Maximizing Profit and the Average Cost Curve

Being able to predict your company’s profit is a very useful tool. In this video, we introduce the third concept you need to maximize profit — average cost. When looked at in conjunction with the marginal revenue and marginal cost, the average cost curve will show you how to accurately predict how much profit you can make!
The usefulness of these tools does not stop there. Sometimes, you can’t make a profit. You’ll have to take a loss. These tools can also show you how to minimize losses, and make decisions on whether a company should enter or exit an industry.
We also define terms such as zero profits and sunk costs in this video.
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- [Alex] Now that we know
how to find the profit

maximization point,
we're going to show

the amount of profit on the diagram
using the average cost curve.

So as I said in the last lecture,

average cost is the cost
per unit of output.

That is, average cost is
total cost divided by Q.

Now remember also
that total cost can be broken down

into fixed costs plus
variable costs.

So we can also write average cost
in a slightly longer format.

Average cost is equal
to fixed cost divided by Q

plus the variable cost divided
by Q, the units of output.

That's a little bit useful
because we're able to see,

get some intuition, for the shape
of a typical average cost curve.

Notice that the fixed costs
don't change with Q.

That's why they're fixed.

So when Q is small -- this number,

suppose fixed cost is 100,

and Q is small -- then this number
is going to be big

like 100 divided by 1.

As Q gets larger, however,
this number --

fixed cost divided by Q --
is going to get smaller,

So when Q is 10, this number
100 divided by 10 becomes 10.

So it goes from 100,
and it goes down, down, down, down,

get's lower and lower and lower
all the time as you divide

by a bigger quantity.

On the other hand, the variable
costs increase with quantity.

Moreover, what we saw
with the marginal cost curve

is that at some point,
your variable costs are going

to increase faster than quantity.

So what's going to happen is
that this number at some point --

variable cost divided by quantity --
is going to get bigger

and bigger and bigger.

So you have two things, one force
is driving average cost down.

That's going to be particularly
strong at the beginning.

Eventually, however,
the second force here is going

to drive average cost up.

So that's going to be our typical
shape of an average cost curve --

falling, reaches a minimum,
and then rising.

So let's draw it like that.

Okay, here's our typical
marginal cost curve,

and here is our marginal
revenue curve, equal to price.

We know that the profit maximizing
point is where marginal revenue

is equal to marginal cost.

Here is our average cost curve
and notice it has the shape

which I described --
it starts off high, it falls,

reaches a minimum,
and then goes right back up again.

Couple of other points to notice
is that the minimum point,

the marginal cost curve goes
through the minimum point

of the average cost curve.

Now that's just a mathematical fact,
but let me give you some intuition.

Instead of cost I want
to talk about average grade

and marginal grade.

So suppose that your
average grade is 80%.

You're doing really pretty good,
but then on your next test

you only get 60% -- lower.

What is that going to do
to your average?

Well, it's going to drive
your average down.

Indeed whenever your marginal
is below your average,

the average must be falling.

On the other hand, suppose
that you're getting 80%,

and on your next test you get 90%.

Great, but what does
that do to your average?

It drives your average up.

Indeed whenever your marginal
is above the average,

the average must be rising.

Now suppose what happens
when you're getting let's say 80%,

and on your next test,
you also get 80%.

Well then your marginal is equal
to your average grade,

and your average grade is flat --
it doesn't change, it's flat.

But what is true for average
and marginal grades is also true

for average cost and marginal cost.

Whenever the marginal cost is
below the average,

the average is falling.

Whenever the marginal cost is
above the average,

the average is rising.

And where marginal is
just equal to average,

the average is flat.

In other words, we are
at the minimum point

of the average cost curve.

Okay, now I said we could use
the average cost curve

to figure out profit --
show profit on the diagram.

We can do that with just
a little bit of rearranging.

Remember that profit is equal
to total revenue minus total cost

and total revenue is
price times quantity -- P times Q.

We also know
that average cost is equal

to total cost divided by quantity.

Let's just rearrange that
to tell us that total cost is equal

to average cost times quantity.

So just take this one
and multiply both sides by Q.

Let's now make these substitutions
into our profit equation.

If we do that, then profit is equal
to total revenue --

price times quantity --
minus total cost --

average cost times quantity.

Now let's take Q out
of both parts of this equation,

and we find that profit
can also be written as price

minus average cost,
all of that times quantity.

That's nice because we can find

all of these elements
on our diagram.

Here's the price.

Here's the average cost
at the profit maximizing quantity.

Let's just show that.
There's the price.

There's the average cost
at the profit maximizing quantity.

