Question

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.

Answer 1

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.