An increase in the price of labor has no effect on which cost curve?

Question

BlackTom AI · Accepted Answer

Average fixed cost (AFC) = Fixed Cost (FC) / Quantity (Q). Fixed costs do not change with variable inputs like labor, so AFC remains unchanged when labor price changes.

1. Relevant concepts and formulas
- Fixed costs (FC): costs that do not vary with output (e.g., rent, insurance) in the short run.
- Variable costs (VC): costs that vary with output (e.g., wages for labor).
- Average fixed cost: AFC = FC / Q.
- Average variable cost: AVC = VC / Q.
- Average total cost: ATC = TC / Q = (FC + VC) / Q = AFC + AVC.
- Marginal cost (MC): the additional cost of producing one more unit, generally derived from the change in variable cost with output: MC = ΔTC / ΔQ ≈ ΔVC / ΔQ.

2. Step-by-step reasoning
- An increase in the price of labor (wage w ↑) raises variable costs because labor is a variable input in the short run. So VC increases.
- AVC = VC / Q therefore increases when VC increases (for a given Q).
- ATC = AFC + AVC will increase because AVC increases; AFC has not changed yet.
- MC depends on the incremental variable cost of extra output (higher wage → higher incremental cost per additional labor input needed → MC increases).
- AFC = FC / Q: since FC remains the same (labor is not a fixed cost), FC does not change and thus AFC stays the same for any given Q.

3. Intermediate algebraic steps
- Before: AFC0 = FC / Q.
- After wage increase: FC (unchanged) ⇒ AFC1 = FC / Q = AFC0. No change.
- VC1 = VC0 + ΔVC (positive). AVC1 = VC1 / Q > AVC0.
- ATC1 = AFC0 + AVC1 > ATC0.
- MC1 = d(VC1)/dQ > MC0.

4. Why the correct answer is correct
Because AFC depends only on fixed costs and output, and wages affect only variable costs, an increase in labor price does not change FC; therefore AFC is unaffected.

5. Why other options are incorrect
- Average-total-cost: ATC increases because AVC rises when labor price increases, so ATC changes.
- Marginal-cost: MC rises because the incremental cost of producing extra units increases with higher wages.
- Average-variable-cost: AVC increases directly since VC rises with higher labor cost.

6. Conclusion
Average-fixed-cost is the curve unaffected by an increase in the price of labor. This matches the provided correct answer: Average-fixed-cost.

An increase in the price of labor has no effect on which cost curve?单项选择题

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