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j. Can you verify that the post-merger total welfare strictly increases in the synergy level a? k. Suppose after the merger, the total output does not change, i.e., Qpre = Qpost. Does the merger increase total welfare? Explain why using only one sentence.

j. Can you verify that the post-merger total welfare strictly increases in the synergy level a? k. Suppose after the merger, the total output does not change, i.e., Qpre = Qpost. Does the merger increase total welfare? Explain why using only one sentence.

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.6P
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Q1. Horizontal Mergers with synergies The market inverse demand is given by P(Q) = 170 - Q. Initially, four firms, 1, 2, 3, and 4, have the symmetric constant marginal cost c = 20 and compete à la Cournot. There is no fixed cost. We will explore the impact of a merger between firms 1 and 2. The newly merged firm is called m. Following the merger, firm m's constant marginal cost reduces to cm = 20 x with 0 < x < 20 representing the synergy resulting from the merger. First, consider the market equilibrium prior to the merger. a. b. C. d. e. Next, consider the market equilibrium after the merger. Note that only firms m, 3, and 4 are still operating in the market. f. h. Write down the profit maximization for firm i, i = 1, 2, 3, 4. Write down the first-order condition for firm i. Solve for the symmetric Nash equilibrium in this Cournot game. In particular, write down each firm's output qe, price pre, total output Qpre, and each firm's profit pre in equilibrium. Calculate the pre-merger total welfare Wpre i. j. k. 1 Write down the profit maximization problems for firms m, 3, and 4 respectively. Write down the first-order conditions for firms m, 3, and 4 respectively. merger. Finally, we compare the equilibrium outcomes before and after the Solve for the asymmetric Nash equilibrium in this post- merger Cournot game. In particular, write down firm m's output qpost, firms 3 and 4's symmetric output post = gost = host, and total output post Calculate the post-merger total welfare Wpre. Find the condition under which the merger is profitable for firms 1 and 2 jointly (in terms of the synergy level 2). Can you verify that the post-merger total welfare strictly increases in the synergy level x? Suppose after the merger, the total output does not change, i.e., Qpre = Qpost. Does the merger increase total welfare? Explain why using only one sentence.
Transcribed Image Text:Q1. Horizontal Mergers with synergies The market inverse demand is given by P(Q) = 170 - Q. Initially, four firms, 1, 2, 3, and 4, have the symmetric constant marginal cost c = 20 and compete à la Cournot. There is no fixed cost. We will explore the impact of a merger between firms 1 and 2. The newly merged firm is called m. Following the merger, firm m's constant marginal cost reduces to cm = 20 x with 0 < x < 20 representing the synergy resulting from the merger. First, consider the market equilibrium prior to the merger. a. b. C. d. e. Next, consider the market equilibrium after the merger. Note that only firms m, 3, and 4 are still operating in the market. f. h. Write down the profit maximization for firm i, i = 1, 2, 3, 4. Write down the first-order condition for firm i. Solve for the symmetric Nash equilibrium in this Cournot game. In particular, write down each firm's output qe, price pre, total output Qpre, and each firm's profit pre in equilibrium. Calculate the pre-merger total welfare Wpre i. j. k. 1 Write down the profit maximization problems for firms m, 3, and 4 respectively. Write down the first-order conditions for firms m, 3, and 4 respectively. merger. Finally, we compare the equilibrium outcomes before and after the Solve for the asymmetric Nash equilibrium in this post- merger Cournot game. In particular, write down firm m's output qpost, firms 3 and 4's symmetric output post = gost = host, and total output post Calculate the post-merger total welfare Wpre. Find the condition under which the merger is profitable for firms 1 and 2 jointly (in terms of the synergy level 2). Can you verify that the post-merger total welfare strictly increases in the synergy level x? Suppose after the merger, the total output does not change, i.e., Qpre = Qpost. Does the merger increase total welfare? Explain why using only one sentence.
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