Question

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 q2 on the vertical axis and q1 on the horizontal axis. Indicate the vertical intercept, horizontal intercept, and slope of the best response function. b. Determine the equilibrium output of each firm in the leader–follower game. Show that this equilibrium lies on firm 2's best response function. Compute profits in the equilibrium for firm 1 and 2. If the leader firm were a monopoly what would the equilibrium and output and price be? Would the monopoly price be higher or lower than in the Stackelberg case. c. Now let the two firms choose their outputs simultaneously. Compute the Cournot equilibrium outputs and industry price. Draw a graph with the Cournot best response functions. Label the intercepts. Also using your computations in part (a) and (b) label the Stackelberg and Cournot output levels. Who loses and who gains when the firms play a Cournot game instead of the Stackelberg one?

Answer #1

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 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 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...

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...

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...

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...

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...

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

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)...

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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