5. There are three firms in the market for respirators and consumer demand is given by...

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5. There are three firms in the market for respirators and consumer demand is given by P = 300 - Q where Q = 91 +92 +93 is the total output in the market. The cost function of firm 1 and firm 2 is given by: Ci(q1) F+12q1 C₂(92) = F + 1292 where F is a fixed cost. Meanwhile firm 3 has a cost function given by C3 (93) = F + 12893 where 8 is a measure of firm 3's cost advantage or disadvantage. This means that if > 1 then firm 3 is a high cost firm and if 8 < 1 then firm 3 is a low cost firm. Assume that the firms each choose their outputs to maximize profits (Cournot competition) a. Find the Cournot equilibrium output for each firm, the product price and the profits of each of the three firms. For this to be an equilibrium, all three firms must at least cover their variable costs. Identify the constraint that & must satisfy for this to be the case. (5 pts) b. Suppose that d = 1 and that when two firms merge, the merged firm's fixed cost is aF where 1 ≤ a ≤ 2. Derive a condition on a and F in order for a merger between firm 1 and 3 to be profitable. How do we interpret this condition? (5 pts) c. Now suppose that F = 0 and that when two firms merge, the merged firm's variable cost is the is the lower of the two firm's costs. Can a merger between firm 1 and 3 be profitable if & ≥ 1 such that firm 3 is a high cost firm? What are the profits of each firm after this merger? Derive a condition on d in order for a merger between firm 1 and 3 to be profitable. (5 pts) 5. There are three firms in the market for respirators and consumer demand is given by P = 300 - Q where Q = 91 +92 +93 is the total output in the market. The cost function of firm 1 and firm 2 is given by: Ci(q1) F+12q1 C₂(92) = F + 1292 where F is a fixed cost. Meanwhile firm 3 has a cost function given by C3 (93) = F + 12893 where 8 is a measure of firm 3's cost advantage or disadvantage. This means that if > 1 then firm 3 is a high cost firm and if 8 < 1 then firm 3 is a low cost firm. Assume that the firms each choose their outputs to maximize profits (Cournot competition) a. Find the Cournot equilibrium output for each firm, the product price and the profits of each of the three firms. For this to be an equilibrium, all three firms must at least cover their variable costs. Identify the constraint that & must satisfy for this to be the case. (5 pts) b. Suppose that d = 1 and that when two firms merge, the merged firm's fixed cost is aF where 1 ≤ a ≤ 2. Derive a condition on a and F in order for a merger between firm 1 and 3 to be profitable. How do we interpret this condition? (5 pts) c. Now suppose that F = 0 and that when two firms merge, the merged firm's variable cost is the is the lower of the two firm's costs. Can a merger between firm 1 and 3 be profitable if & ≥ 1 such that firm 3 is a high cost firm? What are the profits of each firm after this merger? Derive a condition on d in order for a merger between firm 1 and 3 to be profitable. (5 pts) 5. There are three firms in the market for respirators and consumer demand is given by P = 300 - Q where Q = 91 +92 +93 is the total output in the market. The cost function of firm 1 and firm 2 is given by: Ci(q1) F+12q1 C₂(92) = F + 1292 where F is a fixed cost. Meanwhile firm 3 has a cost function given by C3 (93) = F + 12893 where 8 is a measure of firm 3's cost advantage or disadvantage. This means that if > 1 then firm 3 is a high cost firm and if 8 < 1 then firm 3 is a low cost firm. Assume that the firms each choose their outputs to maximize profits (Cournot competition) a. Find the Cournot equilibrium output for each firm, the product price and the profits of each of the three firms. For this to be an equilibrium, all three firms must at least cover their variable costs. Identify the constraint that & must satisfy for this to be the case. (5 pts) b. Suppose that d = 1 and that when two firms merge, the merged firm's fixed cost is aF where 1 ≤ a ≤ 2. Derive a condition on a and F in order for a merger between firm 1 and 3 to be profitable. How do we interpret this condition? (5 pts) c. Now suppose that F = 0 and that when two firms merge, the merged firm's variable cost is the is the lower of the two firm's costs. Can a merger between firm 1 and 3 be profitable if & ≥ 1 such that firm 3 is a high cost firm? What are the profits of each firm after this merger? Derive a condition on d in order for a merger between firm 1 and 3 to be profitable. (5 pts) 5. There are three firms in the market for respirators and consumer demand is given by P = 300 - Q where Q = 91 +92 +93 is the total output in the market. The cost function of firm 1 and firm 2 is given by: Ci(q1) F+12q1 C₂(92) = F + 1292 where F is a fixed cost. Meanwhile firm 3 has a cost function given by C3 (93) = F + 12893 where 8 is a measure of firm 3's cost advantage or disadvantage. This means that if > 1 then firm 3 is a high cost firm and if 8 < 1 then firm 3 is a low cost firm. Assume that the firms each choose their outputs to maximize profits (Cournot competition) a. Find the Cournot equilibrium output for each firm, the product price and the profits of each of the three firms. For this to be an equilibrium, all three firms must at least cover their variable costs. Identify the constraint that & must satisfy for this to be the case. (5 pts) b. Suppose that d = 1 and that when two firms merge, the merged firm's fixed cost is aF where 1 ≤ a ≤ 2. Derive a condition on a and F in order for a merger between firm 1 and 3 to be profitable. How do we interpret this condition? (5 pts) c. Now suppose that F = 0 and that when two firms merge, the merged firm's variable cost is the is the lower of the two firm's costs. Can a merger between firm 1 and 3 be profitable if & ≥ 1 such that firm 3 is a high cost firm? What are the profits of each firm after this merger? Derive a condition on d in order for a merger between firm 1 and 3 to be profitable. (5 pts)