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

itself 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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