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 q, = 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 ofthe constant marginal cost, 6. Table 1 Firm 1\\ Firm 2 q2 = 20 q2 = 15 1,200 20c, 1,200 206 1,300 206, 975 15C 975 156, 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. e) (2 pts.) Suppose that the marginal cost 6 equals 40 and the deadweight loss reduction from leaving the cartel is 250. Calculate the average cost reduction required for a regulator to approve the horizontal merger. f) (2 pts.) Briefly explain how you would use the information from Table 1 to determine whether firm 1 has an incentive to leave the cartel in the context of the dynamic Cournot model. The payoffs remain unchanged in each period. g) (2 pts.) Suppose that the marginal cost c equals 40. Calculate the value for the discount factor r, for which a firm would leave the cartel