Question

Which of the following is the correct formula to calculate 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:

Marginal cost is the change in total cost when one more unit is produced. It helps firms assess whether increasing production is profitable.

Answer 1

The Correct Option is D

Step 1: Understanding Marginal Cost:
Marginal cost (MC) is the additional cost incurred by producing one more unit of output. It plays a crucial role in economics, especially in decision-making regarding optimal production levels. It helps firms determine the cost-effectiveness of producing additional units and whether it is worth expanding output.
Step 2: Deriving the Formula for Marginal Cost:
Marginal cost is derived from the change in total cost (TC) when the quantity of goods produced increases by one unit. The formula for calculating marginal cost is: \[ MC = \frac{\Delta TC}{\Delta Q} \] Where \( \Delta TC \) represents the change in total cost, and \( \Delta Q \) represents the change in output (which, in this case, is always 1 unit). So, the marginal cost for the nth unit can be calculated as: \[ MC_{N} = TC_{N} - TC_{N-1} \] Where \( TC_{N} \) is the total cost of producing \( N \) units, and \( TC_{N-1} \) is the total cost of producing \( N-1 \) units. The difference between the two gives the additional cost of producing the nth unit.
Step 3: Explanation of Other Formulas:
- Option (A) TFC$_{N$ - TFC$_{N-1}$ (Total Fixed Cost):} This formula represents the change in fixed costs, which do not vary with production levels. Since fixed costs remain constant as output increases, this is not a relevant measure of marginal cost.
- Option (B) AC$_{N$ - AC$_{N-1}$ (Average Cost):} This calculates the change in average cost per unit, not the additional cost of producing an extra unit.
- Option (C) AVC$_{N$ - AVC$_{N-1}$ (Average Variable Cost):} This calculates the change in average variable costs, but marginal cost refers to the change in total costs, not just variable costs.
Step 4: Conclusion and Answer:
The correct formula for marginal cost is (D), which is \( MC_{N} = TC_{N} - TC_{N-1} \), because it directly calculates the additional cost of producing one more unit of output.