A firm’s total fixed cost is Rs 30. Its SAC at 5 units of output is Rs 22, and its AVC at 4 units is Rs 18. What is the SMC of the 5th unit, and what happens to AVC as output rises from 4 to 5 units?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → SMC Rs 8; AVC falls
Total cost is SAC × output, and TVC is TC minus TFC. SMC of the 5th unit is the rise in total cost from 4 to 5 units. TFC does not change, so this is the same as the rise in TVC.
Given:
TFC = Rs 30
SAC at 5 units = Rs 22
AVC at 4 units = Rs 18
\( \displaystyle TC_5 = 22 \times 5 = 110 \)
\( \displaystyle TVC_5 = 110 - 30 = 80 \)
\( \displaystyle TVC_4 = 18 \times 4 = 72 \)
\( \displaystyle SMC_5 = 80 - 72 = 8 \)
\( \displaystyle AVC_5 = \frac{80}{5} = 16 \)
SMC is Rs 8, and AVC falls from Rs 18 to Rs 16. The extra unit costs less than the average, so it pulls the average down.
Option (2) SMC Rs 38; AVC rises — 38 is TC5 − TVC4 (110 − 72), which mixes total cost with variable cost.
NCERT (2026-27): “3.7.1 Short Run Costs … At zero level of output, both AFC and AVC are undefined. For the first unit of output, AFC is Rs 20 and AVC is Rs 10. Adding them, we get the SAC equal to Rs 30. The short run marginal cost (SMC) is defined as the change in total cost per unit of change in output …” “… Then, as output increases, SMC falls. AVC being the average of marginal costs, also falls, but falls less than SMC. Then, after a point, SMC starts rising. AVC, however, continues to fall as long as the value of SMC remains less than the prevailing value of AVC. Once the SMC has risen sufficiently, its value becomes greater than the value of AVC. The AVC then starts rising. …” |