3. Oligopoly (15 points) Consider duopoly. Suppose two identical firms are identical. Their total costs are C1 = 20Q1 + 1000 and C2 = 20Q2 + 1000, where Q1 is the output of Firm 1 and @2 the output of Firm 2. The market demand curve is Q = 140 - P. (a) (5 points) Suppose that each firm chooses its profit-maximizing level of output on the assumption that its competitor's output is fixed. Calculate the Cournot equilibrium. How much will each firm produce, and what will its profit be? (b) 2 points) Draw the firms' reaction curves and show the Cournot equilibrium. (c) (3 points) Now suppose firms collude. Find the collusion curve. Calculate the col- lusion equilibrium under the assumption that the collusive output is shared equally. (d) (5 points) On the same diagram, draw the collusion curve and show the collusion equilibrium. Using the diagram, please explain why the collusion equilibrium is not a Nash equilibrium. What is Firm 1's profit-maximizing output when Firm 2 produces its collusive output