6. Duopoly Suppose that two identical firms produce widgets and they are the only firms in the market. Their costs are given by C1 = 30q1 and Co = 30q2, where qi is the output of Firm 1 and q2 is the output of Firm 2. Price is determined by the following industry demand curve: P = 150-Q where Q = q1 + q2. a. Create the reaction functions for each firm. b. Find the Cournot-Nash equilibrium. Calculate the profit of each firm at this equilibrium. c. Suppose the two firms form a cartel to maximize joint profits. How many widgets will be produced? Calculate each firm's profit. d. Suppose Firm 1 abides by the cartel agreement, but Firm 2 cheats by increasing production. How many widgets will Firm 2 produce? What will be each firm's profits? e. Explain why cartels are fragile by nature. Under what circumstances would you predict that a cooperative outcome would be sustainable