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2. Cournot Competition Firms are engaged in Cournot competition (i.e., simultaneously determining their quan- tity). Market-level inverse demand is given by: P 400 IOQ. Firms have the same cost functions: C 40q. (30 points) (a) Let's begin by assuming there are two firms in the market. Solve for equilibrium production levels of each firm, total market quantity, the market price, the profits of each firm, and consumer surplus. Hint: In this case, each firm simultaneously chooses a quantity and then both firms sell all of their quantity at the price such that aggregate demand equals aggregate supply. Start by solving for Firm I's choice of as a function of Firm 2's quantity (12, then solve for Firm 2's choice of as a function of Firm I's quantity ql. Then solve the two equations simultaneously for the two variables Cll and (12.) (20 points) (b) As a brief aside, which will be useful soon, solve for the market quantity, price, and consumer surplus under perfect competition (when each firm in the market takes prices as given). (10 points) (c) (Bonus) Now assume there are N firms engaged in Cournot competition (as before, in part a and b). As a function of N, solve for equilibrium production levels of each firm, total market quantity, the market price, the profits of each firm, and consumer surplus. What happens as N rises? [Hint: 1. think about that one firm is competing against other firms, so the firm chooses q based on (N-1) other firms' quantity. 2. compare to your response in part b). (20 points)