In business calculus, marginal cost is defined as which of the following?

• A. The total cost at output $q$: $TC=C\left(q\right)$
• B. The average cost per unit: $AC=\frac{C\left(q\right)}{q}$
• C. The derivative of the cost function with respect to output: $MC=\frac{dC}{dq}$
• D. The derivative of the cost function with respect to time: $MC=\frac{dC}{dt}$

Answer: (C)

Verified step by step guidance

1. Understand that the total cost function is given by \(\text{TC} = C(q)\), where \(q\) represents the quantity of output produced.
2. Recognize that the average cost per unit is calculated by dividing the total cost by the quantity, expressed as \(\text{AC} = \frac{C(q)}{q}\).
3. Recall that marginal cost represents the rate at which total cost changes as output changes, which means it is the derivative of the total cost function with respect to output.
4. Express the marginal cost mathematically as \(\text{MC} = \frac{dC}{dq}\), indicating how cost changes for a small change in output \(q\).
5. Note that marginal cost is not the derivative of cost with respect to time, so \(\text{MC} \neq \frac{dC}{dt}\); it specifically relates to changes in output quantity.