9. (10 points) The marginal cost of a monopolist's product is $100 per unit at each of two plants. The fixed costs are 200 in administrative overhead and an additional 400 at each plant. Demand is QD = 600040P where QD is the total demand, so inverse demand is P = 150 .025QD and MR = 150 .05QD.

(a) Calculate the price and quantity that maximizes the firm's profits. What is the monopolist's profit at this price?

(b) Calculate the elasticity of demand at the monopoly price and quantity.

(c) Suppose that the monopolist is broken up into two firms. The industry would then be a two firm oligopoly (or duopoly). Explain why it is reasonable to expect each firm would charge less than the monopoly price after the breakup. You can use intuition for price competition or quantity competition (Bertrand or Cournot).