Question

Suppose that two firms compete in the same market producing homogenous products with the following inverse demand function:

*P=1,000-(**Q**1**+**Q**2**)*

The cost function of each firm is given by:

*C**1**=4**Q**1*

*C**2**=4**Q**2*

- 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 as a profit-maximizing single firm. What are the equilibrium market price, total industry output, and each firm’s profits?

Answer #1

b)

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.

SCENARIO 3: Consider an industry consisting of two firms
producing an identical product. The inverse market demand equation
is P = 100 − 2Q. The total cost equations for firms 1 and 2 are TC1
= 4Q1 and TC2 = 4Q2, respectively.
Refer to SCENARIO 3. Suppose that the two firms are Bertrand
rivals. The equilibrium level
of output for firm 1 is:
a. 8.
b. 10.
c. 12.
d. 24.
e. None of the above.

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

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.

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?

SCENARIO 3: Consider an industry consisting of two firms
producing an identical product. The inverse market demand equation
is P = 100 − 2Q. The total cost equations for firms 1 and 2 are TC1
= 4Q1 and TC2 = 4Q2, respectively.
Refer to SCENARIO 3. Suppose that the two firms are Cournot
rivals. The equilibrium level
of output for firm 1 is:
a. 8.
b. 16.
c. 24.
d. 32.
e. None of the above.

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

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...

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