In economics, marginal cost is defined as the derivative of total cost with respect to quantity produced. If total cost is $C\left(q\right)$, which expression represents marginal cost?

• A. $MC\left(q\right)=\frac{dq}{dC}$
• B. $MC\left(q\right)=C\left(1\right)-C\left(0\right)$
• C. $MC\left(q\right)=\frac{C\left(q\right)}{q}$
• D. $MC\left(q\right)=\frac{dC}{dq}$

Answer: (D)

Verified step by step guidance

1. Understand that marginal cost (MC) is defined as the rate of change of total cost (C) with respect to the quantity produced (q). This means MC is the derivative of the total cost function C(q) with respect to q.
2. Recall the notation for derivatives: the derivative of C with respect to q is written as \(\frac{dC}{dq}\), which represents how cost changes as quantity changes.
3. Express the marginal cost mathematically as \(MC(q) = \frac{dC}{dq}\), indicating that MC is a function of q derived from the total cost function C(q).
4. Recognize that this derivative is different from average cost or difference quotients; it specifically measures the instantaneous rate of change, not an average over an interval.
5. Therefore, the correct expression for marginal cost is \(MC(q) = \frac{dC}{dq}\), which matches the definition of marginal cost in economics.