Consider a market demand curve that can be expressed as P = 300 - 3 Q. Each of the firms currently serving the market has a total cost function of the form C = 40 q so MC = ATC = 40. There are no fixed costs.
a. If the market is served by a (short-run) profit-maximizing monopoly, calculate P*, Q*, and profits for the monopolist. Show work.
b. If the market is instead served by a limit-pricing monopolist, calculate P*, Q*, and profits. Assume that each potential entrant has the total cost curve given by C = 105 q. Show work. If the discount rate is 10%, compute the present value of a stream of profits for 3 years for the limit-pricing monopolist of this question. Do not discount the first year’s profits. Show work.
c. Compared to the three-period limit-pricing strategy from part b, should the monopolist use a short-run profit-maximizing strategy instead if it can maintain its monopoly only for a single period? (After that, let’s assume that entry would force its profits all the way to zero.) Explain.