Question

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 equilibrium quantity and price? What is Firm A’s profit?

b. Find the Nash Cournot equilibrium price and output level. What are the firms’ profits?

c. Find the equilibrium price and output level in the market if firm A acts as a Stackelberg leader. What are the firms’ profits?

d. Suppose that the two firms are able to form a cartel. Derive the output each firm will produce, the market price, and the total profit under the cartel solution.

e. Compare the Cournot, Stackelberg, and Cartel outcomes to the monopoly outcome you calculated in part a.

Answer #1

Suppose duopolists face the market inverse demand curve P = 100
- Q, Q = q1 + q2, and both firms have a constant marginal cost of
10 and no fixed costs. If firm 1 is a Stackelberg leader and firm
2's best response function is q2 = (100 - q1)/2, at the
Nash-Stackelberg equilibrium firm 1's profit is $Answer

The market demand function is Q=10,000-1,000p.
Each firm has a marginal cost of m=$0.16. Firm 1, the leader,
acts before Firm 2, the follower. Solve for the Stackelberg-Nash
equilibrium quantities, prices, and profits. Compare your solution
to the Cournot-Nash equilibrium.
The Stackelberg-Nash equilibrium quantities are:
q1=___________ units
and q2=____________units
The Stackelberg-Nash equilibrium price is:
p=$_____________
Profits for the firms are
profit1=$_______________
and profit2=$_______________
The Cournot-Nash equilibrium quantities are:
q1=______________units
and q2=______________units
The Cournot-Nash equilibrium price is:
p=$______________
Profits for the...

Consider two firms with the cost function TC(q) = 5q (constant
average and marginal cost,of 5), facing the market demand curve Q =
53 – p (where Q is the total of the firms’ quantities, and p is
market price).
a. What will be each firm’s output and profit if they make their
quantity choices simultaneously (as Cournot duopolists)?
b. Now suppose Firm 1 is the Stackelberg leader (its decision is
observed by Firm 2 prior to that firm’s decision)....

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....

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...

Suppose there are two firms in the market. Let Q1 be the output
of the first firm and Q2 be the output of the second. Both firms
have the same marginal costs: MC1 = MC2 = $5 and zero fixed costs.
The market demand curve is P = 53 − Q.
(a) (6 points) Suppose (as in the Cournot model) that each firm
chooses its profit-maximizing level of output assuming that its
competitor’s output is fixed. Find each firm’s reaction...

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

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.
9. Refer to SCENARIO 3. Suppose that the two firms are Cournot
rivals. Firm 1’s reaction function is: a. Q1 = 12 − Q2. b. Q1 = 12
− 0.25Q2. c. Q1 = 24 − 0.5Q2. d. Q1...

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...

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