Nearly everyone has gone out to buy a hot new product and found the shelves empty, or arrived at a popular restaurant only to encounter a two-hour wait to get a table. Many might think that the popular restaurant could boost its profits by raising prices. However, recent research by Hyoduk Shin and colleagues shows that businesses may be better off staying the course and not raising prices in spite of more customers than they can serve.

Shin, an assistant professor of Managerial Economics and Decision Sciences at the Kellogg School of Management, cites an example of two restaurants located across the street from each other. The first is a famous, well-established restaurant that is always crowded and has a long line of customers. The other is of lower quality and is almost always half-empty. “The usual intuition is that the well-established restaurant should raise its prices, because it would still be able to sell all its seats and earn a higher return on each of them,” Shin says. However, if the famous restaurant keeps prices low enough, some of the “leftover” customers will choose to go across the street and the other restaurant will “feast on those leftovers.” Rather than compete directly, the two businesses will have found a balance that enables both of them to thrive.

In a research model that Shin developed with Evan L. Porteus, a professor at Stanford University, and Tunay I. Tunca, an associate professor also at Stanford, the two restaurants are called a “leader” and a “follower.” The researchers explain that when capacities are limited, the usual intuition about price competition can be turned upside down. Usually, a firm does not want their competitor to lower prices. But there are situations where the follower wants the leader to do just that: the leader will have to turn away some customers because they will be sold out at the higher price. The “leftover” customers will often turn to the follower across the street. The follower can increase profits by also charging higher prices, knowing that there will be enough of those late-arriving customers who will pay the higher price rather than not eat or try to find another restaurant.

Beyond Restaurants
Restaurants are not the only businesses to feast on leftovers. Airlines are also beneficiaries of this phenomenon. Most people have witnessed the wild fluctuations of airline ticket prices. Shin explains that these fluctuations come from revenue management models that airlines use to try to maximize their profits. The models are based on the reasonable assumption that low-end customers—those who have a low willingness-to-pay—usually purchase their tickets or “arrive” earlier than high-end customers. According to recent research, if an airline is considered to be a monopolist, then the airline should protect its capacity for the late-arriving, high-valuation customers. Yet according to Shin and colleagues’ data, “this intuition can change dramatically when one considers the effect of competition. Under the threat of a competitor, a firm may in fact prefer not to reserve capacity for high-valuation customers, but rather sell out all its capacity to lower-valuation customers [and] leave some high-valuation customers to the competitor.”

Shin and his colleagues believe that independent arrivals—where customers tend to arrive in an order independent of how much they are willing to pay—are typical of retail and restaurant environments, in which customers arrive randomly and are served on a first-come, first-served basis. “Let’s say I see that my ‘follower’ restaurant is always half-empty,” Shin says. “One might think in that case that adding another seat doesn’t add any value. But our paper shows that indeed it does. Even if the restaurant is half-empty, and even if you know the seat will remain empty, there is still a value to adding it, because of the competitive aspect. If you add one more seat, then you pose a greater threat to compete directly—which forces the popular restaurant to cut its price, creating more leftovers to appease you. Even though there’s no direct benefit, adding one more seat yields a strategic benefit, one that is hard for the casual observer to discern.”

On the other hand, Shin adds, the popular restaurant will always have people waiting in line. Is there any value in adding one more seat in that restaurant? “In some cases, yes there would be,” he says. “But in other situations it may actually decrease the popular restaurant’s profits, because of the appeasing-the-competitor aspect. If the popular restaurant adds one more seat, that means one less leftover customer for the follower. To keep the follower appeased so that he won’t engage in direct competition, the leader must provide a certain number of leftover customers, and she must lower her price to do so. And this lower price may end up decreasing total revenues, even though the additional seat is filled.” The leader will be better off not adding any tables even when the restaurant’s patrons usually encounter a two-hour wait to get a table.

Shin and his colleagues stumbled upon another example at a recent conference: rooms in nearby three-star hotels sold for about twice the rate that had been set by the four-star conference hotel, where no rooms remained available. “This situation is consistent with [our claim] in the sense that the conference hotel is the price leader and prices are such that one could easily predict that there would be significant leftover demand,” they write. A conference hotel commits to its rate early. It is fairly limited in its ability to respond to the price adjustments of competing hotels, and, for any given conference, it cannot change capacity much on the margin.

Customer arrival sequence and restaurant capacity also affect the leader and the follower. Arrival sequence is the order in which different types of customers arrive to observe the price and availability of the product and then decide whom to buy from, if at all. Capacity is, of course, the maximum number of customers that can be served.

Concluding that their findings lay “another stepping stone on the way to developing the theory of operations strategy,” Shin and his colleagues express the hope that their work will prompt others to research the effects of pricing under competition with limited capacity, including the role of customer arrival sequences.