Question 3. A monopolist operates in an industry where the demand curve is given by Q(P) = 1000 20P. The monopolist's constant marginal cost is 8. 1. What is the monopolist's prot-maximizing price? Answer: The inverse demand is P(Q) = 50 Q/20, hence MR(Q) = 50 Q/10. Then, MR(Q) = MC 2 50Q/10 = 8 => Q = 420 = P = 29. 2. Calculate the monopoly dead weight loss. Answer: With competition and supply curve horizontal at P = 8, we get Q = 840. Therefore, the consumer surplus is CS (8) = (50 8) - 840 = 17,640. As the supply is horizontal, the producer surplus is PS (8) = 0. The overall welfare is their sum, 17,640. With the monopoly, when P = 29 and Q = 420, the consumer surplus is C S (29) = $(50 29) - 420 = 4,410. The monopolist's profit is (29 8) - 420 = 8,820 and the overall welfare is 4,410 + 8820 = 13,230. Hence, the dead weight loss is 17,640 13.230 = 4,410