Assume there are 2 firms in a market that each simultaneously chooses a quantity. The 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 the P = 160 - 3Q. Also, each firm has constant marginal cost equal to 16. There are no fixed costs.
The marginal revenue of the 2 firms is given by:
- MR2 = 160 - 3q1 - 6q2.
- MR1 = 160 - 6q1 - 3q2
1. Write down the equations of the Best Response Function for each firm.
2. Make a graph for the Best Response Functions of each firm. Put them both on a single graph and find out Cournot-Nash Equilibrium.
3. Discuss how much output wills each firm form in Cournot-Nash equilibrium?
4. Explain what will be the market price of the good?
5. Discuss how much profit does each firm make?
6. Now assume that the 2 firms form a cartel and decide to maximize joint profits and crack profits evenly. They agree to each produce half of the profit maximizing quantity. Discuss how much outputs will each firm form?
7. Now assume that Firm 1 decides to cheat on the agreement. Assuming Firm 2 forms the quantity, write down the equation for the residual demand that faces Firm 1.
8. Discuss how much output should Firm 1 produce to maximize their profit?