Problem 2. Three firms are engaged in (simultaneous) Cournot competition. Total demand is P = 4000 - Q, where Q is the total quantity produced by all firms in the market. The three firms have an identical total cost function C:(q;) = 400q; for i = {1, 2, 3}. 1 Write firm 1 profit as a function of the quantities produced by each firm. 2 What is the best response function of firm 1? 3 What is the equilibrium strategy profile for this game (Hint: note that firms are sym- metric)? 4 What are the quantities produced by each firm in equilibrium? 5 How much profit does each firm earn in equilibrium? 6 Suppose (for this part only) that firm 1 faces a fixed cost of production of 800. So it's total cost function is C1(q1) = 800 + 400q1. What is the best response function of firm 1? 7 Suppose (for this part only) that firm 2 faces a lower marginal cost of 200. So it's total cost function is C2(92) = 200q2. What is the best response function of firm 1? 8 Suppose firm 2 and 3 propose a merger-reducing the number of firms in the industry to two. Would you expect the total quantity produced in the industry to rise or fall following the merger? Explain your answer, but you do not need to calculate the post-merger quantity produced