(DP 1983-10) Some Well-Behaved Composition Functions Involving Nonconcave Argument Functions

Abstract

Quasi-concavity is the criterion for well-behaveness in our composition functions. Negishi (1963) has shown how to generate quasi-concave composition functions when the argument functions are concave. We show here that one can generate quasi-concave composition functions even when the argument functions are nonconcave. The trick is to find interesting and "compatible" subfamilies in the quasi-concave family that, in composition, compensate for non-concavity of the argument functions and as a result keep the composition function within the quasi-concave family.