Question

Two firms, a and b, compete in a market to sell homogeneous
products with inverse demand function P = 400 – 2Q where Q =
Q_{a} + Q_{b}. Firm a has the cost function
C_{a} = 100 + 15Q_{a} and firm b has the cost
function C_{b} = 100 + 15Q_{b}. Use this
information to compare the output levels, price and profits in
settings characterized by the following markets:

- Cournot
- Stackelberg
- Bertrand
- Collusion

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:
a, Cournot
b, Stackelberg
c, Bertrand
d, Collusion

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.

Consider a market with demand p = a − bq. There are two firms.
Both firms produce the same homogeneous product but have different
technologies. Firm A has a cost function cA(qA) = cA × qA and firm
B has a cost function cB(qB) = cB × qB. If necessary, assume that
cA < cB.
(a) Find the equilibrium quantities produced by each firm, the
total equilibrium quantity, and the equilibrium price as a function
of a, b, cA, and...

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?

Suppose that market ( inverse) demand is linear and given by
p(y) = 120-y
Two firms compete in this market. Firm 1 has cost function
ca(y) = 30y while its competitor, Firm B, has cost
cb(y) = y2
i. Suppose that firm 1 is acting alone and acting as a
monopolist. Find the market price and quantity sold assuring firm 1
maximizes its profits.
ii. Suppose that both firms are Cournot competitors. Find the
quantity produced by each firm and...

Two firms compete in a homogeneous product market where the
inverse demand function is P = 10 -2Q (quantity
is measured in millions). Firm 1 has been in business for one year,
while Firm 2 just recently entered the market. Each firm has a
legal obligation to pay one year’s rent of $0.7 million regardless
of its production decision. Firm 1’s marginal cost is $2, and Firm
2’s marginal cost is $6. The current market price is $8 and was...

Two identical firms compete as a Cournet duopoly.
The inverse market demand they face is P = 15 – 2Q.
The cost function for each firm is C(q) = 6Q.
Each firm will earn equilibrium profits of

Two firms compete in a homogeneous product market where the
inverse demand function is P = 10 -2Q(quantity is
measured in millions). Firm 1 has been in business for one year,
while Firm 2 just recently entered the market. Each firm has a
legal obligation to pay one year’s rent of $0.7 million regardless
of its production decision. Firm 1’s marginal cost is $2, and Firm
2’s marginal cost is $6. The current market price is $8 and was set...

Two firms compete in a homogeneous product market where the
inverse demand function is P = 10 -2Q(quantity is
measured in millions). Firm 1 has been in business for one year,
while Firm 2 just recently entered the market. Each firm has a
legal obligation to pay one year’s rent of $0.7 million regardless
of its production decision. Firm 1’s marginal cost is $2, and Firm
2’s marginal cost is $6. The current market price is $8 and was set...

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