ECO- Suppose A Monopolist Faces The Following Demand Curve

1.   Suppose a monopolist faces the following demand curve:

 

P = 596 – 6Q.  If the long run marginal cost of production is constant and equal to $20.

 

a) (5 points) What is the monopolist’s 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 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 = 100 – 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 – 8q₁ – 4q₂

·           MR₂ = 100 – 4q₁ – 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 1’s 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:

 

 

 

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 1’s maximin strategy?

E) (4 points) What is player 2’s 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?