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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- [Prof. Alex Tabarrok] 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

or 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 a 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 a 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.

- [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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