On the optimality conditions of a price-setting newsvendor problem

We analyze a price-setting newsvendor problem with an additive-multiplicative demand. We show that the unimodality of the newsvendor profit function holds when the underlying random term has an increasing failure rate and the demand functions satisfy certain concavity conditions. Furthermore, we show that the optimal price decreases in the order quantity. Finally, we compare our optimality conditions with those existing in the literature.