A firm’s production function is q = x10.5 x20.7. It doubles both inputs. Which chain is correct?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → α + β = 1.2 → new output = 21.2 times the old output → output more than doubles → increasing returns to scale
In a Cobb-Douglas function, add the powers: 0.5 + 0.7 = 1.2. When both inputs rise t times, output rises t1.2 times. With t = 2, output becomes 21.2 times, which is more than double. Since α + β > 1, the function shows increasing returns to scale.
Option (1) α + β = 1.2 → new output = 2 × 1.2 times the old output → output more than doubles → constant returns to scale — Incorrect. Output becomes 2 raised to the power 1.2, not 2 multiplied by 1.2. Output more than doubling is IRS, not CRS.
Option (2) α + β = 1.2 → new output = 21.2 times the old output → output more than doubles → decreasing returns to scale — Incorrect. Output more than doubling is IRS. DRS would mean less than double.
Option (3) α + β = 0.35 → new output = 20.35 times the old output → output less than doubles → decreasing returns to scale — Incorrect. The powers are added (0.5 + 0.7 = 1.2), not multiplied.
Option (4) α + β = 1.2 → new output = 21.2 times the old output → output more than doubles → increasing returns to scale — Correct. Each link holds.
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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