Suppose a monopolist has the following cost function C(Q) = 40Q (with marginal cost MC = 40). Suppose it faces market demand of P = 100-% Q (2 points) (a) Sketch 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 deadweight loss (DWL) associated with the monopoly output? Show your work and explain why the DWL arises. (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 60 units. That is, show that, if the other firm sells 60 units, then the best a firm can do is also sell 60 units. (4 points) (e) What are total profits under Cournot Competition compared to the Monopoly case? Why do they differ? (3 points) (f) What happens to the deadweight loss under Cournot Competition relative to the Monopoly case? Explain why this happens.