Question

Two firms compete to sell a homogenous good in a market characterized by a demand function Q = 250 – 1/4P. Each firm has the same cost function at C(Q) = $200Q. Use this information to compare the output levels and profits in settings characterized by Cournot, Stackelberg, Bertrand, and Collusive behavior.

Answer #1

Two firms, a and b, compete in a market to sell homogeneous
products with inverse demand function P = 400 – 2Q where Q =
Qa + Qb. Firm a has the cost function
Ca = 100 + 15Qa and firm b has the cost
function Cb = 100 + 15Qb. Use this
information to compare the output levels, price and profits in
settings characterized by the following markets:
Cournot
Stackelberg
Bertrand
Collusion

Two firms, a and b, compete in a market to sell homogeneous
products with inverse demand function P = 400 – 2Q where Q = Qa +
Qb. Firm a has the cost function Ca = 100 + 15Qa and firm b has the
cost function Cb = 100 + 15Qb. Use this information to compare the
output levels, price, and profits in settings characterized by the
following markets:
a, Cournot
b, Stackelberg
c, Bertrand
d, Collusion

Suppose that two firms compete in the same market producing
homogenous products with the following inverse demand function:
P=1,000-(Q1+Q2)
The cost function of each firm is given by:
C1=4Q1
C2=4Q2
Suppose that the two firms engage in Bertrand price
competition. What price should firm 1 set in equilibrium? What
price should firm 2 set? What are the profits for each firm in
equilibrium? What is the total market output?
Suppose that the two firms collude in quantity, i.e.,
acting together...

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...

Two firms compete in a Bertrand setting for homogeneous
products. The market demand curve is given by Q = 100 – P, where Q
is quantity demanded and P is price. The cost function for firm 1
is given by C(Q) = 10Q and the cost function for firm 2 is given by
C(Q) = 4Q. What is the Nash-Equilibrium price? What are the profits
for each firm in equilibrium?

Two firms sell identical products and compete as Cournot
(price-setting) competitors in a market with a demand of p = 150 -
Q. Each firm has a constant marginal and average cost of $3 per
unit of output. Find the quantity each firm will produce and the
price in equilibrium.

Consider two firms, Firm A and Firm B, who compete as
duopolists. Each firm produces an identical product. The total
inverse demand curve for the industry is ? = 250 − (?? + ?? ). Firm
A has a total cost curve ?? (?? ) = 100 + ?? 2 . Firm B has a total
cost curve ?? (?? ) = 100 + 2??.
a. Suppose for now, only Firm A exists (?? = 0). What is the
Monopoly...

Consider a market with two identical firms. The market demand is
P = 26 – 2Q, where Q = q1 + q2. MC1 = MC2 = 2.
1. Solve for output and price with collusion.
2. Solve for the Cournot-Nash equilibrium.
3. Now assume this market has a Stackelberg leader, Firm 1.
Solve for the quantity, price, and profit for each firm.
4. Assume there is no product differentiation and the firms
follow a Bertrand pricing model. Solve for the...

In a homogenous good market two firms, A and B, are producing
with the same technology. Firm i’ s total cost function is C(qi) =
10 + 20qi, where i= A,B. The inverse demand function for the good
is given by P(qA+qB) = 150 – (qA+qB).
a) Assume that the firms choose simultaneously their quantities.
Find the market price and determine firm’s profits and consumer
surplus at that price.
b) If the two firms set simultaneously their prices, instead of...

Two firms compete in a market with inverse demand P = 120 − Q.
Firm 1 has cost function C(q1) = 20q1 and Firm 2 has cost function
C(q2) = 10q2. Solve for the Bertrand equilibrium in which firms
choose price simultaneously.

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