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- Now that we know how to find the profit
maximization point, we're going to show

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

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- So as I said in the last lecture, average
cost is the cost per unit of output. That

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is, average cost is total cost divided by
Q. Now remember also that total cost can

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be broken down into fixed costs plus
variable costs. So we can also write

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average cost in a
slightly longer format.

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Average cost is equal to
fixed cost divided by Q plus the

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variable cost divided by Q - the units of
output. That's a little bit useful because

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we're able to see, get some intuition, for
the shape of a typical average cost curve.

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Notice that the fixed costs don't change
with Q. That's why they're fixed. So when Q

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is small, this number, suppose fixed cost
is a hundred and Q is small, then this

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number is going to be big like 100 divided
by 1. As Q gets larger, however, this number -

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fixed cost divided Q - is going to get
smaller, so when Q is 10 this number 100

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divided by 10 becomes 10. So it goes from
100 and it goes down, down, down, down,

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get's lower and lower and lower all the
time as you divide by a bigger

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

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what we saw with the marginal cost curve
is that at some point your variable costs

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are going to increase faster than
quantity. So what's going to happen is

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that this number at some point - variable
cost divided by quantity - is going to get

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bigger and bigger and bigger. So you have
two things one force is driving average

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

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Eventually however, the second force here
is going to drive average cost, uh, up. So

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that's going to be our typical shape of an
average cost curve - falling reaches a

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minimum and then rising. So let's draw it
like that. Okay here's our typical

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marginal cost curve and here is our
marginal revenue curve equal to price. We

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know that the profit maximizing point is
where marginal revenue is equal to

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marginal cost. Here is our average cost
curve and notice it has the shape, which I

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described, it starts off high, it falls,
reaches a minimum, and then goes right back

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up again. Couple of other points to notice
is that the minimum point, the marginal

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cost curve goes through the minimum point
of the average cost curve. Now that's just

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a mathematical fact, but let me give you
some intuition. Instead of cost I want to

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talk about average grade and marginal
grade. So suppose that your average grade

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is 80%. You're doing really pretty good.
But then on your next test you only get

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60% - lower. What is that going to do to
your average? Well, it's going to drive

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your average down. Indeed whenever your
marginal is below your average, the average

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must be falling. On the other hand,
suppose that you're getting, uh, 80% and on

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your next test you get 90%. Great, but what
does that do to your average? It drives your

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average up. Indeed whenever your marginal
is above the average, the average must be

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rising. Now suppose what happens when
you're getting let's say 80%, and on your

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next test you also get 80%. Well then your
marginal is equal to your average grade

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and your average grade is flat - it doesn't
change, it's flat. But what is true for

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average and marginal grades is also true
for average cost and marginal cost.

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Whenever the marginal cost is below the
average, the average is falling. Whenever

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the marginal cost is above the average, the
average is rising. And where marginal is

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just equal to average, the average is flat.
In other words we are at the minimum point

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

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to figure out profit - show profit on the
diagram. We can do that with just a little

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bit of rearranging. Remember that profit
is equal to total revenue minus total cost

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and total revenue is price times quantity -
P times Q. We also know that average cost

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is equal to total cost divided by
quantity. Let's just rearrange that to

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tell us that total cost is equal to
average cost times quantity. So just take

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this one and multiply both sides by Q.
So, let's now make these substitutions into

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our profit equation. If we do that, then
profit is equal to total revenue - price

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times quantity - minus total cost - average
cost times quantity. Now let's take Q out

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of both parts of this equation and we find
that profit can also be written as price

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minus average cost, all of that times
quantity. That's nice because we can find

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all of these elements on our diagram.
Here's the price. Here's the average cost

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at the profit maximizing quantity. Let's
just show that. There's the price. There's

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the average cost at the profit maximizing
quantity. So profit at the profit

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maximizing quantity is this green area
right here. Price minus average cost times

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quantity. So now we have a nice way of
showing in a diagram exactly how much

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profit is. Let's use this tool some more.
Here's another example of the average cost

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curve in action. Remember I said that
profit maximization doesn't necessarily

