Risk Premiums in the Price-Setting Newsvendor Model

Consider a make-to-stock firm that needs to decide its price and order quantity before a selling season without knowing the demand. By charging a different price from the riskless price, the firm can hedge its profits against demand uncertainty either by mitigating its demand risk or by lowering its opportunity cost of stockouts. In this paper, we characterize the behavior of the risk premium under an additive-multiplicative demand model. We show that the sign of the risk premium can be uniquely determined by the elasticities of the mean and of the standard deviation of demand at the riskless price. We also quantify the worst-case magnitude of the risk premium and find that, although the risk premium can be significant, its range of potential values rapidly narrows and becomes relatively insensitive to the specific elasticity values as the mean demand becomes more elastic. Our characterization of the risk premium generates insights into the role of pricing as a hedge against demand uncertainty