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 price to charge is $____.
A) 9.2
B) 8.3
C) 7.4
D) 6.5

Question

Quizplus · Accepted Answer

To find the optimal price for a monopoly, we first need to find 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 MR, we take the derivative of the total revenue (TR = P*q), which is the same as taking the derivative of (10q - 0.01q^2) with respect to q, giving MR = 10 - 0.02q. Setting MR equal to MC, we get 10 - 0.02q = 2 + 0.08q. Solving for q gives q = 80. Substituting q back into the demand equation to find P, we get P = 10 - 0.01(80) = 9.2.

A Firm with Market Power Faces the Demand Function Q