Two companies (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function:
P = 10,000-Qa-Qb
where Qa and Qb are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are:
TCa = 500,000+200Qa+.5Qa^2
TCb = 200,000+400Qb+Qb^2
Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm's output will not change).
a) Determine the long run equilibrium output and selling price for each firm