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♪ [music] ♪

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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

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and marginal grade.

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So suppose that your 
average grade is 80%.

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

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you only get 60% -- lower.

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What is that going to do 
to your average?

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

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Indeed whenever your marginal 
is below your average,

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the average must be falling.

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

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and on your next test you get 90%.

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Great, but what does 
that do to your average?

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It drives your average up.

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Indeed whenever your marginal
is above the average,

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the average must be rising.

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

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

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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.

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

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for average cost and marginal cost.

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Whenever the marginal cost is 
below the average,

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the average is falling.

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Whenever the marginal cost is 
above the average,

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the average is rising.

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And where marginal is 
just equal to average,

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the average is flat.

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In other words, we are 
at the minimum point

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of the average cost curve.

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

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

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

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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.

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We also know 
that average cost is equal

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to total cost divided by quantity.

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

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to average cost times quantity.

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

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

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

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price times quantity --
minus total cost --

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average cost times quantity.

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

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and we find that profit 
can also be written as price

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minus average cost, 
all of that times quantity.

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That's nice because we can find

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all of these elements 
on our diagram.

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Here's the price.

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

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

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

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So profit at the profit 
maximizing quantity is

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this green area right here --

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price minus average cost 
times quantity.

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

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exactly how much profit is.

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Let's use this tool some more.

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

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Remember, I said that profit 
maximization doesn't necessarily

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mean the firm is making 
a positive profit.

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

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You may have to take a loss.

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

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

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marginal revenue curve.

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How does the firm profit maximize?

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It chooses the quantity 
where marginal revenue is

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equal to marginal cost.

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In that case, this quantity is one.

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Now what's the profit 
for the firm?

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Well, as usual we measure 
profit as price minus

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average cost times quantity.

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But notice that price is 
below the average cost

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at the profit maximizing 
quantity of one.

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

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It's a negative quantity.

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

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which is the minimum 
of the average cost curve.

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

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the minimum of its 
average cost curve.

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

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at a point where price is equal
to marginal cost,

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

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So all of this area down here,

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even the profit maximizing 
quantity, will mean a loss.

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

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

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

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

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

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is the breakeven point.

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If the price is less 
than the minimum

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

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If the price is bigger 
than the minimum

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

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So when should a firm enter 
or exit an industry?

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In the long run, the firms will 
enter when price

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is above average cost.

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If price is somewhere 
above the average cost curve

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then the firm can make 
a profit by entering

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and that's what firms want to do.

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

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wherever a profit is possible.

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Firms will exit the industry 
when the price is below

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the average cost curve.

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Then they're going 
to be taking a loss,

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and they're going to want to exit.

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Finally, when the price is 
equal to the minimum

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

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of the average cost curve, 
profits are zero,

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and there's no incentive

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to either exit 
or enter the industry.

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Now you might ask, 
why would firms remain

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in an industry if profits are zero?

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Zero profits, this is just 
a matter of terminology,

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means that at the market price 
the firm is covering all

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

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their ordinary opportunity cost.

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So zero profits means 
everyone is being paid enough

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to make them satisfied.

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

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by normal profits.

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So when an economist 
says zero profits

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just substitute normal profits.

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One more point 
about entry and exit. 


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

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when price falls 
below average cost.

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Or to enter immediately 
when price is above average cost.

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

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For example, suppose 
that that the price of oil is

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currently above the average 
cost of pumping oil,

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

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Well, maybe not necessarily.

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Because entry requires you 
to drill an oil well,

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and 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.

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

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

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What this means is you
don't want to enter

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unless you expect 
the price of oil to stay

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above the minimum 
of the average cost curve

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

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

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

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You have to expect that 
that price is going to stay

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above average cost 
long enough for you

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to recover your entry costs.

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For the same reasons, 
if there are exit costs,

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for example, if you have 
to shutter up the well

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or fill the well with cement 
when you exit the industry

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

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below average cost, 
it may be best to weather

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the storm at least 
for sometime before you exit.

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

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of average cost 
for an extended period of time

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will you want to exit the industry.

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

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

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the lifetime profits can 
still be possible.

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So, entry and exit could be 
quite complicated

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because you've got 
to be thinking

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about the lifetime profits,
not just your immediate profits.

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However, the bottom line
is pretty simple.

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Firms seek profits
and they want to avoid losses.

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

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the average cost
and they can make a profit,

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

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Thanks.

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