Note: The Newsvendor Model with Endogenous Demand

Abstract

T his paper considers a firm's price and inventory policy when it faces uncertain demand that depends on both price and inventory level. The authors extend the classic newsvendor model by assuming that expected utility maximizing consumers choose between visiting the firm and consuming an exogenous outside option. The outside option represents the utility the consumer forgoes when she chooses to visit the firm before knowing whether or not the product will be available. The authors investigate both the case in which the firm's price is exogenous and the case in which price is chosen optimally. The paper makes two contributions. First, the authors show that the firm holds more inventories, provides a higher fill rate, attracts more customers, and earns higher profits when it internalizes the effect of its inventory on demand. Second, the authors show that in the endogenous price case the firm's two-dimensional decision problem can be reduced to two, sequential, single-variable optimizations. As a result, the endogenous-price case is as easy to solve as the exogenousprice case.

Price Commitments with Strategic Consumers: Why It Can Be Optimal to Discount More Frequently … Than Optimal

“…They have value v h for the firm's service. As in Dana and Petruzzi (2001) (and other papers), high-value consumers must incur a positive cost, c < v h , to search the firm to purchase the good or service. These search costs include the time and effort to physically travel to the firm and the mental effort associated with a purchasing decision.…”

“…Others have incorporated similar search costs, generally in a single-firm setting: Baye and Morgan (2001) Alexandrov and Lariviere (2012), and Su and Zhang (2009). Dana and Petruzzi (2001) have fixed prices and focus instead on how search costs influence the firm's capacity choice. Baye and Morgan (2001) study a marketplace for price information for which customers may pay to subscribe or, alternatively, incur search costs to learn the price set by their local firm only.…”

“…Table 3 demonstrates that the capacity investment under no commitment can be large (e.g., on average k 0 /k m = 1 90). As in Dana and Petruzzi (2001), when the firm does not make a price commitment, then it can attract strategic consumers only by over investing in capacity. However, this can be inefficient, and in only a minority of scenarios (662 out of 1,800 scenarios) is the no-commitment strategy able to earn a positive profit.…”

“…Dana and Petruzzi (2001) show that if consumers care about availability-they do not like incurring the cost to search the firm only to learn that they cannot purchase the good or service-then the firm should invest in more capacity than it would if consumers were nonstrategic. (Gaur and Park 2007 find an analogous result in a model with consumer learning and multiple firms.)…”

“…Similarly, adding capacity increases the likelihood that a clearance sale is justified, thereby exciting consumers with the greater prospect of a good deal. However, Dana and Petruzzi (2001) did not consider the possibility that the firm could choose its pricing strategy, in particular the frequency of clearance sales to help draw consumers. We find that it is ineffective to only use excess capacity to attract consumers.…”