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- [Alex] Now that we know 
how to find the profit

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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,

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average cost is the cost 
per unit of output.

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

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Now remember also 
that total cost can be broken down

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into fixed costs plus 
variable costs.

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

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Average cost is equal 
to fixed cost divided by Q

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

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

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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.

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That's why they're fixed.

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So when Q is small -- this number,

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suppose fixed cost is 100,

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

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like 100 divided by 1.

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As Q gets larger, however,
this number --

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

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

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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

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by a bigger quantity.

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

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Moreover, what we saw 
with the marginal cost curve

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is that at some point,
your variable costs are going

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to increase faster than quantity.

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

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

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and bigger and bigger.

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

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

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Eventually, however, 
the second force here is going

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to drive average cost up.

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

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falling, reaches a minimum,
and then rising.

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So let's draw it like that.

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Okay, here's our typical
marginal cost curve,

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

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We know that the profit maximizing 
point is where marginal revenue

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is equal to marginal cost.

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

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

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

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

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the marginal cost curve goes 
through the minimum point

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of the average cost curve.

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

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Instead of cost I want to 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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