Question

1. Consider a market with inverse demand P (Q) = 100 - Q and 5
firms with cost function C(q) = 40q.

(a) Find the Cournot equilibrium outputs, price and profit.

(b) If 4 firms merge with no efficiency gain, do they increase or
decrease their profits? By how much?

(c) Is the result in (b) expected?

(d) What are the effects of this merger on price and social
welfare?

Answer #1

a)

P = 100 - Q

TC = 40Q

MC = 40

Equilibrium Condition in competitive market

P = MC

100 -Q = 40

Q = 60

Cournot Equilibrium output

= (N/N+1)*Competitive output

= (5/6)*60

= 50

P = 100 - 50

= 60

Each firm production = 10 units

Profit = TR - TC

= 50*60 - 40*50

= 1 000

Each Profit = 200

b)

Cournot output when four firms merge:

= (2/3)*60)

= 2*20

= 40

P = 100 -40

= 60

Profit = 40*60 - 40*40

= 2400 - 1600

= 800

Each firm profit = 400

Merged firm profit may not be profitable but single firm profit increases.

c)

it was expected that profit of firm will rise.

d)

Price has increased and quantity produced decreased, so there is fall in social welfare of people or deadweight loss rises when few firms are there in market or number of firm decreases.

1. Consider a market with inverse demand P (Q) = 100 Q and two
firms with cost function C(q) = 20q.
(A) Find the Stackelberg equilibrium outputs, price and total
profits (with firm 1 as the leader).
(B) Compare total profits, consumer surplus and social welfare
under Stackelberg and Cournot (just say which is bigger).
(C) Are the comparisons intuitively expected?
2. Consider the infinite repetition of the n-firm Bertrand game.
Find the set of discount factors for which full...

2) (Merger with cost synergies) Suppose the demand for widgets
is p(Q) = 100 – Q. Initially, there are two firms producing
widgets, each with cost function C(q) = 40q, and these firms engage
in Cournot quantity competition. Now suppose these two firms
propose to merge so as to reduce their marginal costs by 0<?. In
other words, after the merger there will be a monopolist with cost
function CM(q) = (40 – ?)q.
a) For what values of ?...

1. Consider a market with inverse demand P (Q) = 100 Q. A
monopolist with linear cost C(Q) = 20Q serves this market.
(a) Find the monopolistís optimal price and quantity.
(b) Find the price, quantity, proÖt, consumer surplus, and
social welfare under perfect competition.
(c) Find the optimal proÖt, consumer surplus, social welfare
and the deadweight loss for monopoly.
(d) What is the % loss in social welfare as we move from perfect
competition to monopoly.

Consider the Cournot duopoly model where the inverse demand
function is given by P(Q) = 100-Q but the firms have asymmetric
marginal costs: c1= 40 and c2= 60. What is the Nash equilibrium of
this game?

2. Consider two identical firms in a Cournot competition. The
market demand is P = a – bQ. TC1 = cq1 = TC2 = cq2 . a. Find the
profit function of firm 1. b. Maximize the profit function to find
the reaction function of firm 1. c. Solve for the Cournot-Nash
Equilibrium. d. Carefully discuss how the slope of the demand curve
affects outputs and price.

Assume that the inverse demand function for a good is P = 40 –
2Q. A monopolist retailer has exclusive rights to sell this good. A
monopolist manufacturer sells the good to the retailer at price R.
The retailer has an additional marginal cost equal to $2 per unit.
The manufacturer’s marginal cost is $4 per unit.
a. Assume that the two firms remain independent. Determine the
value of R charged by the manufacturer.
b. Now assume that the two...

1) Two firms, a and b, in a Cournot oligopoly face the inverse
demand function p = 300 – Q. Their cost function is c
(qi) = 25 + 50qi for i = a, b. Calculate the
profit maximizing price output combination. (3)

Consider a market with 2 identical firms (a and b). The market
demand is P = 14 - Q
where Q = Qa + Qb. For both firms AC=MC= 2.
A. Solve for the Cournot-Nash reaction functions of each
firm.
B. Solve for the Cournot- Nash equilibrium. Solve for Q, Qa, Qb,
Price, and each firms profit.
C. Compare the Cournot-Nash equilibrium with perfect
competition, and monopoly (you can refer to your results from
question 2, if you’ve already done...

Consider a market with 2 identical firms (a and b). The market
demand is P = 14 - Q
where Q = Qa + Qb. For both firms AC=MC= 2.
A. Solve for the Cournot-Nash reaction functions of each
firm.
B. Solve for the Cournot- Nash equilibrium. Solve for Q, Qa, Qb,
Price, and each firms profit.
C. Compare the Cournot-Nash equilibrium with perfect
competition, and monopoly (you can refer to your results from
question 2, if you’ve already done...

Consider a Cournot market with two firms that have TC(Q) =5Q.
Demand is given by P= 200−2(Q1+Q2).
A) Find firm 1’s profit as a function of Q1 and Q2
B) Find the equilibrium price, quantity sold by each firm, and
profit for each firm.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 19 minutes ago

asked 25 minutes ago

asked 27 minutes ago

asked 31 minutes ago

asked 33 minutes ago

asked 35 minutes ago

asked 35 minutes ago

asked 44 minutes ago

asked 45 minutes ago

asked 1 hour ago

asked 1 hour ago