3. Consider a market for an identical product with four firms. The inverse demand for this product is P = 100 - Q where P is price and Q is aggregate output. The production costs for firms 1 and 2 is given by C(qi) = 10qi where qi is the output of firm i and the production costs for firms 3 and 4 is given by C(qi) = 20qi. That is, firms 1 and 2 have a constant marginal cost of 10 per unit and firms 3 and 4 have a constant marginal cost of 20 per unit. Assume that the firms each choose their outputs to maximize profits (Cournot competition) a. Find the Cournot equilibrium output for each firm, the market price and the profits of each of the four firms. (5 pts) b. Suppose that firms 1 and 2 merge and the merged firm's variable cost is the lower of the two firms' costs. Assume that all other firms continue to act as Cournot competitors after the merger. Calculate the Cournot equilibrium output for each firm, the market price and the profits of each of the three firms. Is this merger profitable? (5 pts) c. Suppose that firms 3 and 4 merge and the merged firm's variable cost is the lower of the two firms' costs. Assume that all other firms continue to act as Cournot competitors after the merger. Calculate the Cournot equilibrium output for each firm, the market price and the profits of each of the three firms. Is this merger profitable? (5 pts) d. Suppose that firms 1 and 3 merge and the merged firm's variable cost is the lower of the two firms' costs. Assume that all other firms continue to act as Cournot competitors after the merger. Calculate the Cournot equilibrium output for each firm, the market price and the profits of each of the three firms. Is this merger profitable? (5 pts)