A Note on Generalized Transfers Principle with Reduced-Form Social Welfare Functions

In most welfare analyses, especially in the literature on normative inequality measurement, it is a commonplace to assume a direct relationship between the distribution of income and social welfare. As a result, this relationship is formally summarized by a single function, called a reduced-form social welfare function. Hence, with reference to some transfer principles, normative considerations are introduced and the shape of the reduced-form is accordingly restricted. In this note, we investigate and question the relevance of this approach. After recognizing that any reduced-form social welfare function merges two elements of very different nature individuals' self-interested preferences over income (an empirical element) and those of the society over utilities (a normative element) it is clear that it is problematic or at least misleading to make assumptions about the shape of the reduced-form social welfare function according to normative considerations only. However, we show that consistency can be restored whenever individuals' preferences can be represented by completely monotone utility functions.