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.