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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- [Alex] 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?

- [Narrator] If you want
to test yourself,

click "Practice Questions."

Or, if you're ready to move on,
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