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Answer on Microeconomics Question for michelle corbett

Question #25424
A manufacturing firm produces output using a single plant. The relevant cost function is C=500+5Q^. the demand curve is P=600-5Q. Find the level of output at which average cost is minimized.
Expert's answer
The level of output at which average cost is minimized can be found in the point, where MR = MC = Pd.
MC = C' = (500+5Q^2)' = 10Q.
Pd = 600 - 5Q
MC = Pd
10Q = 600 - 5Q
15Q = 600
Q = 40 units of output.
So, when Q = 40, the average cost is minimized and profit is maximized.

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