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a. There are 5 firms in an industry that compete by setting quantities simultaneously. Every rm has an identical constant marginal cost of $10 and no fixed costs. Market demand is given by P = 250 4031 + '32 + '35)- i. Suppose Firms 1 and 2 are considering merging into a single firm. So, post-merger, Firms 1 and 2 would be replaced by a single firm that has a constant marginal cost of $10 and no fixed costs. You have been hired by Firms 1 and 2 as a consultant. Use the Cournot model to give advice on the profitability of this merger. ii. Ignore the information in part (i). Suppose, instead, that the five firms are planning to form a cartel. A government policy maker becomes aware of this plan and decides to announce that any cartel discovered in the market will be fined $F. What is the lowest F that would deter the firms from cartelizing the market. Assume that if a cartel is formed, it will certainly be discovered by the government, and that the resulting ne is shared equally among cartel members. Show your work. b. Ignore the information in part (a). Consider Cournot competition in a different market and industry. There are 10 firms, each with a different constant marginal cost ct. Demand is given by P = 400 5(q1 + q; + qm). Suppose the industry is currently in a Cournot equilibrium, and the current market price is $210. If one of the firms is selling an output of 5 units, what must its marginal cost be? Show your work