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Kinked Demand Curve / Oligopolistic market

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Subject: Kinked Demand Curve / Oligopolistic market
Details: The kinked demand curve in an oligopolistic market is represented by the following:
P = 100 - Q and P = 120 - 2*Q

The oligopoly firms have constant marginal costs at MC = 40

A. Determine the profit maximizing level of output.
B. Compute the profit maximizing price.
C. Calculate the upper and lower limits within which marginal cost may vary without affecting the profit maximizing output or the price.

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Please refer to the attachment.

A. Determine the profit maximizing level of output.

The two parts of demand curve intersects at the point where:
P = 100 - Q
P = 120 - 2*Q
(1) - (2): 0 = -20 + Q,
then Q = 20
and P =100 - Q = 80
which means
if Q>= 20, the market demand is P = 120 - 2*Q
if Q< 20, the market demand is P = 100-Q

then ...

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