Help me understand part a-c Q1. Horizontal Mergers with synergiesThe market inverse demand is given by P(Q) = 170 - Q. Initially, fourfirms, 1, 2, 3, and 4, have the symmetric constant marginal cost c = 20and compete à la Cournot. There is no fixed cost. We will explore theimpact of a merger between firms 1 and 2. The newly merged firm iscalled m. Following the merger, firm m's constant marginal cost reducesto cm = 20 x with 0 < x < 20 representing the synergy resulting fromthe 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 onlyfirms 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 Cournotgame. 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 Wprei.j.k.1Write down the profit maximization problems for firmsm, 3, and 4 respectively.Write down the first-order conditions for firms m, 3, and4 respectively.merger.Finally, we compare the equilibrium outcomes before and after theSolve for the asymmetric Nash equilibrium in this post-merger Cournot game. In particular, write down firm m's outputqpost, firms 3 and 4's symmetric output post = gost = host, and totaloutput postCalculate the post-merger total welfare Wpre.Find the condition under which the merger is profitablefor firms 1 and 2 jointly (in terms of the synergy level 2).Can you verify that the post-merger total welfare strictlyincreases 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? Explainwhy using only one sentence.

The Cournot game is used to describe an industry structure in which companies compete on the amount…

a. b. C. 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 Qre, and each firm's profit in equilibrium.

a. b. C. 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 Qre, and each firm's profit in equilibrium.

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Help me understand part a-c

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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Step 1: Introduce the concept of cournot game.

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Step 3: b. Write down the first-order condition for firm i.

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