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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
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 = 9 +9 + 93. Each firm i has marginal cost C, and therefore profit function (9, 92, 93) = (p ci)qi . a) (1.5 marks) Suppose C = 2, C = 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, 92) = (91 +92). b) (1 mark) In equilibrium, we know that the level of output for each firm is q = 40.35, q2 = 39.75, q3 = 39.15. = Compute the profit of firm 1: 7 Compute the profit of firm 2: 7 = (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 (9, 92, 93) = + , so that this new firm would be a multi-plant firm. In equilibrium, the new firm would produce q 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 = q + 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 = q + 9 +93 = would would not would be indifferent towards a herge. y would
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