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.
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.