Suppose a monopolist has the following cost function C(Q) = 50Q (with marginal cost MC = 50). Suppose it faces market demand of P = 200 - Q. (2 points) (a) Sketch the market demand, marginal revenues, and marginal costs. Be neat. (4 points) (b) What is the monopolist's optimal level of output, price, and profits? Show your work. (4 points) (c) What is the DWL associated with the monopoly output? Show your work. (3 points) (d) (Cournot Competition) Now suppose we added a second firm that has identical costs to the monopolist. Show that the resulting Cournot Equilibrium has each firm producing output of 200 units. That is, show that, if the other firm sells 200 units, then the best you can do is also sell 200 units. (3 points) (e) What are profits under Cournot Competition compared to the Monopoly case? Hint: be sure to discuss the market price. (4 points) (f) What happens to the DWL under Cournot Competition relative to the Monopoly case? Explain why this happens.