Question

Consider a Stackelberg game of quantity competition between two firms. Firm 1 is the leader and firm 2 is the follower. Market demand is described by the inverse demand function P = 1000 − 4Q. Each firm has a constant unit cost of production equal to 20.

a) Solve for Nash equilibrium outcome.

b) Suppose firm 2’s unit cost of production is c< 20. What value would c have so that in the Nash equilibrium the two firms, leader and follower, had the same market share?

Answer #1

Consider a Stackleberg game of quantity competition between two
firms. Firm 1 is the leader and Firm 2is the follower. Market
demand is described by the inverse demand function P=1000-4Q. Each
firm has a constant unit cost of production equal to 20.
Solve for the Nash equilibrium outcome in quantities in this
sequential game. What is the equilibrium price? What are the
profits for each firm?
Suppose that firm 2’s unit cost of production is c < 20.
Explain and...

Assume there are two firms in a Stackelberg game. Firm 1 chooses
its output first and Firm chooses its output after knowing what
Firm 1’s output is. Market demand is given by P = 1,000 – 4Q. Each
firm has identical marginal cost of 100. Determine the Nash
equilibrium for this game.

1. Consider the Leader-Follower game in which two firms each
choose a quantity qi to bring to the market, but in sequence. Firm
1 chooses q1, and then being informed of q1, firm w then chooses
q2. The market has an inverse demand function P(Q) = 100 - Q, where
Q = q1 + q2. Assume each firm has a constant marginal cost of
10.
(a) Solve by backward induction, state complete contingency
plans for both firms.
(b) Compute the...

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...

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 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....

Question 4 Consider the following game. Firm 1, the leader,
selects an output, q1, after which firm 2, the follower, observes
the choice of q1 and then selects its own output, q2. The resulting
price is one satisfying the industry demand curve P = 200 - q1 -
q2. Both firms have zero fixed costs and a constant marginal cost
of $60. a. Derive the equation for the follower firm’s best
response function. Draw this equation on a diagram with...

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. Firm 1 is the Stackelberg leader and firm
2 is the Stackelberg follower. The profit of the Stackelberg
follower is:
$864.
$576.
$432.
$288.
$1,152.

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.
Firm 1 is the Stackelberg leader and firm 2 is the Stackelberg
follower. The output of the Stackelberg follower is:
6.
12.
24.
48.
None of the above.

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...

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