Cournot and Stackelberg with Differentiated Products: Consider a different tiated products duopoly in which each firm has cost of producing ci(qi) = qi. If the quantities are q, and q2, the prices are P1 (91, 92) = 3 - 91 - dq2 P2(91, 92) = 3 - dq1 - 92 where de (-1, 1). Consequently the profits of each firm are 71 (91, 92) = (2 - 91 - dq2)91 (Alt + A) 72(91, 92) = (2 - dq1 - 92)92. (a) Suppose first the firms choose quantities simultaneously. i. Give an economic interpretation of d. What does it mean for d to be positive or negative? ii. Solve for the Nash equilibrium quantities in a symmetric equilibrium.iii. Suppose that firms could collude and agree to set the same quantity q1 = 92 = q. What q would they pick? iv. How does the collusive outcome compare to the Nash equilibrium? Explain the economic intuition. (b) Now suppose that firm 1 sets q1 before firm 2 sets q2. i. Solve for the subgame perfect equilibrium of the Stackelberg game for any d. ii. How does the ratio q1/92 vary with d? Explain the economic intuition