Suppose that a monopolist has the following demand curve: P =400 2Q and a constant marginal and average cost ofMC_M= AC_M= 30.

a. Solve for the profit-maximizing level of monopoly output, price, and profits.

b. Suppose a potential entrant is considering entering, but the monopolist has a cost advantage. The potential entrant faces costs MC_PE= AC_PE= 40. Assuming the monopolist continues to profit-maximize, solve for the residual demand curve for the entrant.

c. Assume the potential entrant follows the Cournot assumption about the monopo-list's output. Solve for the potential entrant's output, price, and profits in this scenario. What are the new monopoly profits?

d. Is there a price the monopolist could charge to deter entry? Solve for the limit price and output that will completely deter entry. What is monopoly profit at this point?