TR MR1 = aQ1 = 160 4Q1 2Q2 Similarly, we can derive an expression for marginal revenue for firm 2 as aTR2 MR2 = = 160 4Q2 - 2Q1 aQ2 a. Presuming the firms act as Cournot competitors, choosing quantity to maximize profit, derive the levels of output for each firm, the price, and the profit earned by each firm in equilibrium. (10 points) b. Suppose instead that the two firms behaved as one firm, as a monopolist. For a monopolist in this market, total revenue = PQ = (160-2Q)Q = 160Q - 2Q?, and marginal revenue = 160 - 4Q. Assume the costs are the same, MC = AC =40. What level of total output would the firms choose if they could coordinate to act as a monopolist, and how much would each produce presuming that they split production evenly? What would the price be? What would total profit be, and how much would each firm get (presuming that they split profit evenly)? (10 points) c. Using concepts from our discussion of Nash equilibrium and the cartel example, explain why we might expect it to be difficult for these firms to maintain the monopoly agreement you describe in part (b). If they each act unilaterally in their own best interest once the agreement about monopoly-level production is made, what do we expect to happen? (What will Firm 1 want to do if it believes Firm 2 will stick to its agreement to produce half the monopoly quantity you found in part (b)?) (5 points)