Question

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?

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, 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 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.

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...

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.

Consider two firms competing to sell a homogeneous product by
setting price. The inverse demand curve is given by P = 6 − Q. If
each firm's cost function is Ci(Qi) = 2Qi, then consumer surplus in
this market is:

Suppose there are 2 firms in a market. They face an aggregate
demand curve, P=400-.75Q. Each firm has a Cost Function, TC=750+4q
(MC=4). a. If the 2 firms could effectively collude, how much would
each firm produce? What is aggregate output? What is price? What
are the profits for each firm? Provide a graph illustrating your
answer. b. Suppose instead that the firms compete in Quantity
(Cournot Competition). Calculate each firm's best-response function
using the formulae provided in the book....

Suppose there are two firms operating in a market. The firms
produce identical products, and the total cost for each firm is
given by C = 10qi, i = 1,2, where qi is the quantity of output
produced by firm i. Therefore the marginal cost for each firm is
constant at MC = 10. Also, the market demand is given by P = 106
–2Q, where Q= q1 + q2 is the total industry output.
The following formulas will be...

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 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.

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