Three of the following Cobb-Douglas production functions show the same returns to scale. Which one is the odd one out?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → q = x10.6 x20.6
In a Cobb-Douglas function, the sum of the powers decides returns to scale.
\( \displaystyle 0.5 + 0.5 = 1, \quad 0.8 + 0.2 = 1, \quad 0.3 + 0.7 = 1 \)
\( \displaystyle 0.6 + 0.6 = 1.2 \)
Three functions add up to 1 and show constant returns to scale. q = x10.6x20.6 adds up to more than 1, so it shows 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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