A monopolist\'s demand curve is P = 100-Q and the total cost curve is TC = 16 +

Question

A monopolist's demand curve is P = 100-Q and the total cost curve is TC = 16 + Q^2. The associated marginal cost curve is MC = 2Q. What is the profit maximizing quantity and price, and what will be the economic profit?

I am not quite sure what to do. I don't know if the MC + MR equation applies in this question. I'm truly stumped, and am desperately in need of help. I thank you in advance for your help on this question.

Explanation / Answer

P = 100-Q (demand curve) Revenue R = P*Q = 100Q - Q^2 MR = dR/dQ = 100 - 2Q For optimal R, MR = MC => 100 - 2Q = 2Q => 100 = 4Q => Q = 25 THis is profit maximizing qty. (ANSWER) P = 100 - 2Q = 100 - 50 = 50 This is profit maximizing price. (ANSWER) Economic profit = R - TC => EC = (50*25) - (16+ 25^2) = 1250 - 641 = 609 (ANSWER)

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