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Question 1 (14 pts.) As an analyst at the Competition Bureau, you are tasked to determine under what conditions a cartel would be sustained in a duopoly industry. Each firm could produce two levels of output, q,- = 15 and :1: = 20, for i = {1, 2}. The payoffs, representing each firm's profit, for each of the two firms are reported in Table 1 as a function of the constant marginal cost, c. Table 1 Firm 1\\ Firm 2 . 1,200 20c,1,200 20c 1,300 200,975 15c 975 15c,1,300 20c 1,050 15c,1,050 15c According to a published report, the market quantity Q = 40 corresponds to a duopoly industry and Q = 30 to a monopoly. a) (2 pts.) Calcuiate the range of values for the marginal cost c (if any), for which (q1 = 20,112 = 20) is a pure strategy Nash equilibrium. Show ALL STEPS. b) (2 pts.) Calculate the range of values for the marginal cost c (if any), for which (q1 = 15,112 = 15) is a pure strategy Nash equilibrium. Show ALL STEPS. c) (2 pts.) Calculate the value of the marginal cost :2, for which a cartel is a preferrabie outcome to a duopoly for each firm. d) (2 pts.) Briefly explain why a cartel might generate more profit for each firm but not be chosen by either of them