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mean the firm is making a positive profit.
Sometimes the best you can do is to

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minimize your losses. You may have to take
a loss. For example, suppose that the

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price is below $17. That is, here's the market
price, which is equal to the firm's marginal

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revenue curve. How does the firm profit
maximize? It chooses the quantity where

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marginal revenue is equal to marginal cost.
In that case, this quantity is one. Now

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what's the profit for the firm? Well, as
usual we measure profit as price minus

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average cost times quantity. But notice
that price is below the average cost at

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the profit maximizing quantity of one.
Since price is below average cost, this is

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a loss. It's a negative quantity. It is a
loss. In fact, notice that the breakeven

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price is $17, which is the minimum of the
average cost curve. In order to make a

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profit, the firm at least has to meet the
minimum of it's average cost curve. So at

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any price below $17 we'll be profit
maximizing at a point where price is equal

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to marginal cost, and notice that all of
these prices are below average cost. So

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all of this area down here, even the
profit maximizing quantity, will mean a

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loss. On the other hand, once we get above
$17, above the minimum of the average cost

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curve, then we can price equal to marginal
cost. We can chose the quantities such the

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price is equal to marginal cost. That price
will be above average cost so we'll be

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taking a profit. Therefore, $17, the minimum
of the average cost curve, is the

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breakeven point.
If the price is less than the minimum of

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the average cost curve, we're going to be
taking a loss. If the price is bigger than

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the minimum of the average cost curve, then
we can make a profit. So when should a

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firm enter or exit an industry? In the
long run, the firms will enter when price

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is above average cost. If price is
somewhere above the average cost curve

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then the firm can make a profit by
entering and that's what firms want to do.

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They want to find profit, so they will
want to enter wherever a profit is

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possible. Firms will exit the industry
when the price is below the average cost

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curve. Then they're going to be taking a
loss and they're going to want to exit. So

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finally, when the price is equal to the
minimum of the average cost - it's just

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equal to the bottom of the average cost
curve, profits are zero and there's no

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incentive to either exit or enter the
industry. Now you might ask, why would

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firms remain in an industry if profits are
zero? Zero profits, this is just a matter

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of terminology, means that at the market
price the firm is covering all of its

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costs including enough to pay labor and
capital, their ordinary opportunity cost.

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So zero profits means everyone
is being paid, enough to make

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them satisfied. Zero profits, in other
words, is what normal people mean by normal

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profits. So when an economist says zero
profits just substitute normal profits.

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One more point about entry and exit. It
doesn't always make sense to exit an

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industry immediately when price falls
below average cost. Or to enter immediately

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when price is above average cost. Why not?
Well, there are also entry and exit costs.

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For example, suppose that that the price
of oil is currently above the average cost

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of pumping oil, if you've already got a
well. Should you enter the industry? Well,

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maybe not necessarily. Because entry
requires you to drill an oil well, and

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

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A sunk cost is a cost that once incurred
can never be recovered. So if you enter

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the industry and drill the oil well, you
don't get that money back when you later

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exit the industry. What this means is you
don't want to enter unless you expect the

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price of oil to stay above the minimum of
the average cost curve long enough so

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that you can also recover your entry
costs. So just because the price goes

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above the average cost a little bit, you
don't immediately want to jump into that

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industry. You have to expect that that
price is going to stay above average cost

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long enough for you to recover your entry
costs. For the same reasons, if there are

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exit costs, for example, if you have to
shutter up the well or fill the well with

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cement when you exit the industry as you
do in the United States, then when price

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falls below average cost, it may be best to
weather the storm at least for sometime

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

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average cost for an extended period of
time will you want to exit the industry.

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After all, if the price of oil falls below
the average cost just for a little bit, and

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then it goes back up, the lifetime
profits can still be possible. So, entry

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and exit could be quite complicated
because you've got to be thinking about

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the lifetime profits, not just your
immediate profits. However, the bottom

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line is pretty simple. Firms seek profits
and they want to avoid losses. As a

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result, firms will enter industries when
the price is above the average cost and

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they can make a profit, and they will exit
when the price is below the average cost.

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Thanks.

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