Evanomics

Queuing conundrum

• Evan Davis | Notes on Real Life |
• 23 Feb 07, 09:15 AM

Here’s an old economist conundrum about queues.

Suppose there is a water fountain in a park. It’s a hot day and lots of people want to drink from the fountain. Being awfully British and civilised, they form an orderly queue at the fountain.

Now, if the number of thirsty people strolling past the fountain is large enough, the rate at which people join the queue will exceed the rate at which people satisfy their thirst and leave the queue. So the queue will get longer and longer.

But at some point, thirsty people will reason to themselves that the displeasure of waiting in the queue is not worth the pleasure of the drink at the end. They’ll avoid the wait, and the queue will grow no longer.

So far so good. That’s how life works in many ways.

But this simple account has a devastating implication.

If there are people who are not joining the queue because it’s not worth it, then the people who do join the queue are probably barely getting any positive benefit out of their drinking fountain experience at all. They enjoy the drink, but for them, it is only just worth the wait. It’s a close run thing between bothering to drink or not.

In fact, you might as well not have a drinking fountain on the hot day, as no-one can enjoy it without paying a time penalty that more or less wipes out the benefit.

I hope I’ve explained this properly. It’s a simplified account, and it relies on all the people in the park having a similar taste for drinking and not queuing.

But it shows that when queuing does the rationing, it does a really bad job.

In the park, if you could get a warden to ban people from queuing, and who instead insisted that only random people could drink, (people whose surname begins with A to K for example), the fountain would give more benefit, (although that benefit would be distributed a little unfairly).

There is another alternative that’s a little more equitable. If it’s practical, you can charge people to use the fountain.

Now, those who do pay, have the benefit of drinking without queuing, but they have the cost of paying. So on balance they are better off using the fountain, but probably only just better off. As far as they’re concerned, we haven’t improved things much over the queuing situation: we’ve just changed the pain of queuing by the pain in the purse.

The difference is though, that the money they’ve handed over can be of benefit to someone else, or the population at large. There is an upside to the drinkers’ displeasure, unlike in the case where the queue does the rationing.

Or to put it another way: when you queue – I get no benefit from your pain. When you pay, I probably do.

Now that is a pretty good argument against the use of rationing by queues.

It may not be a good argument for road pricing, but it does explain why economists tend to think of the price mechanism as a better method of rationing things than congestion.

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