Maximizing Profit under Monopoly

AIDS has killed more than 36 million people worldwide. There are drugs available to treat AIDS, but the price of one pill is incredibly high in the U.S. — coming in at 25 times higher than its cost. Why is that? In this video, we show how patent rights have created a monopoly in the U.S. market for AIDS medication, causing pills to be very expensive. In other countries, however, such as India, which does not recognize patents on AIDS medication, prices remain low. Using this example, we go over how monopolies use market power to increase prices.

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- [Alex] Monopoly.
It's not just a game. In this

video we'll talk about how a firm uses
market power to maximize profit. We'll

begin with a controversial example.

This is the AIDS virus. Worldwide, it has

killed more than 36 million people. In the
United States, however, AIDS is no longer

the death sentence that it once was.
Beginning in the mid-1990s, death rates

from AIDS began to fall dramatically with
the introduction of new drugs such as

Combivir. These new drugs are great, but
they're expensive, and they're expensive

not because it costs a lot to manufacture
these drugs. The per-pill costs of

production are actually quite low.
Instead, these drugs are expensive because

they're the subject matter of this
chapter: Monopoly.

GlaxoSmithKline, or GSK, owns the patent
on Combivir and that means that it has the

right to exclude competitors. Only GSK can
legally sell Combivir. The patent gives

GSK a monopoly, or more generally we say
it gives them market power. Market power

is the power to raise price above marginal
cost without fear that other firms will

enter the market.
Now how do we know the price is above

marginal cost? Here's a simple test: in
the United States, Combivir costs around

$12 to $13 per pill. India, however, does
not recognize the patent on Combivir. So

in India, there are many producers of
Combivir who sell in a competitive market.

As we know, in a competitive market, price
will fall to marginal cost and in India

the price of Combivir is about 50 cents
per pill.

Thus, in the United States, the price of
Combivir is about 25 times higher than the

marginal cost.

Let's say a few words about the sources of
market power. The basic idea is that a

firm has market power when it's selling a
unique good and there are barriers to

entry, forces which prevent competitors
from entering the market. Barriers to

entry could include patents as we've
already discussed. There may also be other

government regulations creating barriers
to entry, such as exclusive licenses.

Economies of scale can mean that a single
big firm can sell at lower cost than any

of many small firms, making it difficult
to establish a competitive market even

with free entry. Exclusive access to an
important input. Diamonds, for example, are

found in only a few places in the world.
If you control a number of these diamond

mines, you can monopolize the market for
diamonds, where you will have market power

in the market for diamonds. Technological
innovations can give a firm temporary

market power. A firm with knowledge or
abilities that other firms don't yet have

will have some market power, for example.

Now we'll say a little bit more about
these later. What we want to do now is to

focus on how a firm with market power
chooses to set its price. What is the

profit maximizing price?

So how does a monopolist maximize profit?
By producing at the level of output where

marginal revenue is equal to marginal
cost.

Great! That's the same rule as for a
competitive firm: choose a level of output

where marginal revenue is equal to
marginal cost. The only difference is that

for a competitive firm, marginal revenue
was the same as price, and that's not true

for a monopolist. A monopolist is not a
small share of the market. Since it's

selling a unique good, the monopolist
faces the entire downward sloping market

demand curve.
As a result, marginal revenue is going to

be less than price. Let's show how to
calculate marginal revenue for a

monopolist.

Let's start with the demand curve, and
suppose that we're initially selling two

units. We can sell those two units for $16
apiece. Total revenue therefore is $16

times 2 units, or $32. Now, remember that
marginal revenue is the change in total

revenue from selling an additional unit.
So suppose that we sell an additional

unit, three units in total. We can sell
three units for $14. $14 is the maximum

per unit price we can get when selling
three units.

So when the quantity sold is three,
total revenue is 14

times three, or $42. That means marginal
revenue, the change in revenue from

selling that additional unit, is $10.
Now we can actually arrive at the same

conclusion in another revealing way.
Marginal revenue can be broken down into

two parts. First is the revenue gain from
selling an additional unit. That's just

this area right here. We can sell an
additional unit, the third unit for $14.

