1. Cournot, Collusion and Stackelberg. Fabulous Knitwear and Joint Wool are the only two producers of sweaters in the little town of Mirandola. They compete in quantities. Market demand for sweaters in Mirandola is Q=120-P, where Q is the total quantity exchanged and Q=qFk+qw. Both firms produce with the same technology and their total cost function is TC(q)=30. a. Assume the two firms behave like Cournot oligopolists. Find their reaction functions and plot them in a graph. b. Find the Cournot equilibrium. What are each firm's profits in equilibrium? C. Explain why is q=30 a Nash equilibrium? (hint: if a firm's quantity is different from 30, how would the competitor's choice change?) d. Compare the quantities and profits in the Cournot equilibrium you just calculated to the quantity and profit in the perfectly competitive equilibrium and in the monopoly equilibrium assuming that marginal cost is the same as before. What can you conclude comparing the equilibria? e. One possible strategy for each firm is to produce half of the monopolist quantity. Would the resulting outcome be better than the Cournot outcome for both firms? Explain why this is not the equilibrium outcome of the Cournot game. f. Consider now the case in which firm JW has the opportunity to produce and market its sweaters before FB. Then JW is a Stackelberg leader. Compute the quantities produced by both firms in this case and their profits. Is there a first mover advantage for firm JW? g. Assume that the possibility to become a Stackelberg leader depends on a regulatory change and that both firms can invest in influence and lobbying activities. What is the maximum amount of money that a potential Stackelberg leader would be willing to invest to be given the possibility to become a Stackelberg leaders