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An Oligopoly Firm Faces a Kinked Demand Curve with Segments

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An oligopoly firm faces a kinked demand curve with segments given by: P = 100 - Q and P = 120 - 2Q, where P is the price and Q is the quantity demanded. The firm has a constant marginal cost, MC of $45.
(a) Determine the firm's profit-maximizing level of output and price.
(b) Calculate the (upper and lower) limits within which marginal cost may vary without affecting either the profit-maximizing output or the price.

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The upper and lower limits are computed ...

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