1. (30 points) Suppose a monopolist faces the following demand curve:P = 596 â 6Q. If the long run marginal cost of pr...
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1. (30 points) Suppose a monopolist faces the following demand curve:
P = 596 â 6Q. If the long run marginal cost of production is constant and equal to $20.
a) (5 points) What is the monopolistâs profit maximizing level of output?
b) (5 points) What price will the profit maximizing monopolist charge?
c) (5 points) How much profit will the monopolist make if she maximizes her profit?
d) (5 points) What would be the value of consumer surplus if the market were perfectly
competitive?
e) (5 points) What is the value of the deadweight loss when the market is a monopoly?
f) (5 points) What is the value of the Lerner Index for this monopoly?
2. (30 points) Suppose there are two firms in a market who each simultaneously choose a
quantity. Firm 1âs quantity is q1, and firm 2âs quantity is q2. Therefore the market quantity is Q
= q1 + q2. The market demand curve is given by P = 100 â 4Q. Also, each firm has constant
marginal cost equal to 28. There are no fixed costs.
The marginal revenue of the two firms are given by:
MR1 = 100 â 8q1 â 4q2
MR2 = 100 â 4q1 â 8q2.
A) (6 points) How much output will each firm produce in the Cournot equilibrium?
B) (6 points)What will be the market price of the good?
C) (6 points) What is the deadweight loss that results from this duopoly?
D) (6 points) How much profit does each firm make?
E) (6 points) Suppose Firm 2 produced 10 units of output. How much output should Firm 1
produce in order to maximize profit? (Hint: Use Firm 1âs Reaction Function)
3. (28 total points) Suppose that two players are playing the following game. Player 1 can
choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are
given in the following table:
Player 1
Top
Bottom
Left
6
7
Player 2
Right
5
9
4
5
4
3
where the number on the left is the payoff to Player A, and the number on the right is the payoff
to Player B.
A) (4 points) Does player 1 have a dominant strategy, and if so what is it?
B) (4 points) Does player 2 have a dominant strategy and if so what is it?
C) (2 point each) For each of the following strategy combinations, write TRUE if it is a Nash
Equilibrium, and FALSE if it is not:
i) Top/Left
ii) Top/Right
iii) Bottom/Left
iv) Bottom Right
D) (4 points) What is Player 1âs maximin strategy?
E) (4 points) What is player 2âs maximin strategy?
F) (4 points) If the game were played with Player 1 moving first and player 2 moving second,
using the backward induction method discussed in the class notes, what strategy will each player
choose?
P = 596 â 6Q. If the long run marginal cost of production is constant and equal to $20.
a) (5 points) What is the monopolistâs profit maximizing level of output?
b) (5 points) What price will the profit maximizing monopolist charge?
c) (5 points) How much profit will the monopolist make if she maximizes her profit?
d) (5 points) What would be the value of consumer surplus if the market were perfectly
competitive?
e) (5 points) What is the value of the deadweight loss when the market is a monopoly?
f) (5 points) What is the value of the Lerner Index for this monopoly?
2. (30 points) Suppose there are two firms in a market who each simultaneously choose a
quantity. Firm 1âs quantity is q1, and firm 2âs quantity is q2. Therefore the market quantity is Q
= q1 + q2. The market demand curve is given by P = 100 â 4Q. Also, each firm has constant
marginal cost equal to 28. There are no fixed costs.
The marginal revenue of the two firms are given by:
MR1 = 100 â 8q1 â 4q2
MR2 = 100 â 4q1 â 8q2.
A) (6 points) How much output will each firm produce in the Cournot equilibrium?
B) (6 points)What will be the market price of the good?
C) (6 points) What is the deadweight loss that results from this duopoly?
D) (6 points) How much profit does each firm make?
E) (6 points) Suppose Firm 2 produced 10 units of output. How much output should Firm 1
produce in order to maximize profit? (Hint: Use Firm 1âs Reaction Function)
3. (28 total points) Suppose that two players are playing the following game. Player 1 can
choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are
given in the following table:
Player 1
Top
Bottom
Left
6
7
Player 2
Right
5
9
4
5
4
3
where the number on the left is the payoff to Player A, and the number on the right is the payoff
to Player B.
A) (4 points) Does player 1 have a dominant strategy, and if so what is it?
B) (4 points) Does player 2 have a dominant strategy and if so what is it?
C) (2 point each) For each of the following strategy combinations, write TRUE if it is a Nash
Equilibrium, and FALSE if it is not:
i) Top/Left
ii) Top/Right
iii) Bottom/Left
iv) Bottom Right
D) (4 points) What is Player 1âs maximin strategy?
E) (4 points) What is player 2âs maximin strategy?
F) (4 points) If the game were played with Player 1 moving first and player 2 moving second,
using the backward induction method discussed in the class notes, what strategy will each player
choose?
