Rationing By Racing

One of the critical insights of price theory is that there is always another margin on which people can optimize. This point is important. A common view of non-economists is that markets aren’t always the appropriate means of allocating resources. Economists, however, are trained to ask the question: compared to what? A price theorist recognizes that when a money price is precluded from allocating resources, some other allocation mechanism will emerge. People will optimize on another margin.

As I have written about previously, Yoram Barzel developed a theory of rationing by waiting. The basic idea is that sometimes price is precluded from being used to allocate resources. One alternative to using prices is to allocate through a first-come, first-served mechanism. Under these conditions, people might show up and form a line in order to obtain the good. A natural question that we might ask is whether price theory can tell us anything about the resulting allocation.

The answer is yes. People have a willingness to pay for a good. The fact that a money price is precluded from allocating the good doesn’t change this. If the good is allocated on a first-come, first-served basis, then the willingness to pay can be measured in terms of time. If a person is willing to pay $50 for the good and their wage is $25 per hour, then they should be willing to wait in line for two hours. The length of the line and thus how long a given person will have to wait will be determined by the willingness to pay (measured in terms of time) of the marginal buyer.

Things can get complicated here when it comes to the distribution of the final allocation since people generally have different costs associated with their time. The distribution of the good might change depending on the mechanism. For example, we might get a different allocation of the good when it is rationed by time than when money prices are posted. For example, someone with a high willingness to pay, but also a high opportunity cost of time might be willing to wait less time than someone who had a lower willingness to pay in terms of money prices but a low opportunity cost of time.

Secondary markets can provide an additional complication. Those with a high willingness to pay in terms of money, but with a high opportunity cost of their ...