How to navigate the hidden economics of waiting in line

On a busy day, over 25,000 people visit the Vatican Museum in Vatican City, the world’s smallest country at 0.17 square miles, tucked in the middle of Rome. While the museum boasts one of the greatest collections of art in the world, the main attraction for many people (including me on my first-ever trip abroad) is the Sistine Chapel, with its massive ceiling frescoes painted by Michelangelo at the start of the 16th century.

Getting into the chapel, though, requires a substantial time commitment. The relatively low entrance price of twenty euros means that many more people want to see the chapel than the 5,800 square feet (or 540 square meters) of space can accommodate. If you have not pre-purchased premium tickets to enter the museum, you must wait in a physical line to buy one. That wait time can be as long as three or four hours, particularly during the summer, when there are more tourists. That line is followed by another to go through security to get into the museum. Lines can be even longer on the last Sunday of each month, when the chapel is free to the public.

The Vatican Museum is just one example of the many markets that resolve excess demand by having people wait around for a chance to get a scarce resource. These markets use first-come, first-served rules to allocate things and give you priority for arriving before the allocation gets doled out.

These allocation mechanisms come in two key varieties: lists and lines. The difference between the two is your physical presence. Joining a waiting list requires you to simply put your name down to secure your place in the list. Standing in a line requires you to physically be there. If you leave the line, it usually means you lose your spot, and since keeping your place requires a constant devotion of your time, lines are more costly for market participants and require different strategies.

Falling in line

This investment of time is how lines help achieve allocative efficiency: Those who are willing to wait hours to get their driver’s licenses renewed, experience the thrill of Space Mountain, or view the ceiling of the Sistine Chapel likely value those things more than people who aren’t willing to wait.

Economists have a name for what you must give up while you wait. We call this your opportunity cost. In the case of lines, your opportunity cost is the lost enjoyment or productivity or earnings from whatever you would have been doing if you were not waiting in line.

The advice you can find on the internet for beating the lines at the Sistine Chapel often involves going early, perhaps before the museum opens, to secure a spot toward the front of the line. The economist in me is not sure about this advice. If I arrive an hour before tickets go on sale to be first in line, but the wait would be only forty minutes long if I arrived when the museum opened, I end up waiting longer, not less. 

Whether arriving early shortens my wait depends on when others choose to arrive, and if all tourists follow the same internet advice and arrive an hour early, the lines at opening may be the longest of the day. It is hard to predict when the wait will actually be the shortest.

This is why you are better off considering opportunity cost rather than just waiting time. Rather than going when you think the lines might be shortest, you can go when your opportunity cost is the smallest — ​for example, when you have nothing (or little) better to do. Thinking about opportunity cost can make arriving an hour early seem sensible, even if it increases the total amount of time you wait. 

By arriving before opening, you get your waiting out of the way when other activities are not yet open. Sure, you might give up an hour of sleep or the chance to have a leisurely breakfast, but assuming you value those things less than your other planned activities, queuing up early is probably a good choice. If you’re first in line at the museum, you can see the chapel and still enjoy a packed day visiting other sites in Rome.

Estimated time of arrival

Everyone who waits in a line for the Sistine Chapel eventually gets to see the ceiling. The strategy for first-come, first-served lines gets more complex when you must stand in line for a limited resource that might run out. In cases like this, you must weigh the opportunity cost associated with waiting in line longer against what you expect to gain by getting in line earlier. But assessing what you expect to gain isn’t easy.

When Star Wars: Episode I – ​The Phantom Menace, the first new movie in the franchise in 16 years, hit theaters in May 1999, my best friend Dean and I were determined to see it on the very first day. Our tickets, procured in a first-come, first-served race, were for the 5:00 a.m. show. We had opted for that absurdly early hour not just because it was easier to get tickets for a time when most reasonable people were still asleep but also because it allowed us to convince our parents to let us see the movie on a weekday. Even with its over-two-hour run time, we could see it and still not be late for school.

In those days, you didn’t get assigned to or get to choose your seats when you bought your tickets. Instead, you lined up outside the theater, and you were let in once the doors opened for your showtime. What this meant, of course, was that the earlier you arrived, the better your chances of snagging your desired seat. 

For me and Dean, however, the opportunity cost of arriving early was high, since each hour spent waiting in line for a 5:00 a.m. movie was an hour of lost sleep. But the potential gain was high too: We wanted to see the movie from the perfect seats. So we got up extra early (as early as I could remember waking up for anything). As it turned out, it was not early enough. We arrived at the theater only to find that a long line had already formed for our showtime. We ended up toward the back of that line and were relegated to the front left of the theater in some of the least desirable seats.

Our mistake had been underestimating the intensity of the other fans who had bought tickets for the 5:00 a.m. showing. These fans were so eager to see the movie from good seats that many of them had shown up insanely early. Given the enthusiasm around the movie’s release, we should have known better. As disappointed as we were, we learned an important lesson about the importance of estimating the demand you will face in a first-come, first-served line. Had we known how aggressive other people would be, we might have woken up even earlier (or, more likely, just stayed up all night).

While it might be difficult to guess when others will join a line, it is not impossible. In the case of movie tickets, it’s easy to find out whether it is opening weekend, whether the movie has sold out in the time since you bought your ticket, and whether other showings have sold out. The more excited people are for the movie, the more likely people will want to get there early to snag the best seats.

First-come, first-served lines can achieve allocative efficiency, and although some seats are better than others, most people have an equal opportunity to wake up at 2:00 a.m. to queue up for seats, so the policy scores well on equity. But participating is far from easy for customers (think of all the hours of lost sleep for just our single 5:00 a.m. showtime), which is why some markets have introduced rules to make waiting in line less costly.

“I am to wait, though waiting so be hell”

New York is known for its excellent theater productions, and Shakespeare in the Park is no exception. The performances, which have fixed runs of just a month or so each, often receive rave reviews. And the tickets are free, which means demand regularly outstrips supply.

There are a few ways to secure tickets for Shakespeare in the Park that combine a mix of allocation methods. But the traditional way is with a first-come, first-served line. Tickets are released at noon on the day of the performance, and a line sometimes begins to form outside the park even before it opens, at six a.m. But thanks to a clever design feature of the market rules for tickets, on a typical day, most people don’t line up until around eight or nine in the morning.

That feature is that being closer to the front of the line does not give you access to better seats. Seats are randomly assigned, which means that you have an equal chance of getting primo seats whether you are at the head of the line at six a.m. or you show up at ten a.m. and end up being the last person to get tickets before they run out. So, while you need to arrive early enough to get one of the theater’s 1,800 seats, you have no extra incentive to show up earlier.

These rules may reduce allocative efficiency. If I really want a certain seat, I cannot increase my chances of getting it by waking up earlier. I have just as much chance to get it as you, even if you are close to agnostic about where you sit. But the increase in ease for market participants is likely worth it.

Shakespeare in the Park has one other innovation that makes waiting for tickets less costly, at least for those in their golden years. Those 65 and older get to enjoy a special line where they can sit on park benches in the shade as they wait for the box office to open. They also get access to seats in the theater that do not require taking stairs, which includes the desirable first ten rows.

At first blush, this might seem unfair or inequitable; however, if a market designer knows a certain group of participants is disadvantaged relative to another, ​it might be more equitable to improve things for the disadvantaged groups so that their costs of participating in the market, their outcomes, or both are more equal. 

Achieving equity this way is a major benefit of the line rules for Shakespeare in the Park.