i. Find the condition under which the merger is profitable for firms 1 and 2 jointly (in terms of the synergy level 2). 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.
i. Find the condition under which the merger is profitable for firms 1 and 2 jointly (in terms of the synergy level 2). 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.
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.6P
Related questions
Question
Help me understand part i,j,k
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a4decfa-c86a-4508-ad17-cd6b643e587a%2Fdb468dfe-4a27-40cf-b4cc-7a451dd667ef%2Fq4ftid_processed.png&w=3840&q=75)
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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