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On the Unimodality of the Profit Function of the Pricing Newsvendor



In this note, we study the price-setting newsvendor problem. We use three conditions, the log-convexity of the coefficient of variation, the log-concavity of the deterministic profit function, and the log-convexity of the random noise's expectation conditional on having leftover inventory to establish the log-concavity of the retailer's expected profit function. This new result is complementary to existing results and removes some assumptions in the pricing and inventory coordination literature. It also addresses the conjecture made by Petruzzi and Dada (1999), and can be applied in the pricing game.