Relationships among three assumptions in revenue management

This note discusses the relationships among three assumptions that appear frequently in the pricing/revenue management literature. These assumptions are mostly needed for analytical tractability, and they have the common property of ensuring a well-behaved revenue function. The three assumptions are decreasing marginal revenue with respect to demand, decreasing marginal revenue with respect to price, and increasing price elasticity of demand. We provide proofs and examples to show that none of these conditions implies any other. However, they can be ordered from strongest to weakest over restricted regions, and the ordering depends upon the region.