Di Fara Pizza is a small, single-location pizza place in Brooklyn. According to its Wikipedia entry (yes, it has a Wikipedia entry), it has been named to many, many lists of the best pizza in New York City. The place’s secret sauce is Dom DeMarco, the shop’s owner, who essentially makes every pie. He opened the shop in 1964 and is now 79. He doesn’t work too fast and really does everything right down to slicing basil on to each slice. Consequently, the lines can be a tad long. It is one of the principle things that on-line reviewers comment on:
It’s nice to see that the original pizza making man still has the passion to make pizza. But the wait is ridiculously long and people in there are just too pushy. “Next! What do you want?”
So how does that kind of wait affect their business and the customer experience? That was the topic of discussion of a recent episode of The Gist podcast (Your Food Will Be Ready When You Look Hungry Enough, Oct 12).
The guest of that episode is Dan Pashman, who describes his visit to Di Fara as well as the research he did to put together an episode of his own podcast, The Sporkful (Is This Pizza Worth Waiting For?, Aug 11).
Some of that reporting also ended up in an episode of Freakonomics Radio (What Are You Waiting For?, Aug 10)
That’s right: The man made one trip to Brooklyn and it resulted in three podcast episodes.
The Sporkful and Freakonomics episodes are worth a listening. Both talk about different aspects of managing queues. The former emphasizes more psychology and physiology (especially how waiting affects hunger) while the latter puts more emphasis on the economics of queue.
There are several things in the Freakonomics piece that are worth commenting on. First, is the idea that queues somehow represent a market failure.
Even if you are willing to wait, you’ll have to admit — at least if you think like an economist — that a line represents a certain kind of failure. A failure of supply to seamlessly meet demand.
Felix OBERHOLZER-GEE: There’s somewhere a scarcity. Whenever you see a line, the first thing to ask is what’s the scarcity?
That’s Felix Oberholzer-Gee. He’s an economist at Harvard Business School.
OBERHOLZER-GEE: As a consumer in a market economy, you should expect that everything happens for you instantaneously all the time. Then when that’s not true, you need to ask, “What’s the constraint?” The constraint is sometimes cost, is sometimes availability of skilled personnel, sometimes availability of space, but there’s got to be some constraint otherwise we wouldn’t see a line.
So I will admit that there instances in which queues clearly are about a market failure. When you read about people in Venezuela spending all day in line because they are hoping that a supermarket has the essentials they need, that is a market failure. Indeed, there is a board game exploring the consequences of such failures; it requires players stand in line, engage in bartering etc in order to complete a shopping list. (Apparently, it is sufficiently realistic that it has been banned in Russia.)
But are everyday lines really such a failure? As the quote above notes, queues arise because of system constraints; in the near term, there is not enough capacity. That in part reflects a lack of flexibility. Your local coffee shop cannot have a barista appear instantaneously when a customer walks in even if they have an extra skilled worker on staff. If that worker isn’t at the shop right now, they can’t help. And that worker isn’t there because it is impractical to staff to completely cover all possible demand levels every day. Of course, if the shop knew just who was coming in when to get a coffee, it could staff to meet that demand. But who wants to make appointments to get lattes? Said another way, queuing in many instances is the price we to maintain flexibility. If you don’t want to have to schedule every service you might consume ahead of time, you have to accept queuing.
Another interesting topic in the podcast is the discussion of experiments in which researchers tried to cut into lines in cafeterias, train stations, and food courts both with and without offering payment.
OBERHOLZER-GEE: The most surprising thing, which really is both interesting practically but theoretically speaking, is that while people are much more likely to let you cut in if you offer money, few people actually accept the monetary compensation. … So the typical conversation would go, “Can I cut in? Here’s $5.” You say, “Yes, of course, I’ll let you cut in, but I’m not going to take your money.”
The podcast goes on to discuss various reason why folks might not take payment. For example, if you are leading with offering money, my natural inference is that you are in a terrible hurry and I may just be inclined to help out. This is equivalent to the panicked person showing up the TSA line at the airport worrying that they are going to miss their flight.
