The table shows the output produced with different units of labour (rows) and capital (columns).
| Labour \ Capital | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 1 | 3 | 7 | 10 | 12 | 13 |
| 2 | 3 | 10 | 18 | 24 | 29 | 33 |
| 3 | 7 | 18 | 30 | 40 | 46 | 50 |
| 4 | 10 | 24 | 40 | 50 | 56 | 57 |
| 5 | 12 | 29 | 46 | 56 | 58 | 59 |
| 6 | 13 | 33 | 50 | 57 | 59 | 60 |
A. Doubling both inputs from 2 units each more than doubles output.
B. Doubling both inputs from 3 units each exactly doubles output.
C. With capital fixed at 3 units, the marginal product of the 4th unit of labour is 10.
D. With labour fixed at 4 units, the marginal product of the 5th unit of capital is 10.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A, B and C only
Read each output off the table. Doubling both inputs tests the returns to scale; changing one input with the other fixed gives its marginal product.
A. Doubling both inputs from 2 units each more than doubles output. — Correct. Output goes from 10 at (2, 2) to 50 at (4, 4), which is five times. This is increasing returns to scale.
B. Doubling both inputs from 3 units each exactly doubles output. — Correct. Output goes from 30 at (3, 3) to 60 at (6, 6). This is constant returns to scale.
C. With capital fixed at 3 units, the marginal product of the 4th unit of labour is 10. — Correct. In the capital-3 column, output rises from 30 to 40 as labour goes from 3 to 4 units: 40 − 30 = 10.
D. With labour fixed at 4 units, the marginal product of the 5th unit of capital is 10. — Incorrect. In the labour-4 row, output rises from 50 to 56 as capital goes from 4 to 5 units. The marginal product is 56 − 50 = 6.
NCERT (2026-27): “3.6 Returns to Scale … When a proportional increase in all inputs results in an increase in output by the same proportion, the production function is said to display Constant returns to scale (CRS).” “… For example, suppose in a production process, all inputs get doubled. As a result, if the output gets doubled, the production function exhibits CRS. If output is less than doubled, then DRS holds, and if it is more than doubled, then IRS holds.” “3.3 Total Product, Average Product and Marginal Product Marginal product of an input is defined as the change in output per unit of change in the input when all other inputs are held constant. …” |