Price Ceilings: Misallocation of Resources

Suppose there is a mild winter on the West Coast and a harsh winter on the East Coast. As a result of the weather, people on East Coast will demand more home heating oil, bidding up the price. Under the price system, entrepreneurs will be incentivized to take oil from where it has lower value on West Coast to where it has higher value on the East Coast. But when price controls are in place, even though the demand is still there from the East Coast, there is no signal of a higher price, eliminating the incentive for entrepreneurs to transport oil from west to east. In fact, this happened in the 1970s, resulting in oil going to lower valued uses on the West Coast while many people on the East Coast didn’t have enough oil to heat their homes. In this video, we’ll look at a diagram to visualize this misallocation of resources.

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- 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. 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. 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. 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. 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
1970's. 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 a air force one, if
you recall the example from chapter three.

Down here, are the lowered-valued uses of
the good. This is the rubber ducky, was

down here. Now, at the controlled price of
one dollar, 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. Good 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 one dollar. 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 lost

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, four dollars of value
is created, and consumer surplus is three

dollars. The four dollar of value created
minus the one dollar 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 one dollar. This is the buyer with the

lowest-valued use, but this buyer's still
willing to pay the controlled price. So

that's one dollar 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 four dollars and one
dollar with a value between four dollars

and one dollar. 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 four dollars, plus
one half the minimum possible value which

is one dollar. 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 four dollars and one
dollars, 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?

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