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How much output will each firm produce in the cournot

Suppose there are two firms in a market who each simultaneously choose a quantity. Firm 1's quantity is q₁, and firm 2's quantity is q₂. Therefore the market quantity is Q = q₁ + q₂. The market demand curve is given by P = 130 - Q. Also, each firm has constant marginal cost equal to 25. There are no fixed costs.

The marginal revenue of the two firms is given by:

MR₁ = 130 - 2q₁ -q₂
MR₂ = 130 - q₁ - 2q₂.

A) How much output will each firm produce in the Cournot equilibrium?

B) What will be the market price of the good?

C) What is the deadweight loss that results from this duopoly?

D) How much profit does each firm make?

E) Suppose Firm 2 produced 20 units of output. How much output should Firm 1 produce in order to maximize profit?

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