Five firms compete a la Cournot, setting quantities. They face a demand function P = 130 Q, with Q = q1 + q2 + q3 + q4 + q5. These firms have a marginal cost of 10 and zero fixed costs. (a) Find the equilibrium quantities, price, and profits. [5 marks] (b) Suppose that if firms 1 and 2 merge, they become a Stackelberg leader, and the other three firms are followers. Find the equilibrium quantities, price, and profits after the merger. [10 marks] (c) Show that firms 1 and 2 have a profit incentive to merge. [5 marks] (d) Briefly describe the Merger Paradox. Explain why giving the merging firms a leadership advantage resolves the paradox. [7 marks] (e) Calculate the impact of the merger on the consumer surplus and on the total welfare (i.e. total industry profit plus consumer surplus). Based on your answer, do you think that the competition authorities should block a horizontal merger between firms 1 and 2? [8 marks] (f) Calculate the Herfindahl-Hirschman Index (HHI) of this industry before and after the merger. [5 marks] (g) Using the information provided on page 6, do you think that the US Department of Justice (DoJ) would attempt to block a horizontal merger between firms 1 and 2? Compare with your answer in part (e). [5 marks] (h) Discuss briefly the limitations of this leadership model.