Office Hours: Calculating Monopoly Profit

In our video on Maximizing Profit Under Monopoly, we cover how firms can use their market power to raise the price of a good well beyond its marginal cost. A practice question for this video asked you to find the total profit of a monopolist under certain conditions. In this Office Hours session, Mary Clare Peate, Marginal Revolution University’s Instructional Designer, helps you solve that problem.

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Maximizing Profit Under Monopoly: http://bit.ly/22i0nbT

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[Mary Clare] I've reviewed the data online.
I've talked to a ton of college students.

Everyone is missing this one question.

It's time to make a video.

Today we're going to answer
the following question

from our Microeconomics final exam,

and that is to find total profit
of the monopolist

under the following conditions:

Demand for this good is marked
by P equals 100 minus 2Q,

and this monopolist’s fixed cost is 100,
and his marginal cost is 20.

Now, if you haven't already done so,

check out our video
Maximizing Profit Under Monopoly.

Then, actually try to do
this problem by yourself,

and then come back and we'll
work through this problem together.

Ready?

I'm going to quickly recap
three important truths about a monopoly.

These points are covered in great detail
in our monopoly video,

but they're worth repeating
as they'll form the initial steps

for solving our problem today.

Monopoly truth number one:

Monopolists have market power.

They're a big player in the market.

Or in the classic case,
they're the only player in the market,

which means that the quantity
the monopoly produces

actually affects the market price.

You can think of them
as price makers in their market.

Monopoly truth number two:

When a monopolist is choosing
how much to produce

such that it maximizes its profits,

monopolists behave the exact same way
as their competitive counterparts.

All firms, even the price-makers
of the world,

set marginal revenue
equal to marginal cost

to find that profit maximizing quantity.

And monopoly truth number three:

Because monopolists are price makers,

their marginal revenue is no longer
simply the price of the good

as it is for a competitive firm.

Instead, the monopolist’s marginal
revenue varies with the quantity it sells

and is less than the market price.

As mentioned, these three truths
form the initial steps

for solving our problem today.

First, we actually need to find
the monopolist’s marginal revenue curve.

We then set marginal revenue
equal to marginal cost,

as we always do, to find
that profit-maximizing quantity.

From there, we use quantity

to find the firm's profit-maximizing price.

And finally, once we have
the monopolist’s price and quantity,

we can then find the monopolist’s
total revenue and total cost

to solve for profit.

Step one is to find
the monopolist’s marginal revenue.

The shortcut to finding
the marginal revenue curve

is to simply double the slope
of our demand curve, and that's it.

One thing to note here, that shortcut
only works for linear demand curves.

But that makes it sound
way fancier than it is.

A linear demand curve
is literally just a straight line.

Now, if you'd like me to derive

the marginal revenue curve
in a future video,

just let me know by voting at the end.

In this instance, the slope
of our demand curve is 2.

Double that to 4 and we arrive
at a marginal revenue of 100 minus 4Q.

Step one is complete,
and we can now move on to step two,

which is to set marginal revenue
equal to marginal cost

and solve for the profit-
maximizing quantity.

The monopolist's marginal cost,
as you know, is 20.

Set that equal to the
marginal revenue and solve.

I know you can do this math,

and I know you're
doing this math right now,

so I don't really have to go through it.

After solving, you'll arrive
at a profit-maximizing quantity of 20.

Step two is done, and we can now
move on to step three,

which is to find the market price.

If the monopolist sells 20 units,

what is the maximum price
it can charge as the price maker?

To find out how much consumers
are willing to pay given this quantity,

we turn back to our demand curve

which provides us
with a clear relationship

between the price
and the quantity of a good.

Simply plug Q into the demand curve

and solve for the maximum price
the monopolist can charge.

Again, I know you're going through
these steps right now,

so I don't have to go through each one.

We'll eventually solve for a price of 60,

and now step three is also done.

We now have our monopolist’s
profit-maximizing price and quantity.

To find a monopolist’s profit,
or any firm's profit for that matter,

we need to find how much money
this firm is spending

and subtract it from how much money
this firm is making.

Now, if you're an Econ nerd like I am,

that's just another way of saying:

Find total cost and subtract it
from total revenue.

Total cost, as you know,
is fixed cost plus variable cost.

And we know from the initial conditions

that fixed costs are 100
and marginal costs are 20.

Plug these back into the equation
to arrive at a total cost of 500.

Total revenue is simply the units sold,
or the quantity, times the price.

After plugging in our price and quantity,
we'll arrive at a total revenue of 1200.

And now, all we need to do

is subtract our total cost
from our total revenue

to arrive at the firm's profit of 700.
And that's it!

As always, please let me know
what other concepts and questions

you'd like me to cover.

And if you'd like to challenge yourself,

we've included some additional questions
for you to try at the end.

Thanks.

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