Should a firm charge on a per-use basis or sell subscriptions when its service experiences congestion? Queueing-based models of pricing primarily focus on charging a fee per use for the service, in part because per-use pricing enables the firm to regulate congestion-raising the per-use price naturally reduces how frequently customers use a service. The firm has less control over usage with subscription pricing (by definition, with subscription pricing customers are not charged proportional to their actual usage), and this is a disadvantage when customers dislike congestion. However, we show that subscription pricing is more effective at earning revenue. Consequently, the firm may be better off with subscription pricing, even, surprisingly, when congestion is intuitively most problematic for the firm: e.g., as congestion becomes more disliked by consumers. We show that the absolute advantage of subscription pricing relative to per-use pricing can be substantial, whereas the potential advantage of per-use pricing is generally modest. Subscription pricing becomes relatively more attractive if consumers become more heterogeneous in their service rates (e.g., some know they are "heavy" users and others know they are "light" users) as long as capacity is fixed, the potential utilization is high, and the two segments have substantially different usage rates. Otherwise, heterogeneity in usage rates makes subscription pricing less attractive relative to per-use pricing. We conclude that subscription pricing can be effective even if congestion is relevant for the overall quality of a service. Should a …rm charge on a per-use basis or sell subscriptions when its service experiences congestion? Queueing-based models of pricing primarily focus on charging a fee per use of the service, in part because per-use pricing enables the …rm to regulate congestion -raising the per-use price naturally reduces how frequently customers use a service. The …rm has less control over usage with subscription pricing (by de…nition, with subscription pricing customers are not charged proportional to their actual usage), and this is a disadvantage when customers dislike congestion. However, we show that subscription pricing is more e¤ective at earning revenue. Consequently, the …rm may be better o¤ with subscription pricing, even, surprisingly, when congestion is intuitively most problematic for the …rm: e.g., as the industry moves to a standard of faster service, or as congestion becomes more disliked by consumers. We show that the absolute advantage of subscription pricing relative to per-use pricing can be substantial whereas the potential advantage of per-use pricing is generally modest. Furthermore, the relative attractiveness of subscription pricing is enhanced if the …rm is able to earn third-party revenue from each transaction (e.g., if the …rm acts as a platform in a two-sided market). We conclude that subscription pricing can be e¤ective even if congestion is relevant for the overall quality of a service.How should a …rm price ...

Should Consumers Be Strategic?

Restaurant delivery platforms collect customer orders via the Internet, transmit them to restaurants, and deliver the orders to customers. They provide value to restaurants by expanding their markets, but critics claim they destroy restaurant profits by taking a percentage of revenues and generating congestion that negatively impacts dine-in customers. We consider these tensions using a model of a restaurant as a congested service system. We find that the predominant industry contract, in which the platform takes a percentage cut of each delivery order (a “commission”), fails to coordinate the system because the platform does not internalize its effect on dine-in revenues; this leads to prices that are too low, reducing the restaurant’s margins and leaving money on the table for both firms. Two commonly proposed remedies to this problem (commission caps and allowing the restaurant to set a price floor on the platform) can increase restaurant revenue but do not solve the coordination issue. We thus propose an alternative, practical coordinating contract that is a variation of the current industry standard: for each delivery order, the platform pays the restaurant a percentage revenue share and a fixed fee. We show that this contract, appropriately designed, coordinates the system, protects restaurant margins by ensuring a lower bound on its revenue per delivery order, and allocates revenue between the restaurant and the platform with a high degree of flexibility. This paper was accepted by Victor Martinez-de-Albeniz, operations management.

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