Table 15-6
A monopolist faces the following demand curve:
-Refer to Table 15-6. If the monopolist has a constant marginal cost for her product equal to $7, what is her profit-maximizing price?
A)$6
B)$9
C)$12
D)$15

Question

Table 15-6
A monopolist faces the following demand curve: 
-Refer to Table 15-6. If the monopolist has a constant marginal cost for her product equal to $7, what is her profit-maximizing price?
A)$6 
B)$9 
C)$12 
D)$15

Quizplus · Accepted Answer

To find the monopolist's profit-maximizing price, we need to first find the monopolist's marginal revenue (MR) function. Since the demand function is linear, the MR function is also linear and has a slope that is twice as steep as the demand function. So, we can find MR by doubling the slope of the demand function:

MR = 30 - 4Q

To maximize profit, the monopolist should set MR equal to her marginal cost (MC), which is given as $7. So, we have:

30 - 4Q = 7
23 = 4Q
Q* = 5.75

The monopolist should produce and sell Q* units of her product. To find the profit-maximizing price, we can plug Q* into the demand function:

P* = 30 - 2Q*
P* = 30 - 2(5.75)
P* = 30 - 11.5
P* = 18.5

So, the monopolist's profit-maximizing price is $18.5, which is closest to choice (C) $12.

Table 15-6 A Monopolist Faces the Following Demand Curve