Consider an industry consisting of two firms which produce a homogeneous commodity. The industry demand function is Q = 100 - P, where Q is the quantity demanded and P is its price. The total cost functions are given as C = 50q for firm 1, and C = 60q2 for firm 2, where Q = 91 +92. a. (6 points) Suppose both firms are Cournot duopolists. Find and graph each firm's reaction function. What would be the equilibrium price, quantity supplied by each firm and their profits? b. (5 points) Now suppose the firms start acting as Stackelberg duopolists. Suppose in particular that firm 1 acts as the leader, whereas firm 2 acts as the follower. Find the new equilibrium price, quantity produced by each firm and the profits. Comment on equilibrium price, total output and total surplus in comparison to the Cournot equilibrium. c. (5 points) Suppose the two firms merge into one firm. Compare the profits in this case with those under the Cournot conditions assumed in (a) above. d. (4 points) If the firms got into a Bertrand competition, what is likely to happen? You do not need to solve the problem; just explain verbally.