A monopolistically competitive firm faces demand given by this equation: P = 50 - Q. It has no fixed costs and its marginal cost is $20 per unit. What quantity will the firm produce when it is maximizing its profits?
A) 10
B) 15
C) 20
D) 25

Question

Quizplus · Accepted Answer

To maximize profits, a monopolistically competitive firm produces where marginal revenue (MR) equals marginal cost (MC). Here, the firm's demand can be rewritten as Q = 50 - P. So, the firm's total revenue (TR) is:
TR = P * Q
TR = (50 - Q) * Q
TR = 50Q - Q^2
Now, we find the marginal revenue (MR) function by taking the derivative of TR with respect to Q:
MR = dTR/dQ = 50 - 2Q
Setting MR equal to MC (which is $20) and solving for Q:
50 - 2Q = 20
2Q = 30
Q = 15
Therefore, the firm will produce 15 units when it is maximizing its profits.

A Monopolistically Competitive Firm Faces Demand Given by This Equation