### Each firm produce in the cournot-nash equilibrium

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Suppose there are two firms in a market that 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 = 160 - 3Q. Also, each firm has constant marginal cost equal to 16. There are no fixed costs.

The marginal revenue of the two firms are given by:

MR1 = 160 - 6q1 - 3q2
MR2 = 160 - 3q1 - 6q2.

A)Write the equations of the Best Response Function for each firm.

B)  Graph the Best Response Functions of each firm. Put them both on a single graph and identify the Cournot-Nash Equilibrium. Be sure to label your graph carefully and accurately.

C)  How much output will each firm produce in the Cournot-Nash equilibrium?

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

E)How much profit does each firm make?

F) Now suppose that the two firms form a cartel and decide to maximize joint profits and split the profits evenly. They agree to each produce half of the profit maximizing quantity. How much output will each firm produce? (Hint: If the two firms form a cartel, they will produce together the same amount of output as a monopolist would produce.)

G) Now suppose that Firm 1 decides to cheat on the agreement. Assuming Firm 2 produces the quantity given in F), write the equation for the residual demand that faces Firm 1.

H) If Firm 1 expects Firm 2 to produce the amount of output in F), how much output should Firm 1 produce to maximize their profit?

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