A homogeneous products duopoly faces a market demand function given by P = 300 - 3Q, where Q = Q1 + Q2. Both firms have a constant marginal cost MC = 100.
a) What is Firm 1's profit-maximizing quantity, given that Firm 2 produces an output of 50 units per year? What is Firm 1's profit-maximizing quantity when Firm 2 produces 20 units per year?
b) Derive the equation of each firm's reaction curve and then graph these curves.
c) What is the Cournot equilibrium quantity per firm and price in this market?
d) What would the equilibrium price in this market be if it were perfectly competitive?
e) What would the equilibrium price in this market be if the two firms colluded to set the monopoly price?
f) What is the Bertrand equilibrium price in this market?
g) What are the Cournot equilibrium quantities and industry price when one firm has a marginal cost of 100 but the other firm has a marginal cost of 90?