7. If you know that when a firm produces 10 units of output, total costs are $1,030 and average fixed costs are $10, then total fixed costs are:
A. $5
B. $100
C. $1,020
D. $1,040

Question

7.    If you know that when a firm produces 10 units of output, total costs are $1,030 and average fixed costs are $10, then total fixed costs are:
A.    $5
B.    $100
C.    $1,020
D.    $1,040

BlackTom AI · Accepted Answer

Average fixed cost (AFC) equals total fixed cost (TFC) divided by quantity produced (Q): AFC = TFC / Q.

1) Relevant knowledge points and concepts
- Total cost (TC) is the sum of total fixed cost (TFC) and total variable cost (TVC): TC = TFC + TVC.
- Average fixed cost (AFC) is TFC divided by output: AFC = TFC / Q.
- Average total cost (ATC) = TC / Q = AFC + AVC (average variable cost).

2) Step-by-step reasoning
Given: Q = 10 units, TC = $1,030, AFC = $10. Use the AFC definition to find TFC, then check consistency with TC.

3) Calculations with intermediate steps
AFC = TFC / Q
10 = TFC / 10
Multiply both sides by 10:
TFC = 10 × 10 = $100.

Optional consistency checks:
ATC = TC / Q = 1,030 / 10 = $103 per unit.
Since ATC = AFC + AVC, AVC = ATC − AFC = 103 − 10 = $93.
Then TVC = AVC × Q = 93 × 10 = $930.
Check: TFC + TVC = 100 + 930 = $1,030 = TC, consistent.

4) Why the correct answer is correct
The correct answer follows directly from the definition of AFC. Multiplying AFC ($10) by the number of units (10) yields the total fixed cost of $100. This is internally consistent with the given total cost and computed variable costs.

5) Why the other options are incorrect
- A ($5): Far too small; would imply AFC = 0.5 per unit (5 / 10), contradicting given AFC = $10.
- C ($1,020): Likely a miscalculation (e.g., TC − AFC = 1030 − 10), but subtracting an average per-unit value from total cost is not valid. TFC cannot be 1,020 because that would exceed TC.
- D ($1,040): Also invalid (TC + AFC), which mixes averages and totals incorrectly and gives TFC greater than TC.

6) Conclusion
Total fixed costs are $100, which matches answer B.

7. If you know that when a firm produces 10 units of output, total costs are $1,030 and average fixed costs are $10, then total fixed costs are: A. $5 B. $100 C. $1,020 D. $1,040单项选择题

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