Suppose a monopoly has constant marginal costs of $40 per unit. Demand for the monopolist’s product is Q = 100 - 0.5P.

i. What are the profit maximizing price and quantity for this monopoly? Explain how you arrived at your answer.
ii. How many units of the product would the competitive market supply? What would the equilibrium price be? Explain how you arrived at your answer.
iii. Calculate how much consumer surplus would be lost if this market started off as perfectly competitive but then became monopolistic.
iv. Calculate how much producer surplus would be gained if this market started off as perfectly competitive but then became monopolistic.
v. Briefly explain how your answers to parts iii and iv relate to the deadweight loss created by the monopoly.

i. MR = 200 - 4Q. Setting MR = MC gives Q = 40, P = 120.
ii. Demand is P = 200 - 2Q. Setting demand equal to MC gives Q = 80, P = 40.
iii. Under perfect competition CS = 6400. Under monopoly CS = 1600. Therefore, consumers lose 4800 in surplus due to the formation of the monopoly.
iv. Under perfect competition PS = 0. Under monopoly PS = 3200. Thus monopoly status gives the producer 3200 more in surplus.
v. The difference between what is lost by consumers and what is gained by producers is the deadweight loss. In this problem is amounts to 1600.