Question

Consider the following market: Two firms compete in quantities, i.e., they are Cournot competitors. The firms produce at constant marginal costs equal to 20. The inverse demand curve in the market is given by P(q) = 260 − q.

a. Find the equilibrium quantities under Cournot competition as well as the quantity that a monopolist would produce. Calculate the equilibrium profits in Cournot duopoly and the monopoly profits.

Suppose that the firms compete in this market for an infinite number of periods. The discount factor (per period) is δ, δ ∈ (0, 1).

b. The firms would like to collude in order to restrict the total quantity produced to the monopoly quantity. Write down strategies that the firms could use to achieve this outcome.

c. For which values of δ is collusion sustainable using the strategies of subquestion (2)? [Hint: Think carefully about what the optimal deviation is.]

Answer #1

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.

Two firms compete in quantities. The firms are perfectly
symmetric, which makes the math easy! The inverse demand is given
by P= 80 − 0.5Q, where Q is total market demand. Each firm has
total costs c(q) = 20q.
a) Find the Cournot quantities, price, and profit of each
firm.
b) Now calculate the quantities, price and profit of each firm
if the two firms equally split the monopoly quantity (i.e. if they
collude).
c) Now calculate the quantities, price...

Two identical firms compete as a Cournot duopoly. The inverse
market demand they face is P = 128 - 4Q. The cost function for each
firm is C(Q) = 8Q. The price charged in this market will be
a. $32.
b. $48.
c. $12.
d. $56.

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 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

Consider a Cournot model with two firms, firm 1 and firm 2,
producing quantities q1 and q2, respectively. Suppose the inverse
market demand function is: P = 450 – Q where Q denotes the total
quantity supplied on the market. Also, each firm i = 1,2 has a
total cost function c(qi) = 30qi. a) What is the Nash equilibrium
of this Cournot game ? What is the market prices ? Compute each
firm’s profit and the industry profit. b)...

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...

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

Two firms compete with quantities as in Cournot. Each firm has a
marginal cost of $12. The industry demand is P=48-2Q. How much
output will each firm produce individually?

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