So profit at the profit
maximizing quantity is

this green area right here --

price minus average cost
times quantity.

So now we have a nice way
of showing in a diagram

exactly how much profit is.

Let's use this tool some more.

Here's another example
of the average cost curve in action.

Remember, I said that profit
maximization doesn't necessarily

mean the firm is making
a positive profit.

Sometimes the best you can do
is to minimize your losses.

You may have to take a loss.

For example, suppose
that the price is below $17.

That is, here's the market price,
which is equal to the firm's

marginal revenue curve.

How does the firm profit maximize?

It chooses the quantity
where marginal revenue is

equal to marginal cost.

In that case, this quantity is one.

Now what's the profit
for the firm?

Well, as usual we measure
profit as price minus

average cost times quantity.

But notice that price is
below the average cost

at the profit maximizing
quantity of one.

Since price is below average cost,
this is a loss.

It's a negative quantity.

It is a loss. In fact, notice
that the breakeven price is $17,

which is the minimum
of the average cost curve.

In order to make a profit,
the firm at least has to meet

the minimum of its
average cost curve.

So at any price below $17,
we'll be profit maximizing

at a point where price is equal
to marginal cost,

and notice that all of these
prices are below average cost.

So all of this area down here,

even the profit maximizing
quantity, will mean a loss.

On the other hand, once we get
above $17, above the minimum

of the average cost curve, then we
can price equal to marginal cost.

We can chose the quantities such
the price is equal to marginal cost.

That price will be above average
cost, so we'll be taking a profit.

Therefore, $17, the minimum
of the average cost curve,

is the breakeven point.

If the price is less
than the minimum

of the average cost curve,
we're going to be taking a loss.

If the price is bigger
than the minimum

of the average cost curve,
then we can make a profit.

So when should a firm enter
or exit an industry?

In the long run, the firms will
enter when price

is above average cost.

If price is somewhere
above the average cost curve

then the firm can make
a profit by entering

and that's what firms want to do.

They want to find profit,
so they will want to enter

wherever a profit is possible.

Firms will exit the industry
when the price is below

the average cost curve.

Then they're going
to be taking a loss,

and they're going to want to exit.

Finally, when the price is
equal to the minimum

of the average cost --
it's just equal to the bottom

of the average cost curve,
profits are zero,

and there's no incentive

to either exit
or enter the industry.

Now you might ask,
why would firms remain

in an industry if profits are zero?

Zero profits, this is just
a matter of terminology,

means that at the market price
the firm is covering all

of its costs, including enough
to pay labor and capital,

their ordinary opportunity cost.

So zero profits means
everyone is being paid enough

to make them satisfied.

Zero profits, in other words,
is what normal people mean

by normal profits.

So when an economist
says zero profits

just substitute normal profits.

One more point
about entry and exit.

It doesn't always make sense
to exit an industry immediately

when price falls
below average cost.

Or to enter immediately
when price is above average cost.

Why not? Well, there are
also entry and exit costs.

For example, suppose
that that the price of oil is

currently above the average
cost of pumping oil,

if you've already got a well.
Should you enter the industry?

Well, maybe not necessarily.

Because entry requires you
to drill an oil well,

and drilling an oil well is
a sunk cost -- literally in this case.

A sunk cost is a cost that once
incurred can never be recovered.

So if you enter the industry
and drill the oil well,

you don't get that money back
when you later exit the industry.

What this means is you
don't want to enter

unless you expect
the price of oil to stay

above the minimum
of the average cost curve

long enough so that you can
also recover your entry costs.

So just because the price goes
above the average cost a little bit,

you don't immediately
want to jump into that industry.

You have to expect that
that price is going to stay

above average cost
long enough for you

to recover your entry costs.

For the same reasons,
if there are exit costs,

for example, if you have
to shutter up the well

or fill the well with cement
when you exit the industry

as you do in the United States,
then when price falls

below average cost,
it may be best to weather

the storm at least
for sometime before you exit.

Only if you expect the price
of oil to stay below your minimum

of average cost
for an extended period of time

will you want to exit the industry.

After all, if the price of oil falls
below the average cost

just for a little bit,
and then it goes back up,

the lifetime profits can
still be possible.

So, entry and exit could be
quite complicated

because you've got
to be thinking

about the lifetime profits,
not just your immediate profits.

However, the bottom line
is pretty simple.

Firms seek profits
and they want to avoid losses.

As a result, firms will enter
industries when the price is above

the average cost
and they can make a profit,

and they will exit when the price
is below the average cost.

Thanks.

- [Narrator] If you want to test
yourself, click, "Practice Questions."

Or, if you're ready to move on,
just click, "Next Video."

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