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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 cost. 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 it a bigger
quantity. On the other hand, the variable cost 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 the 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 is that do to your average? It drives our
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. Here's the market price which is equal to the firms 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 is 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 will 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 payed 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 costs literally in this case.
A sunk costs 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 cost. 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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