An industry is composed of two firms who act as Cournotduopolists.

1. An industry is composed of two firms who act as Cournotduopolists. Suppose the demand curve for the good is: Q=100-P and the total cost function is TC=1,000,000+15q.

A. Determine the reaction functions for each duopolist.
B. Determine the profit maximizing price and quantity for a Cournot-Nash equilibrium.
C. Draw the picture of the reaction functions, and the point where equilibrium takes place.
D. If the duopolists collude and act as a monopolist, what amount will they produce?
E. Draw the contract curve which illustrates their choices for (d) above.



2. Dan decides to produce a new blue colored cola, SKY, designed to compete with the major brands of coke and pepsi. Analysts have determined that the demand curve for SKY cola is P=102-2Q, where P is the price and Q is the quantity (in crates) of cola. The total cost for producing the cola is given by TC=700+2Q+0.5Q^2

A. Dan’s company is currently producing 15 crates of SKY cola per day and selling them for $57.50 per crate. Chris, the company auditor, wants to know if it is maximizing profits. Is it? Explain with numerical evidence.

B. How much excess capacity is SKY working with (excess capacity is that which falls below minimum AC)?




3. Suppose that the demand equations of women and men for admission to basketball games are given by
Pw:price charged to women. Pm: price charged to men
qw, qm: quantity of tickets for women, men respectively

Pw=6-(1/8000)qw
Pm=10-(1/8000_qm

Moreover, suppose that the total seating capacity of Madison Square Garden is fixed at 56,000. If the ticket sellers practice third degree price discrimination and would like to fill the Garden,
A. What prices should men and women be charged for a ticket?
B. Can you determine the elasticity of demand for each market?


4. Suppose the total cost function of large post officeis TC=1,200+0.10Q where TC is the total cost per day and Q is the quantity of mail. The demand function is Q=40,000=100,000P where Q is the quantity of mail and P is the price per piece of mail.

A. SET up the problem to show how you would solve for a situation in which the post office would break even. (DO not solve the problem, just set it up.)

B. What price should the post office charge in order to maximize profits?

C. Suppose government forces the post office to operate at the perfectly competitive price. What would that price and output be? Would the post office earn a profit or loss?

5. A monopolist has its domestic market protected by law from foreign competition. The domestic demand curve for its product is given by:

Pdom=120-Qd/10

The firm can also export to the world market, where the price is Px=80 independent of the quantity, Qx exported. The monopolists marginal cost curve is

MC=50+Q/10 where Q=Qx+Qd

A. Find the profit maximizing output, Q and its division between the two markets.

B. Compare the prices and demand elasticity’s in the domestic versus the world market.