Application exercise. Suppose that two firms, A and B, are duopolists in a market, and that they produce qA and qB units, respectively, of a homogeneous good. Also suppose that the industry demand for the good is given by P = f (qA,qB) = 80−qA−qB, where P denotes market price; and that the total cost of producing the good by firm A is CA = 5qA and the total cost of producing the good by firm B is CB = 0.1q2 B. Suppose again that the two firms decided to enter into collusion and form a monopoly. Find the quantities that firms A and B (i.e. qA and qB) should produce so that the monopoly profit will be maximum. Also find the maximum monopoly profit and the market price.
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