Duopoly: Two identical firms have MC = $3 (no fixed costs) and face a market demand of QD = 9-P. a) If the firms compete on the basis of price: i. What kind of duopoly is this? ii. If they compete a finite number of times what price will each firm choose? Why? How much profit will each firm earn ? iii. If they compete an indefinite number of times under what circumstances can they sell at a higher price? What is this price and how much profit will each earn in a Nash Equilibrium? What is the optimal discount factor? b) If the firms are competing on the basis of quantity (one the leader other the follower): i. What kind of duopoly is this? ii. What are the firms reaction functions? iii. Assume one firm enters the market first. Find the profit maximizing price output and profit of the leader and the follower .