(DP 1989-08) Geometric Properties of Explicitly Quasiconcave Functions

Abstract

Quasiconcave functions are characterized by the convexity of the upper level sets. It is natural to ask what additional properties are required to characterize explicitly quasiconcave functions, (which contain the strictly quasiconcave functions). We show that these additional properties can be expressed in terms of the properties of and relationship between the level set, the upper level set, the boundary and the profile of the upper level set.