A Note on Lerner Index, Cross-Elasticity and Revenue Optimization Invariants

We study common properties of retail pricing models within a general framework of calculus of variations. In particular, we observe that for any demand model, optimal de-seasoned revenue rate divided by price elasticity is time invariant. We also obtain a generalization of a well known inverse relationship between price elasticity of demand and Lerner index. These invariance results are illustrated by two contrasting examples of markdown optimization and optimal continuous replenishment