Question

Two firms, firm 1 & firm 2, in a Stackelberg sequential duopoly are facing the market demand given by P = 140 – 0.4Q, where P is the market price and Q is the market quantity demanded. Firm 1 has (total) cost of production given by C(q1) = 200 + 15q1, where q1 is the quantity produced by firm 1. Firm 2 has (total) cost of production given by C(q2) = 200 + 10q2, where q2 is the quantity produced by firm 2. The firms produce identical product. Firm 1 makes its choice of quantity first and credibly commits to it. Firm 2 observes firm 1’s choice, believes it to be credible, and then choses its own quantity. Find

18. Equilibrium quantity produced by firm 1 in the Cournot-Stackelberg equilibrium.

19. Equilibrium quantity produced by firm 2 in the Cournot-Stackelberg equilibrium.

20. Equilibrium profits earned by firm 1 in the Cournot-Stackelberg equilibrium.

21. Equilibrium profits earned by firm 2 in the Cournot-Stackelberg equilibrium.

Answer #1

A product is produced by two profit-maximizing firms in a
Stackelberg duopoly: firm 1 chooses a quantity q1 ? 0, then firm 2
observes q1 and chooses a quantity q2 ? 0. The market price is
determined by the following formula: P ( Q ) = 4 ? Q , where Q =
q(1) +q(2) . The cost to firm i of producing q i is Ci( qi ) =
q^2)i . (Note: the only difference between this problem and...

Two firms compete as a Stackelberg duopoly. Firm 1 is the market
leader. The inverse market demand they face is P = 62 - 2Q, where
Q=Q1+Q2. The cost function for each firm is C(Q) = 6Q. Given that
firm 2's reaction function is given by Q2 = 14 - 0.5Q1, the optimal
outputs of the two firms are:
a. QL = 9.33; QF = 9.33.
b. QL = 14; QF = 7.
c. QL = 6; QF = 3....

Consider an asymmetric Cournot duopoly game, where the two firms
have different costs of production. Firm 1 selects quantity q1 and
pays the production cost of 2q1 . Firm 2 selects quantity q2 and
pays the production cost 4q2 . The market price is given by p = 12
− q1 − q2 . Thus, the payoff functions are u1 (q1,q2) = (12 − q1 −
q2 ) q1 − 2q1 and u2 ( q1 , q2 ) = (12...

Consider a duopoly with two firms with the cost functions:
Firm 1: C1(q1)=5q1
Firm 2: C2(q2)=5q2
The firms compete in a market with inverse demand
p = 300 - 8Q
where Q=q1+q2. The firms compete in a
Cournot fashion by choosing output simultaneously.
What is the Nash-Cournot equilibrium output of firm 1? Round to
nearest .1

N firms, in a Cournot oligopoly are facing the market demand
given by P = 140 – 0.4Q, where P is the market price and Q is the
market quantity demanded. Each firm has (total) cost of production
given by C(qi) = 200 + 10qi, where qi is the quantity produced by
firm i (for i from 1 to N).
New firms would like to enter the market if they expect to make
non-negative profits in this market; the existing...

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...

There is a Cournot duopoly competition between Firm 1 and Firm
2. The inverse demand function is given by P(Q)=100-q, where
Q=q1+q2 and qi denotes the quantity produced by firm i for all iÎ
{1, 2} and the cost function is given by ci(qi)=10qi. Describe this
problem as a normal-form game. Find pure-strategy Nash Equilibria
for both firms.

Suppose there are two firms in a market who each simultaneously
choose a quantity. Firm 1’s quantity is q1, and firm 2’s
quantity is q2. Therefore the market quantity is Q =
q1 + q2. The market demand curve is given by
P = 160 - 2Q. Also, each firm has constant marginal cost equal to
10. There are no fixed costs.
The marginal revenue of the two firms are given by:
MR1 = 160 – 4q1 – 2q2
MR2...

Two firms in a Cournot duopoly produce quantities Q 1 and Q 2
and the demand equation is given as P = 80 - 2Q 1 - 2Q 2. The
firms' marginal cost are identical and given by MCi(Qi) = 4Qi,
where i is either firm 1 or firm 2.
a. Q1 = 80 - 4Q2 and Q2 = 80 - 4Q1.
b. Q1 = 10 - (1/4)Q2 and Q2 = 10 - (1/4)Q1.
c. Q1 = 80 - 2Q2...

Answer the following question(s) based on this information: Two
firms in a Cournot duopoly produce quantities Q 1 and Q 2 and the
demand equation is given as P = 80 - 2Q 1 - 2Q 2. The firms'
marginal cost are identical and given by MCi(Qi) = 4Qi, where i is
either firm 1 or firm 2. Based on this information firm 1 and 2's
respective optimal Cournot quantity will be: a. Q1 = 40 and Q2 = 40...

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