Log-concave functions and transformations thereof

TL;DR

This paper reviews and corrects existing work on log-concave functions, adds new results relevant to monotone hazard rates, and demonstrates an application in monopoly pricing where demand curve properties influence revenue function concavity.

Contribution

It provides corrections, additional results, and an application linking demand curve log-concavity to revenue function concavity.

Findings

Strict log-concavity of demand implies strict concavity of revenue.

Enhanced understanding of log-concave functions in economic modeling.

Corrections and extensions to previous literature on log-concavity.

Abstract

I summarize Bagnoli and Bergstrom (2005)'s review on log-concave functions, make several corrections, and augment the discussion with further results that can be useful in obtaining monotone hazard rate. I also provide an application of monopoly pricing, where strict logconcavity of demand curve implies strict concavity of the revenue function.