If total costs rise from £400 to £421 and the average cost falls from £40 to £38, what is the marginal cost?

Question

BlackTom AI · Accepted Answer

Let's lay out the problem step by step and check each option carefully.
First, note the given: total cost rises from £400 to £421, so the change in total cost ΔTC = 421 − 400 = £21.
We are told the average cost falls from £40 to £38. To relate average cost (AC) and total cost (TC) to output (Q), use AC = TC / Q. Initially, AC = £40 and TC = £400, so the initial output is Q1 = TC / AC = 400 / 40 = 10 units. After the change, AC = £38 and TC = £421, so the new output is Q2 = 421 / 38 ≈ 11.07 units. Although the exact output isn’t a neat integer, marginal cost is defined as the change in total cost when output increases by one unit (MC ≈ ΔTC / ΔQ).
From Q1 to Q2, output increased by roughly 1 unit (10 to about 11). The total cost increased by £21, so the marginal cost per extra unit is MC ≈ £21 / 1 ≈ £21. This aligns with the standard interpretation that MC equals the additional cost incurred by producing one more unit.
Now, evaluate the options:
- Option A: £-2. A negative marginal cost would imply that producing an extra unit reduces total cost, which contradicts the observed increase in total cost from £400 to £421. Therefore this is incorrect.
- Option B: £2. A marginal cost of £2 would correspond to a much smaller increase in total cost than the actual £21 observed for the extra unit, so this is not consistent with the data given. Hence incorrect.
- Option C: £21. This matches the calculated change in total cost associated with producing the additional unit (approximately one more unit of output), so this is correct.
- Option D: £38. This value corresponds to the new average cost, not the marginal cost, and would be inappropriate as a marginal cost figure in this context. Therefore incorrect.
In summary, the only option that coherently explains the observed cost increase per additional unit of output is £21, while the others conflict with the definitions or the numerical changes provided.

If total costs rise from £400 to £421 and the average cost falls from £40 to £38, what is the marginal cost?单项选择题

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