Which of the following describes the behavior of the fixed cost per unit?

Question

BlackTom AI · Accepted Answer

Fixed costs are expenses that remain unchanged in total regardless of output; fixed cost per unit is the total fixed cost divided by the number of units produced.

1) Relevant concepts:
- Total fixed cost (F): constant over the relevant range (e.g., rent, salaried management).
- Fixed cost per unit = F / Q, where Q is quantity produced.
- This is an inverse (per-unit) relationship: as Q increases, F/Q decreases.

2) Step-by-step reasoning:
- Start from the definition: fixed cost per unit = F / Q.
- Holding F constant, if Q increases the denominator increases, so the quotient falls.
- If Q decreases, the denominator decreases, so the quotient rises.

3) Calculations / intermediate steps (numerical example):
- Let F = $1,000.
- If Q = 100 units: fixed cost per unit = 1,000 / 100 = $10.00.
- If Q = 200 units: fixed cost per unit = 1,000 / 200 = $5.00.
- If Q = 50 units: fixed cost per unit = 1,000 / 50 = $20.00.
These intermediate results show the per-unit cost falls as production rises.

4) Why the correct answer is correct:
- Because fixed cost per unit equals F divided by Q, increasing Q spreads the same total cost over more units, lowering the cost allocated to each unit. Mathematically F/Q is a decreasing function of Q (for F>0).

5) Why the other choices are incorrect:
- "Decreases with decreasing production": wrong — decreasing production reduces Q, so F/Q increases, not decreases.
- "Remains constant with changes in production": wrong — total fixed cost is constant, but per-unit cost changes with Q.
- "Increases with increasing production": wrong — this implies a direct relationship; the real relationship is inverse, so per-unit cost decreases as production rises.

6) Conclusion:
The fixed cost per unit decreases with increasing production, which matches the provided correct answer: "decreases with increasing production."

Which of the following describes the behavior of the fixed cost per unit?Single choice

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