Given below are two statements:
Statement I: For the production function Q = 5L1/2K1/2, doubling both L and K exactly doubles the output.
Statement II: The production function Q = 2L2K2 exhibits decreasing returns to scale.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Statement I is correct but Statement II is incorrect.
In q = x1αx2β, raising both inputs t times raises output tα + β times. So the sum of the powers decides returns to scale: equal to 1 is CRS, more than 1 is IRS, less than 1 is DRS.
Statement I: For the production function Q = 5L1/2K1/2, doubling both L and K exactly doubles the output. — True. The powers add up to 1/2 + 1/2 = 1, so doubling both inputs doubles output (CRS).
Statement II: The production function Q = 2L2K2 exhibits decreasing returns to scale. — False. The powers add up to 2 + 2 = 4, which is more than 1. Doubling both inputs makes output 24 = 16 times, which is increasing returns to scale.
NCERT (2026-27): “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.”
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