To determine the marginal cost of the 3rd unit of output from the provided table, we first need to understand what marginal cost (MC) is. Marginal cost is the additional cost incurred when producing one more unit of a good or service. It can be calculated by finding the difference in total cost when output increases by one unit.
Step-by-Step Explanation
- Identify Total Costs: From the table, we can extract the total costs associated with each level of output:
- Total cost for 1 unit = 20
- Total cost for 2 units = 32
- Total cost for 3 units = 42
- Total cost for 4 units = 48
-
Total cost for 5 units = 50
-
Calculate Marginal Cost for the 3rd Unit:
- To find the marginal cost of the 3rd unit, we need to calculate the change in total cost when output increases from 2 units to 3 units.
- The formula for marginal cost (MC) is:
[
MC = \text{Total Cost at n units} - \text{Total Cost at (n-1) units}
]
-
Here, ( n = 3 ):
[
MC = \text{Total Cost at 3 units} - \text{Total Cost at 2 units}
]
[
MC = 42 - 32 = 10
]
-
Conclusion: Therefore, the marginal cost of producing the 3rd unit of output is 10.
Explanation of Other Options
-
Option A: 12: This option is incorrect because it does not reflect the actual change in total cost between the 2nd and 3rd units. The calculation shows that the increase in cost is only 10.
-
Option B: 6: This option is also incorrect. It underestimates the increase in total cost when moving from 2 to 3 units. The actual increase is 10, not 6.
-
Option D: 2: This option is incorrect as well. It significantly underestimates the marginal cost. The difference in total cost is much larger than 2.
Common Pitfalls
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Misunderstanding Marginal Cost: Students often confuse marginal cost with average cost. Remember, marginal cost is about the cost of producing one additional unit, while average cost is the total cost divided by the number of units produced.
-
Forgetting to Use the Correct Units: Always ensure you are looking at the correct units of output when calculating marginal costs.
Revision Summary
- Marginal cost is the additional cost of producing one more unit of output.
- It is calculated by finding the difference in total costs between two consecutive output levels.
- For the 3rd unit, the marginal cost is calculated as ( MC = 42 - 32 = 10 ).
- Always differentiate between marginal cost and average cost to avoid confusion.
The correct answer is
C. 10.