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A Monopolists inverse demand function is ?? = 360 - 3??. The company can produce output at two facilities; the cost of producing in plant 1 is ??1 = 400 + 3?? 2 and the cost of producing in plant 2 is ??2 = 500 + ?? 2 .
a. If only firm 1 is owned by the firms then what is the optimal quantity the monopoly should sell in the market and at what price? What is the amount of profit it can earn from the market?
b. If both firms are owned by the monopolist then provide the equation for the monopolist's marginal revenue function (Note: ?? = ??1 + ??2 in this case)
c. Determine the profit maximizing level of price and output for each facility.
d. From profit perspective should the monopoly produce only in firm 1 or in both firms?
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