Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem

We consider a single-period inventory model in which a risk-averse retailer faces uncertain customer demand and makes a purchasing-order-quantity and a selling-price decision with the objective of maximizing expected utility. This problem is similar to the classic newsvendor problem, except: (a) the distribution of demand is a function of the selling price, which is determined by the retailer; and (b) the objective of the retailer is to maximize his/her expected utility. We consider two different ways in which price affects the distribution of demand. In the first model, we assume that a change in price affects the scale of the distribution. In the second model, a change in price only affects the location of the distribution. We present methodology by which this problem with two decision variables can be simplified by reducing it to a problem in a single variable. We show that in comparison to a risk-neutral retailer, a risk-averse retailer in the first model will charge a higher price and order less; whereas, in the second model a risk-averse retailer will charge a lower price. The implications of these findings for supply-chain strategy and channel design are discussed. Our research provides a better understanding of retailers' pricing behavior that could lead to improved price contracts and channel-management policies.