When a proportional increase in all inputs results in an increase in…

The correct answer is Option (4) → Decreasing returns to scale

In the long run a firm can change all its inputs. The returns to scale describe what happens to output when all inputs are increased in the same proportion, say all doubled. Comparing the rise in output with the rise in inputs gives three cases:

• Constant returns to scale: output rises in the same proportion; doubling all inputs doubles output.

• Increasing returns to scale: output rises in a larger proportion; doubling all inputs more than doubles output.

• Decreasing returns to scale: output rises in a smaller proportion; doubling all inputs less than doubles output.

Here output rises by only half the proportion of the inputs: when every input doubles, a rise of 100 per cent, output rises by just 50 per cent. Output growing more slowly than the inputs is the third case, decreasing returns to scale.

Why the other options are incorrect

• Option (1) Increasing returns to scale — Incorrect. Increasing returns need output to rise by more than the inputs; here it rises by less.

• Option (2) Constant returns to scale — Incorrect. Constant returns need output to rise in the same proportion as the inputs; a rise of only half that proportion is less than proportionate.

• Option (3) Law of variable proportion — Incorrect. This law is about the short run, when one input is increased while the others are held fixed, and it explains how the marginal product of that input first rises and then falls. The question increases all inputs together, which is a matter of returns to scale.

Note: A same/similar question was asked in CUET (UG) in the papers below.

* A similar question.