2. Homogeneous Cournot with Multiple Firms Suppose that in a market there are N 2 2 firms, all of which have the same constant- returns-to-scale technology with marginal cost c 2 0, so that Ci(qi) = cqi for all firms i. The market demand is given by P(Q) = A - BQ, where Q = _: qi is the aggregate market output. Assume that A > c and B > 0. In this problem we will solve for the Cournot equilibrium in this market. (a) 5 marks Denote the joint output of all firms other than i by Q-;, so that Q-i = _qi = Q-qi. ifi Derive the best-response function of firm i as a function of Q-i. (b) 5 marks Prove that in equilibrium all firms produce the same output: qi = q; for all i and j. [Hint: First, express qi -q; as a function of Q-; and Q-; using the best-response functions. Then express Q-; - Q-i as a function of qi and q; using the definition of Q-i (and Q-;). Finally, put these two results together to get qi - q; = 0.] (c) 2 marks Use the fact that all firms produce the same output in equilibrium to express Q and Q- (for an arbitrary firm) as functions of qi and N. (d) 3 marks Plug your results from (c) into the best-response function to solve for qi. Use this to get Q. (e) 5 marks Calculate the equilibrium market price and the firms' profits in equilib rium