Overview of Quasiconcavity and its Applications in Economics

摘要

Quasiconcavity is the most inclusive class of generalized concave functions,211u001ebroad enough to include both concave and convex shapes. Moreover, since 211u001equasiconcavity is the mirror image of quasiconvexity, the analysis of 211u001equasiconcavity may be interpreted as the analysis of curvature characteristics in 211u001egeneral. The majority of economics-oriented mathematical works treat curvature 211u001echaracteristics in the framework of quasiconcavity (strict quasiconcavity). The 211u001evarying definitions of quasiconcavity are not completely equivalent. They are 211u001eused interchangeably, and the extent of overlap between each definition and the 211u001edefinitions of closely-related concepts eludes those who do not deal with these 211u001eissues on a regular basis. Over the past decades, several works have appeared 211u001eunder the rubric of 'generalized concavity' to standardize the criteria for 211u001equasiconcavity and for concepts closely related to it.