3. (30 points) Merger in cournot market with fixed cost: Suppose there are 3 firms competing in a cournot oligopoly by choosing quantities. Each firm has a marginal cost of 20. Suppose the fixed cost of each firm is given by F' = 100. The demand in the market is given by p = 140 ) where Q = q; + g2 + gs. (a) Find the Nash equilibrium of this game. Find the profit of each firm after accounting for fixed costs. (b) Now suppose that firm 2 and firm 3 decide to merge. The merged firm needs to pay the fixed cost only once. Find the new Nash equilibrium with firm 1 and the merged firm. Find the profit of both firms after accounting for fixed costs. () Was the merger of firm 2 and 3 a good decision for their shareholders? Are firm 1's shareholders happy about the merger? (d) Suppose the Anti-trust authority has the objective of maximizing the sum of profits and the consumer surplus in the economy. Is the antitrust authority happy about this merger?' (e) Now suppose that the fixed cost is I. Find the range of values of F' for which it is profitable for firm 2 and firm 3 to merge