That's the revenue gain. But, in order to
sell that additional unit, we had to lower

the price on the previous units that we
were selling, so there's also a revenue

loss. We were receiving $16 per unit when
we sold just two units. When we sell three

units, we have to lower the price to $14,
so we lose $2 per unit on these previous

units for a total loss of $4. So marginal
revenue is just the revenue gained: $14,

minus the revenue loss, $4, or $10 just as
before.

Notice also that the revenue gain is just
the price of the third unit, so since it's

the revenue gain minus the revenue loss,
we can also see right away that for a

monopolist, marginal revenue must be less
than the price.

Okay, let's remember where we're going. We
want to find the profit maximizing price,

which is the level of output where
marginal revenue is equal to marginal

cost. But do we need to go through this
tedious process to find marginal revenue

for each unit? No. There's a shortcut, and
that's what I'm going to show you next.

Here's the shortcut for finding marginal
revenue, and this will work for any linear

demand curve, and those are the only ones
we're really going to be working with in

this class, so it'll work just fine for
us. Take a linear demand curve, then the

marginal revenue curve begins at the same
point on the vertical axis as the demand

curve, and it has twice the slope. So if
we were to write the demand curve in

inverse form as P is equal to A minus B
times Q, then the marginal revenue curve

is equal to A minus 2B times Q. That's it.
Pretty simple. Let's give a few more

examples.
Let's use our shortcut on these two

different demand curves. In the first
case, the marginal revenue curve begins at

the same point on the vertical axis. It
has twice the slope. So notice what that

means is that if the demand curve hits the
horizontal axis at 500, the marginal

revenue curve must hit the horizontal axis
at 250. More generally, since it has twice

the slope, the marginal revenue curve
splits the distance between the vertical

axis and the demand curve in half. So the
distance from the vertical axis to the

marginal revenue curve is half the total
distance to the demand curve, throughout

the length of the marginal revenue curve.
Okay, what about our second demand curve?

Notice that it hits the horizontal axis at
200, therefore the marginal revenue curve

must hit the horizontal axis at 100.
Pretty simple, and again, this will work

for any linear demand curve, any demand
curve which we're going to see in this

course.

Great. We're now ready for the big payoff:
how a firm uses market power to maximize

profit. So here is our demand curve and
our marginal revenue curve with twice the

slope. Let's introduce the marginal cost
curve. We're going to make it flat at 50

cents per pill. How does the firm maximize
profit? Well it compares for each unit the

revenue for selling that additional unit
compared to the cost of selling that unit.

If the marginal revenue is bigger than the
marginal cost, then that's a profitable

unit to sell, so the firm keeps producing
so long as marginal revenue is bigger than

marginal cost. That is, it produces until
marginal revenue is equal to marginal

cost. That point tells us the profit
maximizing quantity of output, in this

case, 80 million pills.
Now what is the maximum amount per pill

that we can sell these 80 million pills
for? Where do we find that? We find that

by looking up to the demand curve.
Remember the demand curve tells us the

maximum willingness to pay. So the maximum
willingness to pay for pill is $12.50.

Eighty million units, that's the profit
maximizing quantity, $12.50, that's that

profit maximizing price per unit.
One more curve - let's remember our average

cost curve. If we introduce this curve we
can now show profits on the diagram, just

as we did with the competitive firm. The
profit is the price minus the average

cost, in this case that's $10 per pill,
times the quantity, in this case 80

million units, so profit is the shaded
area given right here.

So now we've got everything. Whenever we
have a monopoly question, we have a demand

curve, we draw the marginal revenue curve,
we draw a marginal cost curve if it's not

given. We can then find the profit
maximizing output quantity that's given

when marginal revenue is equal to marginal
cost. We go up to the demand curve to find

the profit maximizing price. The
difference between the price and average

cost gives us the profit per unit, times
the total number of units gives us total

profit.
Okay. That's our big lesson for today.

What we're going to do next time is look
at, how does the difference between price

and marginal cost, how does the mark-up
vary? And what we're going to show is the

mark-up varies with the elasticity of
demand. Remember, I told you elasticity of

demand would come back. Well here we're
going to use it again in our next lecture.

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