11.a. Profit-Maximization by a Monopolist
A monopoly is a firm that is the exclusive seller of a product with which there are no close substitutes. The
monopoly retains this control because it is not possible for other firms to enter into that particular market; therefore,
eliminating competition over the selling of that product. This concept is known as barriers to entry.
The fundamental difference between a competitive firm and a monopolistic firm is the monopoly’s influence over
the price of its product or output. This arises because a competitive firm is too small in relation to its market in
which it operates to have any control over the price of its output. However, a monopoly does not face this dilemma
because it is the only producer in its market so it adjusts the price of its output by simply changing the quantity it
supplies. This illustrates the characteristic of a monopolistic firm as a price maker. Since monopolies are the only
producer in its market and are price makers they face a downward sloping market demand curve and thus must sell
at a lower price in order to sell more output.
Like a competitive firm, a monopoly operates at maximum profit where its marginal revenue equals its marginal
cost. However, its marginal revenue curve is no longer equal to its demand curve because the downward sloping
quality of its demand curve causes the monopoly to lower its prices in order to increase the quantity, resulting in less
revenue per extra unit of output. Therefore, in order to find the price a monopoly charges you must determine the
profit-maximizing quantity where its marginal revenue equals its marginal cost and then go up to its demand curve
at that quantity.
Below are two examples that provide first a conceptual understanding then second a numerical explanation of a
monopoly’s profit-maximization.
Example #1:
Imagine there is some sort of monopoly over a product of software, like Microsoft. In columns 1 and 2 of Table
11.a.1 we can see the demand schedule for this particular monopoly. From this you can see that as the quantity
increases the price decreases, representing the downward sloping demand curve characteristic of monopolies. The
third column computes the firm’s total revenue which calculates the quantity sold (column 1) times the price
(column 2). By looking solely at this column we would conclude this firm should produce at a quantity of 3 or 4.
However, we can take it one step further by computing the firm’s profit by subtracting the firm’s total cost (column
4) from its total revenue (column 3) at each quantity. This column indicates that at 4 units the firm will experience a
loss in profit even though it appeared the firm was earning its highest revenue at 4 units.
As a result, you must use the firm’s marginal cost and marginal revenue to accurately calculate its profit
maximization. Marginal cost can be computed by calculating the increase in the total cost (column 4) from an
additional unit of output (column 1) produced. Similarly, marginal revenue can be computed by calculating the
change in total revenue (column 3) from an additional unit of output (column 1) sold. Once those values have been
computed you can compare the firm’s marginal cost and marginal revenue values to determine the actual profit
maximization. From the table it is evident that the firm’s marginal cost is less than its marginal revenue up until the
second unit is sold. However, if the firm were to produce the third unit it would cost the firm $4 while that third unit
only brought in $2 of additional revenue. Therefore, from the table we can conclude that this monopolistic firm’s
profit-maximizing quantity is about 2 units and its profit-maximizing price is about $5.
Quantity
Price
Total Revenue
(P x Q)
Total
Cost
0
1
2
3
4
5
6
$7
6
5
4
3
2
1
$0
6
10
12
12
10
6
$3
5
8
12
17
23
30
Table 11.a.1
Profit
(TR - TC)
$-3
1
2
0
-5
-13
-24
Average Total
Cost
(TC / Q)
$∞
5
4
4
4.25
4.6
5
*Black numbers indicate given values, while red numbers indicate calculated values.
Marginal
Cost
Marginal
Revenue
>
>
>
>
>
>
>
>
>
>
>
>
$2
3
4
5
6
7
$6
4
2
0
-2
-4
Once, you have a firm understanding of how the numbers in Table 11.a.1 are computed the next step is to transfer
the numbers onto a graph in Figure 11.a.1. In this figure it is evident that this firm’s profit–maximizing quantity is
about 2, while its profit-maximizing price is about $5 which is what consumers will be willing to pay for 2 units. In
order to calculate the profit received by this firm we need to calculate the firm’s average total cost at every quantity
by dividing the firm’s total cost by quantity. This is illustrated in the column 6 of Table 11.a.1. Since we already
know the profit-maximizing quantity is about 2 we just look at the average total cost value at the quantity of 2 in the
table which is $4. Now that we have all of these values we just need to plug it into the total profit equation
(P –ATC) x Q which equals a total profit of $2 ((5-4) x 2). This total profit of $2 is illustrated by the purple rectangle
in Figure 11.a.1.