What the podcast fails to discuss is that a world in which people routinely try to buy out people in line would create all sorts of problems. While it would let those in a real hurry to credibly express their need, it would also create the potential for speculators. Someone with a low waiting cost could join the line and offer up their spot as they approached the front of the line. An economist might describe that as creating a secondary market to reallocate a scarce resource to those who value it most (comments along these lines are made in the podcast). However, this arrangement would also draw in additional bodies to the system and make lines longer than they otherwise would be. That, in turn, would affect the decision of newly arriving customers of whether or not to join the queue. If I ran the queue, I would want to put the kibosh on such behavior.
Freakonomics also discusses one of the most famous results in the economics of queues. Consider a market in which everyone values a service a $10 and all have a cost of waiting of $2 per minute. Thus if the wait for service exceeds 5 minutes, the wait is too long to make the service worthwhile — even if it is free. Think of something like a water fountain and that each customer would use the fountain for one minute. If customers arrive over time, they will join the queue if there are fewer than five people in the system. Otherwise they will leave. This all straightforward and seems efficient. No one joins if their wait would be too long. However, it turns out that the system is inefficient in the sense that overall waiting costs are too high. This result is due to Pinhas Naor, who showed that too many people join the queue because they don’t recognize the externality they impose on others. It may be rational for me to become the fifth person in line, but it also means that the average line will be longer than if, say, the line were never over four people long.
Naor’s solution to this was to charge a price equal to the externality imposed on other customers. But there is another possibility: Don’t serve people first-in, first-out.
LANDSBURG: I teach economics at the University of Rochester. I write books about economics.
In his book More Sex Is Safer Sex, Landsburg describes a line-standing solution first proposed by an Israeli economist named Refael Hassin.
LANDSBURG: Professor Hassin’s wonderful idea is that instead of sending people to the back of the line, we send people to the front of the line. Each newcomer comes to the front of the line and pushes everyone else backward. … And you know, you might think, “Well, this way some people never get served at all.” That’s true. But under the current system some people never get served at all, namely the ones who are not willing to wait an hour. The same number of people are being denied service either way. The question is: how long are people waiting in line along the way? If we can minimize that, that would be great.
The problem with the usual queue is that people don’t internalize the impact they have on those who arrive after them, but if customers are served in reverse order, they are very, very aware of who arrives after them.
Now there are some obvious problems with this proposal that are discussed in the podcast (e.g., how do you keep someone from leaving the queue and instantly rejoining) but there are a couple of other points to make. First, the dynamics of this system are very different from the original Naor model. In the Naor model, some customers choose not to join the queue because it is too long. Here, everyone joins the queue but some will abandon when they get pushed too far back. Consequently, everyone will experience some waiting cost and some will have nothing to show for it. Assuming that everyone has linear waiting cost (i.e., waiting 4 minutes costs twice as much as waiting 2 minutes) is tantamount to assuming that everyone is risk neutral in time (i.e., people only care about the average wait and not the variability of that wait). That’s obviously a stretch but may not be unreasonable if we are talking about short waits. However, even if we are talking about short waits, people are likely to react negatively when they wait but find themselves leaving without being served. Finally, one of Professor Landsburg’s statement above is incorrect: The same number of people will not be served under last-in, first-out as under first-in, first-out. Serving in reserve order reduces the wait and results in a shorter line. For a fixed capacity, that can only be achieved if fewer customers are served.
A final quote to comment upon:
LANDSBURG: Making people wait does select for people who need the help more desperately. And that is a good thing about making people wait. But you still wouldn’t want to make them wait in line because there is a better way to deal with it. And a better way to deal with it is to let them pay a little extra to go into a premium queue.
But do priority queues always make customers better off? That is, if customers have some variation in their cost of waiting, do they necessarily benefit from being able to buy their way to faster service? It turns out this is not necessarily so. Even if everyone is not budget constrained, a priority scheme that puts those with higher waiting costs does not necessarily increase consumer surplus relative to serving customers first-in, first out. (This shows up in a paper a colleague and I are finishing up.) This is true even if using priority queues is socially efficient.