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Homework answers / question archive / What is the homogeneous-good duopoly Cournot equilibrium if the market demand function is Q = 4000 - 1,000p, and each firm's marginal cost is $0
What is the homogeneous-good duopoly Cournot equilibrium if the market demand function is Q = 4000 - 1,000p, and each firm's marginal cost is $0.28 per unit?
The Cournot-Nash equilibrium occurs where
q1 equals _____
and q2 equals _____
The equilibrium output is
First we rewrite the demand function as follows:
Now consider producer 1, who chooses quantity to maximize profit, taking as given . The total revenue is
and the marginal revenue is:
To maximize profit, producer 1 sets marinal revenue to marginal cost, i.e.,
Similarly, we can derive the best response function for producer 2, which is:
Solving these system of equations, we have:
