3. Consider a market for an identical product with four firms. The inverse demand for this product is P = 150-2Q where P is price and Q is aggregate output. The production costs for firms 1 and 2 is given by C(qi) = 5qi where qi is the output of firm i and the production costs for firms 3 and 4 is given by C(q) = 10qį. That is, firms 1 and 2 have a constant marginal cost of 5 per unit and firms 3 and 4 have a constant marginal cost of 10 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. (10 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 1 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)
3. Consider a market for an identical product with four firms. The inverse demand for this product is P = 150-2Q where P is price and Q is aggregate output. The production costs for firms 1 and 2 is given by C(qi) = 5qi where qi is the output of firm i and the production costs for firms 3 and 4 is given by C(q) = 10qį. That is, firms 1 and 2 have a constant marginal cost of 5 per unit and firms 3 and 4 have a constant marginal cost of 10 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. (10 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 1 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)
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
ChapterB: Differential Calculus Techniques In Management
Section: Chapter Questions
Problem 5E
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Transcribed Image Text:3. Consider a market for an identical product with four firms. The inverse demand for this product is P = 150-2Q
where P is price and Q is aggregate output. The production costs for firms 1 and 2 is given by C(qi) = 5qi
where qi is the output of firm i and the production costs for firms 3 and 4 is given by C(q) = 10qį. That is,
firms 1 and 2 have a constant marginal cost of 5 per unit and firms 3 and 4 have a constant marginal cost of 10
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. (10 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 1 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)
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