HW 5

A monopoly firm is the only seller of a single good Q. Its marginal costs of producing Q are MC(Q)=25Q. Inverse demand for Q is D(Q)=665Q. a. Derive the monopolist's marginal revenue curve. Plot this curve, a straight line, on a diagram with Q on the horizontal axis and P (which is $/Q ) on the vertical axis. b. Compute the monopolist's profit-maximizing level of output QM. What price, PM, will the monopolist set? Indicate these on your figure. c. Compute the monopolist's profits revenue (a rectangle) and its cost (a triangle) when it sells QM at a price of PM. What is its profit? Shade and label the area representing profit, M, on your figure. d. Compute the consumer surplus for consumers of Q at the monopoly outcome. Shade and label this area. e. Now suppose the suppliers of Q are many in number, but that their aggregate supply curve is exactly the same as the monopolist's MC curve, so we have inverse market supply of S(Q)=25Q. Compute the competitive equilibrium price and quantity P and Q. Compute the consumer surplus and producer surplus at this outcome. f. Compute the deadweight loss due to monopoly power in this market. Deadweight loss is another triangle.