Impact of Uncertainty and Risk Aversion on Price and Order Quantity in the Newsvendor Problem

TLDR

The study examines a single‑period inventory model where a risk‑averse retailer sets order quantity and selling price to maximize expected utility, extending the classic newsvendor by allowing demand distribution to depend on price. The authors aim to analyze how two distinct price‑dependent demand mechanisms influence optimal pricing and ordering decisions. They model price as either scaling the demand distribution or shifting its location, and reduce the two‑decision problem to a single‑variable optimization. Compared to a risk‑neutral retailer, a risk‑averse retailer charges a higher price and orders less under the scaling model, but a lower price under the shifting model, offering insights that could improve price contracts and channel‑management policies.

Abstract

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; where as, 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.