Problem 3: (20 points) The memory chip industry is a duopoly. The two firms, Intel and AMD, compete through Cournot quantity-setting competition. The demand curve for the industry is P = 90 - Q, where Q is the total quantity produced by Intel and AMD. Each firm has a marginal cost of 30. {You must show each step in answering the questions below. If you just write the correct answer, you will not get any credit.} a. (6 points) Find the Cournot equilibrium price, quantity produced by each firm, and the profit of each firm. b. (6 points) What is the monopoly price and quantity with the given demand and cost function? What is the monopoly profit? Is the monopoly profit larger or smaller than the sum of profits of the two firms that you calculated in part a? Can the two firms collude over monopoly profit (form a cartel) if they interact only once? c. (8 points) Suppose the two firms interact infinitely. Find the discount factor 6 such that the two firms are able to cooperate over the monopoly outcome using a trigger strategy. You must specify what the trigger strategy is for each firm. You must also clearly derive the profit from cooperation and profit from cheating and then solve the relevant inequality to find the value of 6