A firm’s capital is fixed at 2 units, each costing Rs 50. The wage is Rs 20 per unit of labour. The table shows its output with 2 units of capital.
| Labour (units) | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Output (units) | 3 | 10 | 18 | 24 | 29 | 33 |
What is the SAC of producing 24 units, and roughly what is the SMC per unit when output rises from 24 to 29 units?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → SAC Rs 7.50; SMC Rs 4
Capital is the fixed input, so its cost is TFC. Labour is the variable input, so its cost is TVC.
Given:
TFC = 2 × Rs 50 = Rs 100
Wage = Rs 20 per unit of labour
24 units need 4 labour; 29 units need 5 labour
\( \displaystyle TC_{24} = 100 + 4 \times 20 = 180 \)
\( \displaystyle SAC = \frac{180}{24} = 7.50 \)
\( \displaystyle TC_{29} = 100 + 5 \times 20 = 200 \)
\( \displaystyle SMC = \frac{200 - 180}{29 - 24} = \frac{20}{5} = 4 \)
SAC is Rs 7.50 and SMC is about Rs 4 per unit.
Option (1) SAC Rs 7.50; SMC Rs 20 — Rs 20 is the cost of the extra worker, not of each extra unit of output.
Option (2) SAC Rs 3.33; SMC Rs 4 — Rs 3.33 is the AVC at 24 units (80/24), variable cost only.
Option (3) SAC Rs 4.17; SMC Rs 4 — Rs 4.17 is the AFC at 24 units (100/24), fixed cost only.
SAC, AVC and AFC are three different averages: SAC uses total cost, AVC variable cost only and AFC fixed cost only.
NCERT (2026-27): “3.7.1 Short Run Costs … The short run average cost (SAC) incurred by the firm is defined as the total cost per unit of output. …” “… Similarly, the average variable cost (AVC) is defined as the total variable cost per unit of output. …” “The last column in table 3.3 gives a numerical example for the calculation of SMC. Values in this column are obtained by dividing the change in TC by the change in output, at each level of output. …” |