Monopolist Question

A market is characterized by a demand curve that can be expressed as P = 400 – 5 Q. Each of the firms currently serving the market has a total cost function of the form C = 50 q. There are no fixed costs. a. If the market is served by a monopolistic firm that practices limit pricing, calculate single-period P*, Q*, and profits for the limit-pricing monopolist. Assume that each potential entrant has the total cost curve given by C = 150 q. Show work. b. If the discount rate is 3%, 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 in part b, should the monopolist use a (short-run) profit-maximizing strategy instead if its demand curve shifts down by a constant $20 in period 2 and by another $20 in period 3 due to entry? Show work and explain.