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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- 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 a hundred 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 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, uh, 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, uh, 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.
So, 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 it's 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. So

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.

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