Two Companies (A and B) Are Duopolists That Produce Identical

Essay

Two companies (A and B) are duopolists that produce identical products. Demand for the products is given by the following demand function:
P = 10,000 - Q_A- Q_B
where Q_A and Q_B are the quantities sold by the respective firms and P is the selling price.Total cost functions for the two companies are:
TC_A = 500,000 + 200Q_A + .5Q_A²
TC_B = 200,000 + 400Q_B + Q_B²
Assume that the two firms act independently as in the Cournot model (that is, each firm assumes that the other firm's output will not change). Determine the long-run equilibrium output and selling price for each firm.