measures that are derived from social welfare considerations. Departing from this unilateral position, this study introduces a fundamental equation of income, and derives from it a dual relationship between: (I) utility and disutility functions; (II) social welfare and diswelfare functions; and (III) social welfare functions and income inequality measures. The utility, disutility and loss functions corresponding to Gini, Theil, generalized entropy, Atkinson, Zenga and Pareto income inequality measures are also deduced. Thus the fundamental equation of income provides the rationale to the determination of the social welfare bases of an income inequality measure and conversely, the income inequality bases of a social welfare function. The probabilistic interpretation of the set of economic units as a sample space and the introduction of the following three principles: (I) the social and individual aversion to poverty; (II) the social aversion to inequality; and (III) the interpersonal comparisons of utility and disutility provide the basic conceptual and methodological structures to the determination and analysis of the utility, disutility and loss functions properties corresponding to the income inequality measures object of inquiry, including their relative sensitivities to income transfers.