Question

Oligopoly and Monopolistic Competition. Please show work.

The local steel market has an inverse demand function for a metric ton of steel: P = 1450 - Q

Donald and Justin are the only two steel miners in the market who sell metric tons of steel. They both have a constant marginal and average cost of $100 per metric ton. Both farmers simultaneously determine the quantity of steel they ar going to bring to the market. They do not conger beforehand, and the price is determined by the market after they arrive at the steel exchange market.

a. What are Donald and Justin's best response functions?

b. What are the Cournot equilibrium quantities and the market price?

c. What would be the price that Donald and Justin would charge if they choose to collude?

d. Will the collusion agreement last? Why or why not? (Be sure to show your reasoning)

e. Explain in detail how a monopolistically competitive firm can set its price greater than the marginal cost.

Answer 1

A) P=1450-q1-q2

Let Justin Producer 1 and Dustin producer 2

MR1=1450-2q1-q2

MC=100

MR1=MC1

1450-2q1-q2=100

Q1=675-0.5q2{ best response function of Justin}

By symmetry,.

Q2=675-0.5q1{ best response function of Dustin}

B) putting q1 into q2,

Q2=675-0.5(675-0.5q2)

Q2=0.5*675/0.75=450

Q1=675-0.5*450=450

Q=2*450=900

P=1450-900=550

C) They will produce monopoly output and charge monopoly price.

MR=1450-2q

MC=100

1450-2q=100

Q=1350/2=675

P=1450-675=775

D)

Q1=Q2=675/2=337.5

Given q1=337.5

Best move for Dustin,

Q2=675-0.5*337.5=506.25

So each firm has INCENTIVE to increase their output and earn more Profit. That is why collusion won't last long.