Two firms compete in a market to sell a homogeneous product with inverse demand

Question

Two firms compete in a market to sell a homogeneous product with inverse demand function P = 600 – 3Q. Each firm produces at a constant marginal cost of $300 and has no fixed costs. Use this information to compare the output levels and profits in settings characterized by Cournot, Stackelberg, Bertrand, and collusive behavior.

COURNOT OUTCOME

What is the Cournot output for each firm?

What are the Cournot profits for each firm?

STACKELBERG OUTCOME

What is the Stackelberg leader output?

What is the Stackelberg follower output?

What are the Stackelberg leader’s profits?

What are the Stackelberg follower’s profits?

BERTRAND OUTCOME

What is the Bertrand market-level output?

What are the Bertrand profits for each firm?

COLLUSIVE OUTCOME

What is the collusive market-level output?

What are the collusive industry-level profits?

Explanation / Answer

1= 2 = $3,333.33

l=$3750, f = $1875

Model Output Profit Cournot outcome Q1=Q2=33.33 units

1= 2 = $3,333.33

Stackleberg Outcome Ql=50 units, Qf= 25 units

l=$3750, f = $1875

Bertrand Outcome market output = 100 unit zero Collusiove Outcome Market output = 50 units industry profit = $7500

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