A firm raises all its inputs from 2 units of labour and 3 units of ca…

A firm raises all its inputs from 2 units of labour and 3 units of capital to 4 units of labour and 6 units of capital, and its output rises from 20 to 44 units. It then raises the inputs from 4 units of labour and 6 units of capital to 6 units of labour and 9 units of capital, and output rises to 66 units. Input prices do not change. Which is correct?

Answer & explanation

Correct answer: option 1

The correct answer is Option (1) → IRS in the first step and CRS in the second; LRAC falls and then stays the same

Compare the rise in output with the rise in all inputs. Then use the link between returns to scale and LRAC.

First step: inputs double (2 → 4, 3 → 6).

\( \displaystyle \text{Output: } \frac{44}{20} = 2.2 \text{ times} \;\Rightarrow\; \text{IRS} \)

Second step: inputs rise 1.5 times (4 → 6, 6 → 9).

\( \displaystyle \text{Output: } \frac{66}{44} = 1.5 \text{ times} \;\Rightarrow\; \text{CRS} \)

With input prices fixed, cost rises in the same proportion as inputs. Under IRS output grows faster than cost, so LRAC falls; under CRS both grow alike, so LRAC stays the same.

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).”

“When a proportional increase in all inputs results in an increase in output by a larger proportion, the production function is said to display Increasing Returns to Scale (IRS) Decreasing Returns to Scale (DRS) holds when a proportional increase in all inputs results in an increase in output by a smaller proportion. …”

“3.7.2 Long Run Costs … It must be the case that as long as IRS operates, average cost falls as the firm increases output. DRS implies that if we want to increase the output by a certain proportion, inputs need to be increased by more than that proportion. As a result, cost also increases by more than that proportion. So, as long as DRS operates, the average cost must be rising as the firm increases output. CRS implies a proportional increase in inputs resulting in a proportional increase in output. So the average cost remains constant as long as CRS operates. …”