A firm with market power faces the demand function q = 1,000 - 100P. The firm's marginal cost function is MC(q) = 2 + 0.08q. If the firm behaves as a single-price monopoly, the optimal output to produce is $____.
A) 90
B) 80
C) 70
D) 60

Question

Quizplus · Accepted Answer

To find the optimal output for a monopoly, we first need to determine the marginal revenue (MR) and set it equal to the marginal cost (MC). The demand function is q = 1,000 - 100P, which can be rearranged to P = 10 - 0.01q to find the inverse demand function. The total revenue (TR) is P*q = (10 - 0.01q)q. The marginal revenue (MR) is the derivative of TR with respect to q, which is MR = 10 - 0.02q. Setting MR equal to MC gives us 10 - 0.02q = 2 + 0.08q. Solving for q gives us q = 80.

A Firm with Market Power Faces the Demand Function Q