4.Assume that two companies (A and B) are duopolist who produce identical products. Demand for the products is given by the following linear demand function: P=200-Qa -Qb

where Qa and Qb are the qualities sold by the respective firms and P is the selling price. Total cost functions for the two companies are:

TCa=1500+55Qa+Qa^(2)

TCb=1200+20Qb+2Qb^(2)

Assume that the firms act independently as in the Cournot model (that is, 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

(B) determine Firm a, Firm b, and total industry profits at the optimal solution found in part(a)

5.Consider exercise 4 (above). Assume that the firm for m a cartel to act as a monopolist and maximize total industry profit (sum of Firm A and Firm B profits)

(A) determine the optimum output and selling price for each firm

(B) determine Firm A and B, and total industry profits at the optimal solution found in part (A)

(C) show that the marginal costs of the two firms are equal at the optimal solution found in part (A)