PLEASE EACH AND EVERY STEP, THANK YOU!!

Suppose that there are two firms producing a homogenous product and let the market demand be given by Q(P) = 120 - -. For simplicity assume that each firm operates with zero total cost. (a) (10 points) Assuming that firms compete over quantities, find the price best-response functions of firms I and 2. Draw a diagram that shows the BRFs and the equilibrium. Are outputs strategic substitutes or complements? Find each firm's Cournot equilibrium output, price, profit, and total surplus. Define Nash equilibrium and argue that it is indeed a Nash equilibrium. (b) (10 points) Show that the duopolists have incentives to collude. Find their joint profit-maximizing price, output, and profit: find each firm's output and profit. Is collusion a Nash equilibrium? If not, what is the optimal defection for each firm? Show this game in a 2X2 matrix form. What does this imply about the Nash equilibrium or the stability of their collusive agreement? Is it a Prisoner's Dilemma Type? (c) (10 points) Suppose now that firms play the above game in repeated interaction indefinitely (infinite repetition). Firms negotiate for a full cooperation (collusion to become monopoly) and use Grim-trigger strategies: in the event of any defection from collusion, firms go back to their Best responses and thus Nash equilibrium arises, Find the critical discount factor that makes free collusion dynamically sustainable? (d) (10 points) Suppose now that these two firms compete in quantities but one firm (say firm 1) is a leader moving first in setting its output and another firm (say firm 2) is a follower, moving second in setting its output. Find the Stackelberg equilibrium output, price and profit for each firm. Does the leader enjoy benefits from moving first? Find the total surplus. (e) (5 points) Suppose now that these two firms compete in Bertrand fashion. Find each firm's Bertrand equilibrium price, output, profit, and total surplus, Does Bertrand Paradox arise? Why