Two identical firms compete simultaneously as a Cournot duopoly. The market demand is P = 200 - 2~ where Q stands for the combined output of the two firms, Q = q, + q2. The total cost function for firm 1 is C1 = 60 + 16ql. The total cost function for firm 2 is C2 = 50 + 24q2.
a) Derive the best-response functions for these firms expressing what ql and q2 should be in this Cournot oligopoly.
b) Find the optimal quantity for each firm, the market price, and the profit each firm earns in this Cournot oligopoly.
c) Now suppose that with the same market demand and cost conditions as above, Firm 1 may bring its product to market earlier and choose its output level earlier than Firm 2 by spending an additional investment of 200. Explain carefully if Firm 1 will benefit from being first to market.
d) Should firm 2 try to undercut Firm 1 on price and try to gain additional sales by reducing its price below Firm l's level? Explain.