Given below are two statements:
Statement I: Under decreasing returns to scale, to double the output, the inputs need to be increased by less than double.
Statement II: For the production function q = x10.7 x20.5, doubling both inputs more than doubles the output.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Statement I is incorrect but Statement II is correct.
Statement I: Under decreasing returns to scale, to double the output, the inputs need to be increased by less than double. — Incorrect. Under DRS output rises by a smaller proportion than the inputs. So to double the output, inputs must be raised by more than double.
Statement II: For the production function q = x10.7 x20.5, doubling both inputs more than doubles the output. — Correct. The powers add up to 0.7 + 0.5 = 1.2, which is more than 1. So the function shows IRS, and doubling both inputs more than doubles the output.
NCERT (2026-27): “Shapes of the Long Run Cost Curves … 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. …” “Cobb-Douglas Production Function … When α + β = 1, we have q1 = tq0. That is, the output increases t times. So the production function exhibits CRS. Similarly, when α + β > 1, the production function exhibits IRS. When α + β < 1 the production function exhibits DRS.” |