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 firms form a cartel to maximize total industry profits (sum of Firm A and Firm B profits). Determine the optimum output and selling price for each firm.