Question

You are the manager of a monopolistically competitive firm. The present demand curve you face is P = 100 – 4Q. Your cost function is C(Q) = 50 + 8.5Q2.

1. What level of output should you choose to maximize profits?
2. What price should you charge?
3. What will happen in your market in the long run? Explain.

Answer 1

P = 100 - 4Q

Total Revenue (TR) = P * Q = 100Q - 4Q^²

MR (first derivative of TR with respect to Q) = 100 - 8Q

C(Q) = 50 + 8.5Q^²

MC (first derivative of TC with respect to Q) = 17Q

i) At equilibrium, MR = MC

100 - 8Q = 17

Q = 10.375

To maximize profit, produce must produce output level of 10.375

ii) At output level of 10.375, P = 100 - 4 * 10.375 = 58.5

iii) TR at output level of 10.375 is 606.94

TC at output level of 10.375 is 964.94

It result in net loss of 358.

In long run, firms with higher fixed cost will exit the industry due to net loss in short run.