Price Ceilings: Misallocation of Resources

Welcome back. Another cost of price ceilings is that they misallocate resources. This is actually a point not covered in most textbooks, but it's very important. And it's going to be important not just to understand price controls, but also to give us real insight and deeper understanding into how the price system works. Let's get started.

Let's begin with an intuitive, but a real and important example. Suppose that over here on the west coast of the United States, we're having a very mild winter. Temperatures are high. The sun is shining. No problems. Let's suppose however, that on the east coast the winter is really bad. It's cold. There's a lot of snow and so forth. As a result of the weather, the people on the east coast are going to be demanding a lot of home heating oil. So the demand for heating oil goes up, and because of that increase in demand we get a higher price of heating oil.

Now, what are entrepreneurs going to do? Seeing this signal of a higher price, they're going to be incentivized to take oil from where it has low value, over here on the west coast, and bring it to where the oil has high value on the east coast. So oil will flow from the west to the east. It will flow from areas where it has low value. In response to the signal of the higher price, it will flow to areas where it has higher value. Now, let us suppose, that as in the 1970s, we now have a price control on oil. So it is illegal for the price of oil to increase. Well, as before, with the price control, we're going to get higher demand but no higher price. There will not be that signal of a higher price, and because there isn't a signal there won't be an incentive to bring oil from where it has low value to where it has high value. So the oil will no longer flow.

As a result, people over here on the west coast, they're going to be using that oil for low-value items, things like heating their swimming pool. At the same time, people on the east coast may not have enough oil to heat their homes. In fact, this is exactly what happened in the 1970s. There was a misallocation of oil because of the price controls. Oil was used in some low uses, some low-value uses such as heating swimming pools, at the same time when there wasn't enough oil for the high-valued uses. That's what we mean by misallocation of resources. Let's take a look at how we can show this in a diagram.

Here's our standard diagram of the shortage. Let's remember from chapter three that we could read the demand curve in the following way. At the top of the demand curve are the highest-valued uses for the good. This is Air Force One, if you recall the example from chapter three. Down here, are the lower-valued uses of the good. This is the rubber ducky, was down here. Now, at the controlled price of $1, Qs units are going to be supplied. Given that Qs units are going to be supplied, the most valuable uses for those units are these uses up here. These are the high-valued uses. In a free market, these uses or users would outbid the other uses. Goods would flow from the low-valued uses to the high-valued uses, and these would end up being the uses which would be supplied in a free market.

Here's the key point -- the price control prevents the highest-valued uses from outbidding the lower-valued uses. As a result, some oil will flow to lower-valued uses. In other words, as a result of the price control, some rubber duckies will end up being produced even when we don't have enough oil to fly jet aircraft. These uses or users will not be able to outbid these guys down here because of the price control, because the price is limited to $1. By the way, these guys have the really low-valued uses, but they're not even willing to pay the controlled price. They're not even being willing to pay the dollar, so they won't get any oil at all, which is a good thing, because they have very low-valued uses. On the other hand, the high-valued uses, they're not going to be able to outbid these guys, so some of the oil is going to be misallocated. It's going to go to low-valued uses even when there's not enough to satisfy all of the highest-valued uses.

The most important point is the one I just gave -- that with price controls prices no longer serve their signaling and incentive function, and as the result, we get the misallocation of resources. Resources no longer flow from their high-valued uses to their low-valued uses, and as a result of that, we get less use out of our resources. We get less value from our resources. I want to show also, that you can use the diagram to quantify this a little bit, to show this on a diagram.

Let's ignore the wasteful time in search costs from price control, and what we want to do is to compare the maximum consumer surplus given Qs, given Qs is supplied, with a loss under, say, random allocation. So suppose that any use which is willing to pay the controlled price is equally likely to be allocated a unit of the good, in this case, a unit of the gasoline. How much will that reduce value? How much will that reduce total consumer surplus? Let's take a look at how to do this.

Let's just remind ourselves that if the gasoline goes to the highest-valued uses, that is there are Qs units, and if these Qs units were to flow to the highest-valued uses, then consumer surplus would be given by the area underneath the demand curve above the price. So it would be given by this green area. This is the maximum consumer surplus available from Qs units. This is the way we would get the most out of these Qs units. We would get the most value by allocating it to the highest-valued units, and then the total consumer surplus created would be this amount right here.

Let's now compare with random allocation. Because the good is not necessarily allocated to the highest valued uses with a price control, consumer surplus is going to be less than the amount which we just showed. How much less? Let's do some calculations, and to do that to build our intuition, we're going to consider how one gallon of gasoline might be allocated under the best and worst conditions for random allocation. So we're going to take one gallon of gasoline, and we're going to allocate it randomly. Suppose we were really lucky. What's the best case for random allocation? Suppose we're really unlucky. What's the worst case for random allocation? Let's take a look.

The best case scenario for random allocation, is that this one gallon of gasoline goes to the buyer with the highest-valued use. Which buyer is that? It's this buyer up here. In that case, $4 of value is created, and consumer surplus is $3. The $4 of value created minus the $1 for the price. What's the worst case? The worst case scenario, is that the buyer with the lowest-valued uses randomly ends up with the good, with the gallon of gasoline. In that case, the value created is $1. This is the buyer with the lowest-valued use, but this buyer's still willing to pay the controlled price. So that's $1 of value created or consumer surplus of zero. It costs them a dollar. They get something which is worth a dollar to them. So the consumer surplus is zero.

Those are the best and worst cases for randomly allocating one gallon of gasoline. Using that intuition, let's look at a scenario where a gallon of gasoline is randomly allocated with equal probability to any user who is willing to pay the controlled price. That is the gallon of gasoline is randomly allocated to any user between $4 and $1, with a value between $4 and $1. In this case, because it's an equal probability, a uniformed distribution, the average value, turns out we can calculate it easily, it's just one half times the maximum $4, plus one half times the minimum possible value, which is $1. The average use to which gasoline will be put will be $2.50. Let's in fact put that on the diagram. When the good is randomly allocated to any user between a value of $4 and $1, the average use will have a value of $2.50. That means that the consumer surplus is this green area right here -- the difference between the average value and the controlled price.

Here's the key point. Remember, earlier we showed that the maximum value would have been the area underneath the highest-valued users, underneath the demand curve for the highest-valued users, up to the quantity supplied. The maximum value, the maximum consumer surplus from Qs units, if all those Qs units went to the highest-valued users, is the red plus the green. When the gasoline is instead allocated randomly, sometimes it goes to a high-valued user, but sometimes it goes to a low-valued user. Then on average, the value of that gasoline is less. We get less value out of that gasoline when it is allocated randomly than when it is allocated by the price system. As a result, consumer surplus is considerably lower under random allocation than it is when it's allocated by the price system, which maximizes the consumer surplus.

That's just a diagrammatic way of illustrating our first example of what happens when we don't have the price system. Oil no longer flows from its low-valued uses to its high-valued uses, so we get less value from the same resources. The resources become worth less than they were before, because they're no longer allocated to the highest-valued uses.

We've now covered all the five important effects of price controls: shortages, reductions in product quality, wasteful lines and other search costs, a loss in gains from trade, and a misallocation of resources. Next, we're going to apply all of these ideas to rent control. Since we understand the ideas, we should move through that fairly quickly. And then we're going to look at price floors. What happens when the government says you cannot sell a good for less than a certain amount?