Example #2:
Given the equations…
Demand (D): P=50-Q and
Total Cost (TC): P=80+20Q+
Find the profit-maximizing quantity and price as well as the total profit of this monopolistic firm. Illustrate in
graphs…
In order to calculate the profit maximizing quantity of a monopoly you need to find the quantity in which the
firm’s marginal cost equals its marginal revenue. In order to calculate the firm’s marginal revenue equation you
need to calculate the firm’s total revenue equation and then take the derivative of the firm’s total revenue to give you
its marginal revenue. To find the marginal cost equation you just take the derivative of its total cost equation…
TR = P x Q = (50-Q)Q = 50Q MR = 50 – 2Q
MC=dTC/dQ=20+Q
Now we can set the firm’s marginal cost equal to its marginal revenue so that we can calculate its profitmaximizing quantity…
MC = MR
20 + Q = 50 – 2Q
3Q = 30
= 10
Next, you need to plug Q = 10 into the Demand equation in order to calculate the profit-maximizing price of the
monopoly…
D: P = 50 – 10
= 40
 Once you have calculated the profit maximizing quantity and price of the monopoly you need to calculate the
equation for the average total cost curve in order to compute total profit of the monopolistic firm. The average total
cost curve is computed by dividing the total cost equation by quantity. Once the firm’s average total cost curve is
calculated you need to plug Q = 10 into this equation in order to calculate the firm’s price on the average total cost
curve at the profit-maximizing quantity…
=
ATC: P =
+ 20 +
P=
+ 20 +
= 33
Now that these values have all been calculated you can determine the total profit of this monopolistic firm one of
two ways. First, you can compute the total profit by subtracting the firm’s total cost from its total revenue. Second,
you can manipulate the total profit equation (TR – TC) in terms of price, quantity, and average total cost and then
solve for total profit...
Total Profit = TR – TC
Total Profit = TR – TC
= (50Q –
) – (80 + 20Q +
)
=(
–
)xQ=(
– ATC) x Q
= (50(10) –
) – (80 + 20(10) +
)
= (P – ATC) x Q
= 400 – 330
= (40 – 33) x 10
= 70
= 70
Look at Figure 11.a.2 and Figure 11.a.3 to see how all of the calculations above can be illustrated in graphs.
In Figure 11.a.2 the purple triangle represents the total profit = 70 calculated above. From the graph we can see
how the equation (P – ATC) x Q is used. The yellow area represents the total cost = 330 calculated above and the
two areas put together equal the total revenue (330 + 70 = 400). If you compare the two figures you can see that
the yellow rectangle in Figure 11.a.2 is represented in Figure 11.a.3 by the point on the total cost curve where it
has a quantity of 10. Also, in Figure 11.a.3 you can see what total revenue equals by looking at the point on the
total revenue curve where is has a quantity of 10. This value is represented by the purple and yellow areas
combined. Therefore, the purple area (total profit = 70) in Figure 11.a.2 can also be represented by the red line
between the total cost and total revenue curves in Figure 11.a.3. Another interesting piece of information we can
take away from Figure 11.a.3 is a proof of why a firm maximizes profits where its marginal cost equals it
marginal revenue. This figure indicates that the slopes of the total cost and total revenue (the blue lines) curves are
equal. Another name for these curves is the marginal cost and marginal revenue because the slope of the total cost
is the marginal cost while the slope of the total revenue curve is the marginal revenue. Since these lines’ slopes
equal at the profit-maximizing output we can conclude that a monopolistic firm operates at maximum profit
where its marginal revenue equals its marginal cost, which we achieved in Figure 11.a.2.
Study Questions:
1.
2.
3.
4.
Why is a monopoly’s demand curve downward sloping and what affect does this have on its profitmaximization price and quantity?
What should a monopoly do if its price equals its average total cost?
a. Increase output
b. Lower its price
c. Nothing, it is making zero profits
d. Decrease output
e. Raise its price
f. It is not a monopoly
What should a monopoly do if its price equals its marginal cost?
a. Increase output
b. Lower its price
c. It is making zero profits
d. Decrease output
e. Raise its price
f. It is not a monopoly
What is characteristic of a monopoly’s marginal revenue curve?
a. It is the same as its demand curve
b. It decreases as quantity sold increases
c. It is a horizontal line
d. It increases as quantity sold decreases
Answers:
1.
2.
3.
4.
Since monopolies are the only producer in its market they are able to adjust their own prices. However,
given that they are the only firm in the market they face the market demand curve where they have to lower
prices if they want to increase output. This decrease in price from an increase in quantity illustrates the
characteristic of a downward sloping demand curve. Since monopolies face a downward sloping demand
curve their marginal revenue no longer equals their demand because the price of the output is decreasing as
more output is produced and therefore less revenue is made per extra unit of output. To find its profitmaximization you need to go where its marginal revenue curve equals its marginal cost curve to find the
quantity and then up to its demand at that quantity to find the price. Since the marginal revenue curve no
longer equals its demand curve the price always ends up being above the firm’s marginal cost curve in a
monopoly, rather than equal to its marginal cost curve like a competitive firm.
C. Nothing, it is making zero profits
F. It is not a monopoly
A. It decreases as quantity sold increases