9. Assume that (1) the 10 identical firms in a purely oligopolistic industry form a centralized cartel, (2) the total market demand function facing the cartel is Q_D = 240 -10P and P is given in dollars, and (3) each firm's SMC is given by $1q for q > 4 units, and factor prices remain constant. Find (a) the best level of output and price for this cartel, (b) how much each firm should produce if the cartel wants to minimize costs of production, and (c) how much profits the cartel will make if the SAC of each firm at its best level of output is $12. (d) Why do we study cartel models if cartels are illegal in countries such as the U.S.?