1. The inverse demand curve for crude oil is p = 600 10Q), where () = ; + is the total output in the oil industry. The number of barrels of oil produced by Firm 1 is , and , is the corresponding quantity for Firm 2. The two cost functions are 1 (1) = 60g; and C(q2) = 30gs. a. First suppose the firms form a cartel and choose output levels to maximize joint profits. What is the output at each firm and what is the equilibrium price? In particular, do both firms produce positive levels of output? b. Now suppose the firms choose output simultaneously and independently to maximize their own profits. Find the Nash equilibrium (the Cournot outcome) of this game. What is the output at each firm and what is the equilibrium price