In the market for good X, two firms supply differentiated products and their monthly demand functions are as follows:
Firm 1: 9₁ = 400-3p₁ + P₂
Firm 2: 92 = 400-3p₂ + P₁
The marginal cost of production for both firms is $60 per unit, and there are no fixed costs.
a) Suppose that the two firms operate according to a Cournot duopoly model with zero conjectural variation. Derive the reactions function for Firm 1 and Firm 2, each.
b) What is the output level, price and profit for each firm at the Cournot-Nash equilibrium?
c) Now, suppose that Firm 1 is the Stackelberg leader and Firm 2 is the follower. What is the output level, price and profit for each firm at the Stackelberg equilibrium?
d) Now, suppose that there are no barriers to entry into the market for good X, and threatened competition from potential entrants forces both firms to set prices that would apply under perfect competition. What is the output level, price and profit for each firm at equilibrium?