On Assumptions Ensuring a Strictly Unimodal Revenue Function

This note discusses the relationships among three assumptions which appear frequently in the pricing literature. Each of these assumptions ensures that a “revenue function” is strictly unimodal over the region of interest. The three assumptions are decreasing marginal revenue with respect to demand, decreasing marginal revenue with respect to price and decreasing price elasticity of demand. We provide proofs and examples to show that none of these conditions is more restrictive than any other, but they can be ordered from strongest to weakest when restricted to certain parameter regions.