Question

Which of the following formula is correct for calculating marginal cost?

• A. \( MC_n = TFC_n - TFC_{n-1} \)
• B. \( MC_n = AC_n - AC_{n-1} \)
• C. \( MC_n = AVC_n - AVC_{n-1} \)
• D. \( MC_n = TC_n - TC_{n-1} \)

Hint:

Remember that "marginal" in economics always refers to the change associated with one additional unit. So, Marginal Cost is the change in Total Cost for one more unit.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Marginal Cost (MC) is the additional cost incurred in the production of one more unit of a good or service.

Step 2: Key Formula or Approach:
The formula for marginal cost is the change in total cost (\(\Delta TC\)) divided by the change in the number of units produced (\(\Delta Q\)). When producing just one more unit (\(\Delta Q = 1\)), the formula simplifies.
\[ MC = \frac{\Delta TC}{\Delta Q} \]

Step 3: Detailed Explanation:
To find the marginal cost of the \(n^{th}\) unit, we subtract the total cost of producing the previous \(n-1\) units from the total cost of producing \(n\) units.
This is represented by the formula:
\[ MC_n = TC_n - TC_{n-1} \] Let's analyze the other options: \begin{itemize} \item (A) is incorrect because Total Fixed Cost (TFC) does not change with output, so its difference would be zero. \item (B) and (C) are incorrect as they represent the change in average costs, not the marginal cost itself. \end{itemize}

Step 4: Final Answer:
The correct formula for calculating the marginal cost of the \(n^{th}\) unit is \( MC_n = TC_n - TC_{n-1} \). Thus, option (D) is correct.