A. Two firms, A and B, both have costs C(O = 250;. Market demand is Q: 100 - 2P, 0: 0A + 03. (1) a. If this market were perfectlyr competitive, what would market price, quantity, and prots be? b. If this market were operating as a cartel, what would market price, quantity. and profits be? (2) Assume the market is operating as a Cournot duopoly. a. What is firm A's profit function? b. What is rm A's reaction function? c. What is firm A's output? What are market output and price? d. What is firm A's profit? (3) Assume the market is a Stackelberg duopoly, and firm A is the leader. a. What is firm A's profit function? b. What is firm A's output? c. What is firm B's output? What are market output and price? d. What is firm A's profit? What is firm B's profit? (4) Assume that A and B have agreed to create a cartel in which each member keeps the profit produced by hisfher own output. a. If A decides to cheat, and A assumes that B will produce the agreedupon level (namely, half the total amount from (1) b.), how much will A produce? b. How much profit does each firm receive if A cheats and B does not? What is each firm's profit if mt_h firms cheat? c. This problem can be analyzed using a payoff matrix. Fill in the payoffsfprofits for each firm in a matrix like this one: Cooperate Cheat Cooperate Cheat d. From this matrix, what can you conclude about the possibility of maintaining the cartel