I am confused on this question. Can someone help me solve it? Consider the marke

Question

I am confused on this question. Can someone help me solve it?

Consider the market for steel which is made of two identical firms (U.S. Steel and Bethlehem) which have identical marginal costs of $5. The demand for steel is Q^D = 80 - 4P Suppose the firms compete ala Cournot. What is the equilibrium price and quantity for each firm? Suppose the firms acted as a collusive cartel. What is the equilibrium price and quatinty for the combined firms? Suppose the firms compete ala Bertrand. What is the equilibrium price and quantity for each firm?

Explanation / Answer

Demand funciton: P=20-0.25Q = 20-0.25(Q1+Q2) = 20-0.25Q1-0.25Q2

MR1 = 20-0.5Q1-0.25Q2

MR2 = 20-0.25Q1-0.5Q2

a)

MC1 = MC2 = 5

When firms act as Cournot duopolists,

Set MR1=MC1 and MR2=MC2

That is, 20-0.5Q1-0.25Q2=5

Q1=30-0.5Q2

Q2=30-0.5Q1

Substitute the 2 equations into each other to get the values of Q1 and Q2

This comes out to be: Q1*=Q2*=20 and P*=10

b)

Under collusion.

Demand function becomes: 2Q=80-4P or, P=20-0.5Q

MR=20-Q

MC=5

Equate MR=MC

This makes 20-Q=5

Q*=15, thus Q1=Q2=150/2=7.5 units and P=$16.25

c)

Under Bertrand, instead of Q=Q1+Q2, make P=P1+P2 and repeat the steps as part (a)

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