The demand equation for a good produced by a monopolistically competitive firm is P = 10 - Q. If the firm has no fixed costs and variable costs of $2 per unit, what is the value of the firm's monopoly profits when it sets a price that maximizes its monopoly profits?
A) $7
B) $12
C) $15
D) $16

Question

Quizplus · Accepted Answer

To maximize monopoly profits, we need to find the quantity where marginal revenue (MR) equals marginal cost (MC). We know that the demand equation is P = 10 - Q, so we can derive MR as follows:

MR = change in total revenue / change in quantity
MR = (P x change in quantity + Q x change in P) / change in quantity
MR = (10Q/Q + Q x (-1)) / 1
MR = 10 - 2Q

We also know that the MC is constant at $2. Setting MR equal to MC, we get:

10 - 2Q = 2
Q = 4

So the profit-maximizing quantity is 4 units. Plugging this back into the demand equation, we get:

P = 10 - Q
P = 10 - 4
P = 6

Therefore, the price that maximizes monopoly profits is $6 per unit. To find the profit, we need to calculate the total revenue (TR) and total cost (TC) at this quantity:

TR = P x Q
TR = 6 x 4
TR = 24

TC = $2 x 4
TC = $8

Profit = TR - TC
Profit = $24 - $8
Profit = $16

So the value of the firm's monopoly profits when it sets a price that maximizes its monopoly profits is $16. Therefore, the answer is D.

The Demand Equation for a Good Produced by a Monopolistically