Correct Option: B. Average total cost will increase
Detailed Explanation:
To understand why the correct answer is B, we need to delve into the concepts of Marginal Cost (MC) and Average Total Cost (ATC).
- Definitions:
- Marginal Cost (MC): This is the additional cost incurred by producing one more unit of a good or service. It reflects the change in total cost when output is increased by one unit.
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Average Total Cost (ATC): This is the total cost of production divided by the number of units produced. It represents the average cost per unit.
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Relationship Between MC and ATC:
- The relationship between MC and ATC is crucial in determining how ATC behaves as output changes.
- When MC is less than ATC, producing an additional unit will lower the ATC because the cost of that additional unit is less than the average cost of the units already produced.
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Conversely, when MC is greater than ATC, producing an additional unit will increase the ATC because the cost of that additional unit is higher than the average cost of the units already produced.
-
Why ATC Increases When MC > ATC:
- If a firm is currently producing at a level where MC exceeds ATC, it means that the cost of producing the next unit is higher than the average cost of the units already produced.
- Therefore, when the firm produces one more unit, the higher cost of that unit pulls the average up.
- Mathematically, if we denote the current total cost as TC and the current quantity as Q, the ATC can be expressed as:
[
ATC = \frac{TC}{Q}
]
- If we produce one more unit, the new total cost becomes ( TC + MC ) and the new quantity becomes ( Q + 1 ). The new ATC will be:
[
ATC_{new} = \frac{TC + MC}{Q + 1}
]
- Since ( MC > ATC ), the increase in total cost (due to the higher marginal cost) will result in a higher average total cost.
Why Other Options Are Incorrect:
- Option A: Average total cost will decrease:
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This is incorrect because if MC is greater than ATC, the additional cost of producing one more unit is higher than the average cost, which cannot lead to a decrease in ATC.
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Option C: Average total cost will remain unchanged:
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This option is incorrect because ATC cannot remain unchanged when MC is greater than ATC. The very definition of marginal cost indicates that producing an additional unit incurs a different cost, which will affect the average.
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Option D: Average total cost will equal marginal cost:
- This statement is misleading in this context. ATC equals MC only at the minimum point of the ATC curve. If MC is greater than ATC, ATC is still rising and has not yet reached the level of MC.
Common Pitfalls:
- Students often confuse the relationship between MC and ATC. Remember that the direction of change in ATC is determined by whether MC is above or below ATC.
- It’s also important to visualize the cost curves. A typical cost curve graph shows that when MC is above ATC, the ATC curve is sloping upwards.
Revision Summary:
- When MC > ATC, producing an additional unit increases ATC.
- ATC is calculated as total cost divided by quantity produced.
- The relationship between MC and ATC is crucial for understanding cost behavior in production.
- Always remember that the behavior of ATC is influenced by the cost of the next unit produced (MC).