Price Ceilings: Lines and Search Costs

In this video, we're going to take a look at another effect of price ceilings: wasteful lines and other search costs. Let's get started.

It's important to understand that price controls do not eliminate competition. Competition for scarce goods is an ever present force under all forms of social organization. What price controls do is they change the form that competition takes. So in a market, demanders compete by pushing prices up. Suppliers compete by pushing prices down. When we have price controls, that shifting of prices is no longer possible. But competition remains -- it just takes other forms. Here's an example of musical chairs. The quantity demanded exceeds the quantity supplied. There's a shortage. But there's still lots of competition, lots of scrambling to get hold of those goods which are in short supply.

So let's take a closer look at some of the forms that competition takes when we have price controls and shortages. So suppose there's a price control on gasoline and oil, making it illegal to compete for these goods by pushing the price up. Nevertheless, there are other ways of competing. Some buyers, for example, might try bribing the station owners. This is not necessarily the first thing which would happen in the United States, but in other places and countries this is extremely common.

Having a cousin who works in the factory which is producing the good which is in shortage is extremely important. Using one's political connections, being part of the political elite is extremely important for obtaining goods, which are in shortage. Even in the United States, remember that firms also need oil and gasoline in order to operate. And in the 1970s when there was a shortage of oil, firms appealed to the Department of Energy, they lobbied their Congressman and their Senator to obtain an allocation of oil for their firm.

For consumers, another way to obtain the good is to be willing to wait in line. Now time waiting in line is also a cost. So let's ask, "How long will the line get?" We can use our model to understand willingness to wait in line and how long the lines will get. Let's take a look. So here's our supply and demand diagram of the shortage. Remember that at the controlled price we read the quantity demanded off the demand curve, Qd, and at the controlled price we read the quantity supplied off the supply curve, Qs. So Qs is the actual amount of gasoline supplied given the controlled price of $1.

Now, here is the key question: How much are buyers willing to pay for a gallon of gasoline, when Qs is the amount which is being supplied? How much are buyers willing to pay? What is the most they are willing to pay for a gallon of gasoline? Well remember, we can read that off the demand curve -- that's what the demand curve tells us. So at the controlled price, when the quantity supplied is Qs, buyers are willing to pay $3 per gallon of gasoline. They're only allowed to pay in money $1. So, if a buyer were to obtain a gallon of gasoline at a controlled price of $1, that's actually worth to them $3.

That explains why people are willing to wait in line for a long time in order to get gasoline, because the shortage has reduced the quantity supplied. It's raised the willingness to pay for gasoline, but it hasn't raised the price of gasoline. Therefore people are willing to wait in line. And, in fact, the line will grow until on the margin the time price plus the money price will be equal to the willingness to pay.

So the line will grow until the money price, which is $1/gallon, plus the time price, the time wasted in line, which will grow up until it's $2/gallon, until the total price equals the willingness to pay. Why is that? Well, imagine that that were not the case. Imagine that you could obtain a gallon of gasoline which is worth $3 for you. And you only had to pay a dollar plus 50 cents in waiting time. Well that would be a great deal. So people will be willing to wait in line so long as the total price, the money price plus the time price, is less than the willingness to pay. This means that the line will continue to grow until the total price is equal to the willingness to pay.

So, if we now take the time price, which is the difference between the willingness to pay and the controlled price, times the quantity -- that gives us the total value of wasted time. So, another effect of price controls -- it creates long lines in order to compete to get the good instead of bidding the price up, they bid in terms of being willing to wait in line. And those lines are wasteful, creates a lot of wasted time. Let's take a look with a numerical example.

Okay, here's a simple numerical example to bring this home. Suppose that buyers value their time at $10/hour, and that the average fuel tank holds 20 gallons. Now imagine that a buyer arrives early at the gasoline station and they wait one hour. The total cost of the gasoline is then $20, $1/gallon times 20 gallons in money cost, plus $10 in time cost. They waited an hour and they value their time at $10/hour. So the total cost of the gasoline is then $30. It took $30 worth of time and money in order to get 20 gallons. So the implied cost per gallon is $1.50/gallon.

However, remember that given the quantity supplied, given the shortage, the value of gasoline is $3/gallon. So this buyer managed to obtain something which is worth $3/gallon for only $1.50 per gallon. That's a good deal so other buyers are going to bid up the price by arriving earlier and earlier. And this is going to push up the time cost. The money cost is fixed because of the price control, but the time cost can still increase. In fact, the line will lengthen until the total cost of obtaining 20 gallons of gasoline equals $60 or $3/gallon. In other words, the buyers will end up spending $20 in money cost plus $40 in time cost, or four hours of waiting.

So we're able to calculate approximately how long the line will get. It will get four hours worth of time. So this again illustrates that competition does not go away when we have price controls. Instead, competition takes different forms, and one of those forms is -- instead of bidding up the money price, the time price is bid up and we get long and wasteful lines. So what we've just seen is that in a free market, buyers compete to obtain goods by bidding up money prices. And when we have price controls, one way that buyers compete to obtain goods is by bidding up time prices, by being willing to wait in line.

So what's a better form of competition? Bidding or paying in money or paying in time? Does it make a difference? After all, some people have got more money, some people have got more time, is it just a matter of preference? No. It is much better to have an economic system where competition takes the form of bidding in money than it takes the form of bidding in time. Why? Paying in time is much more wasteful.

When you bid in terms of money, the money goes to the station owner. The money does not disappear. That purchasing power is transferred from the consumer to the producer. On the other hand, when buyers bid in terms of time, when they wait in line, that waiting in line is just lost. It's not transferred to the producer. When you wait in line for four hours to obtain gasoline, the seller of gasoline doesn't get to add four hours to his lifespan. So that waiting in line is just a total loss. When you pay in money, the purchasing power is transferred to the station owner. When you pay in terms of time, the value of that time is simply lost. It benefits no one.

Okay, quick reminder of where we are. Price ceilings have five important effects. We've looked at shortages and reductions in product quantity. We've just completed wasteful lines and other search costs. Up next, a loss in gains from trade, and then a misallocation of resources.