A powerful tool for analyzing concave/convex utility and weighting functions

Abstract

This paper shows that convexity of preference has stronger implications for weighted utility models than had been known hitherto, both for utility and for weighting functions. Our main theorem derives concave utility from convexity of preference on the two-dimensional comonotonic cone, without presupposing continuity. We then show that this, seemingly marginal, result provides the strongest tool presently available for obtaining concave/convex utility or weighting functions. We revisit many classical results in the literature and show that we can generalize and improve them.