Question
Find the output level at which average cost is minimum.
Answer :
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For a firm, the average cost (AC) is the cost incurred per unit of output. It is obtained by dividing total cost by the level of output. If (Q) represents the output level and (C(Q)) represents the total cost, then [ AC=\frac{C(Q)}{Q} ] To find the output level at which average cost is minimum, we differentiate the average cost function with respect to output and equate the derivative to zero. [ \frac{d(AC)}{dQ}=0 ] Since [ AC=\frac{C(Q)}{Q} ] using the quotient rule, [ \frac{d(AC)}{dQ} ================ \frac{Q\frac{dC}{dQ}-C(Q)}{Q^2} ] For average cost to be minimum, [ \frac{Q\frac{dC}{dQ}-C(Q)}{Q^2}=0 ] Since (Q^2\neq0), [ Q\frac{dC}{dQ}-C(Q)=0 ] Therefore, [ \boxed{Q\frac{dC}{dQ}=C(Q)} ] or [
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