2. Phebe and John are the head economists of two firms who act as Cournot duopolists. Suppose the demand curve for the good is: P = 50-2Q and the total cost function for each firm is TC = 10 + 2q. a. Determine the reaction functions for each duopolist b. Determine the profit maximizing price and quantity for this Cournot-Nash equilibrium. c. Draw the picture of the reaction functions, and the point where equilibrium takes place. d. Suppose in their off hours between discussing market equilibria rather heatedly and drinking tremendous amounts of Sky, they decide to collude and act as a monopolist, what amount will they produce and what will the price be? e. Draw the contract curve which illustrates their choices for (d) above. f. Suppose Dariel, a noted economist tries to persuade the firms to act in the best interests of society and to charge the perfectly competitive price. Determine this perfectly competitive price and quantity.