Suppose there are two firms in a market who each simultaneously choose a quantit

Question

Suppose there are two firms in a market who each simultaneously choose a quantitiy. 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=120-3Q. Also, each firm has constant marginal cost equal to 12. There are no fixed costs.

The marginal revenue of the two firms are given by:

MR1=120-6q1-3q2

MR2=120-3q1-6q2

A. How much output will each firm produce in the Courtnot-Nash 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 10 unites of output. How much output should Firm 1 produce in order to maximize profit?

Explanation / Answer

a) MR1=MC 120-6q1-3q2=12 2q1+q2= 36 and MR2 =MC 2q2+q1 = 36 solving we get q1=12 q2=12 b/ price = 120-72 = 48 profit for firm 1 = 48*12-12*12 = 432 for firm 2 = 48*12-12*12 = 432

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