A market comprises three firms i E {1,2,3} competing in quantities. Inverse market demand is given...

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A market comprises three firms i E {1,2,3} competing in quantities. Inverse market demand is given by p(Q) = 800 - 5Q, where Q = 9₁ +9₂ + 93. Each firm i has marginal cost C₁, and therefore profit function ¹₁ (9₁, 92, 93) = (p − ci)qi . a) (1.5 marks) Suppose C₁ = 2, C₂ = 5, and c3 = 8. Find the best response functions for each firm by filling numbers in the blanks below. 9 (92,93) = 92 (91,93) 93 (91, 92₂) = (91 +92). b) (1 mark) In equilibrium, we know that the level of output for each firm is q₁ = 40.35, q2 = 39.75, q3 = 39.15. = Compute the profit of firm 1: 7₁ Compute the profit of firm 2: 7₂ = (92 +93). = (91 +93). c) (1.5 marks) Firms 1 and 2 are considering a merger. Under the merger, a new firm would be created with profit function 12 (9₁, 92, 93) = π₁ + π₂, so that this new firm would be a multi-plant firm. In equilibrium, the new firm would produce q₁ in plant 1. In equilibrium, the new firm would produce 92 merge. d) (2 marks) The total profit of the new firm in equilibrium would be in plant 2. Hence assuming firms 1 and 2 split the profits evenly, the firms The total profit of the monopolist firm in equilibrium is e) (3 marks) Now, suppose that all three firms are considering a merger! In equilibrium, what quantity would this monopolist produce? Q = q₁ + 92 +93 = Hence, assuming that firms 1, 2, and 3 split the profits evenly, the firms ◆ merge. ◆ Hence assuming firms 1 and 2 split the profits evenly, the firm e) (3 marks) Now, suppose that all three firms are considering this monopolist produce? Q = q₁ + 9₂ +93 = would would not would be indifferent towards a herge. y would A market comprises three firms i E {1,2,3} competing in quantities. Inverse market demand is given by p(Q) = 800 - 5Q, where Q = 9₁ +9₂ + 93. Each firm i has marginal cost C₁, and therefore profit function ¹₁ (9₁, 92, 93) = (p − ci)qi . a) (1.5 marks) Suppose C₁ = 2, C₂ = 5, and c3 = 8. Find the best response functions for each firm by filling numbers in the blanks below. 9 (92,93) = 92 (91,93) 93 (91, 92₂) = (91 +92). b) (1 mark) In equilibrium, we know that the level of output for each firm is q₁ = 40.35, q2 = 39.75, q3 = 39.15. = Compute the profit of firm 1: 7₁ Compute the profit of firm 2: 7₂ = (92 +93). = (91 +93). c) (1.5 marks) Firms 1 and 2 are considering a merger. Under the merger, a new firm would be created with profit function 12 (9₁, 92, 93) = π₁ + π₂, so that this new firm would be a multi-plant firm. In equilibrium, the new firm would produce q₁ in plant 1. In equilibrium, the new firm would produce 92 merge. d) (2 marks) The total profit of the new firm in equilibrium would be in plant 2. Hence assuming firms 1 and 2 split the profits evenly, the firms The total profit of the monopolist firm in equilibrium is e) (3 marks) Now, suppose that all three firms are considering a merger! In equilibrium, what quantity would this monopolist produce? Q = q₁ + 92 +93 = Hence, assuming that firms 1, 2, and 3 split the profits evenly, the firms ◆ merge. ◆ Hence assuming firms 1 and 2 split the profits evenly, the firm e) (3 marks) Now, suppose that all three firms are considering this monopolist produce? Q = q₁ + 9₂ +93 = would would not would be indifferent towards a herge. y would

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a The best response functions for each firm can be found by maximizing their profit function with re... View the full answer