Please answer question 5 ONLY, question 4 is given for context as question 5 refers to the model in q 4.

Question 4: [20 pts] Imagine three identical perfectly competitive firms, each with constant MC-2 and facing an industry inverse demand curve equal to P = 26 - Q. (a) Assume the three firms enter into a cartel agreement in which they agree to all set the monopoly price and share the monopoly profits three ways. If they do as promised, find the equilibrium price, the total industry profits and the profits received by each firm (Suppose Fixed Cost equals to 0 for all three firms). (b) Discuss that, in a one-shot game (i.e. the world ends after one period), each firm has an incentive to "cheat". That is, each firm would make more profit by lowering its price just below the monopoly level, conditional on its cartel partners still pricing at the monopoly level. (You only need to show this for one firm since the others are identical.) Conclude that cartels in one-shot games are inherently unstable.Question 5: [20 pts] Continuing with the previous question, instead assume that an infinite period game in which firms agree to collude by setting the monopoly price each period every period forever. Assume the discount factor equals to r. (a) Suppose the trigger strategy is "In each period, set price equal to the monopoly price, provided each firm has set price equal to the monopoly price in every past period since the agreement began. If any firm did not set the monopoly price as required in any past period, then set price equal to marginal cost (i.e. now and forever after)." How high does the discount factor have to be to make the cartel stable? (b) How does your answer to (a) change if it takes two periods for firms to detect "cheating" instead of one