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A Cartel Is Maximizing Profit at a Price of $38

Question 72

Essay

A cartel is maximizing profit at a price of $38.12 per ton for its product. The demand curve for the members' product is given by the following equation:
Q = 216,200 - 5000P, so that MR = 43.24 - .0004Q
Suppose that there are three firms in the cartel with the following respective marginal cost functions:
MC1 = 3 + .003Q1
MC2 = 2 + .003875Q2
and
MC3 = 2.6 = .004Q3
How much output should be allocated to each cartel member? Assume that Q is yearly output in tons and that MC is marginal cost per ton)

Correct Answer:

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Total cartel output is found at:
Q = 216...

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