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

Marketing Jan 15, 2021

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 _____

Expert Solution

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.,

, which is the best-response function for producer 1.

Similarly, we can derive the best response function for producer 2, which is:

Solving these system of equations, we have:

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