Question

Consider a market with two identical firms. The market demand is P = 26 – 2Q, where Q = q1 + q2. MC1 = MC2 = 2.

1. Solve for output and price with collusion.

2. Solve for the Cournot-Nash equilibrium.

3. Now assume this market has a Stackelberg leader, Firm 1. Solve for the quantity, price, and profit for each firm.

4. Assume there is no product differentiation and the firms follow a Bertrand pricing model. Solve for the Bertrand equilibrium and calculate output, price, and profit for each firm.

Answer #1

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...

Consider a market with 2 identical firms (a and b). The market
demand is P = 14 - Q
where Q = Qa + Qb. For both firms AC=MC= 2.
A. Solve for the Cournot-Nash reaction functions of each
firm.
B. Solve for the Cournot- Nash equilibrium. Solve for Q, Qa, Qb,
Price, and each firms profit.
C. Compare the Cournot-Nash equilibrium with perfect
competition, and monopoly (you can refer to your results from
question 2, if you’ve already done...

Consider a market with 2 identical firms (a and b). The market
demand is P = 14 - Q
where Q = Qa + Qb. For both firms AC=MC= 2.
A. Solve for the Cournot-Nash reaction functions of each
firm.
B. Solve for the Cournot- Nash equilibrium. Solve for Q, Qa, Qb,
Price, and each firms profit.
C. Compare the Cournot-Nash equilibrium with perfect
competition, and monopoly (you can refer to your results from
question 2, if you’ve already done...

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...

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...

1) Suppose the monopoly has broken up into two separate
companies. The demand function is P=105-3Q. The firms do not
collude and the firms have identical marginal cost functions
(MC1=MC2=40.). Also assume they are Cournot duopolists. Determine
the quantity and price of each firm.
Quantity for firm 1: ________
Quantity for firm 2: ________
Price in each market: $_________
2) Now assume these firms are acting like Bertrand duopolists. What
quantity will each firm produce and what will be the...

Suppose a drug manufacturer sells a new drug for twitchy feet.
The market demand curve for the drug is P=110-2Q, where P is the
market price and Q is the market quantity. Also suppose the
marginal cost for manufacturing is 10/ unit.
A) Assuming the firm is an unregulated monopolist, what
quantity and price should the firm offer?
Quantity =.
Price = $
B) Now suppose, the manufacturer has identified two separate
classifications of cusC) Suppose the monopoly has broken...

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...

Consider a market with two firms whose products are identical.
The market demand curve is p = a − bq where a > 0 and b > 0,
and where q = q1 + q2. Firm i’s profits are πi(q1, q2) = pqi − cqi
. Assume that the firms move in sequence, with firm 1 choosing q1
first, and then firm 2 choosing q2; however, assume firm 2 observes
q1 before choosing q2.
(a) What is a Nash equilibrium...

2. Consider two identical firms in a Cournot competition. The
market demand is P = a – bQ. TC1 = cq1 = TC2 = cq2 . a. Find the
profit function of firm 1. b. Maximize the profit function to find
the reaction function of firm 1. c. Solve for the Cournot-Nash
Equilibrium. d. Carefully discuss how the slope of the demand curve
affects outputs and price.

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