The derivative, dAC(Q) / dQ = (1/Q₂) {Q(dC / dQ)

Question

The derivative, dAC(Q) / dQ = (1/Q₂) {Q(dC / dQ) - C(Q)}, illustrates that when

Quizplus · Accepted Answer

The derivative given shows that the relationship between output Q and average cost AC(Q) depends on the relationship between marginal cost MC(Q) and AC(Q). Since the first term in the derivative, Q(dC/dQ), represents the change in average cost due to changes in marginal cost, we can see that when MC(Q) < AC(Q), this term will be negative, indicating that average costs decrease as output increases. The second term, -C(Q), is always negative and represents the effect of fixed costs on average cost. Therefore, when MC(Q) < AC(Q), the derivative is negative and average costs decrease as output increases. Hence, option B is the correct choice.

The Derivative, DAC(Q) / DQ = (1/Q2) {Q(dC / DQ)