Consider the production function q = x10.6 x20.5, where x1 and x2 are the amounts of two factors. How many of the following statements are correct?
(A) It is a Cobb-Douglas production function.
(B) If both inputs are doubled, output becomes 21.1 times the old output.
(C) It shows decreasing returns to scale.
(D) With x1 = 0, output is zero whatever the amount of x2.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Three
A function of the form q = x1αx2β is a Cobb-Douglas production function. Doubling both inputs multiplies output by 2α + β, and the sum α + β decides the returns to scale. Here α + β = 0.6 + 0.5 = 1.1.
(A) It is a Cobb-Douglas production function. — Correct. It has the Cobb-Douglas form, with α = 0.6 and β = 0.5.
(B) If both inputs are doubled, output becomes 21.1 times the old output. — Correct. With t = 2, output becomes 20.6 + 0.5 = 21.1 times the old output.
(C) It shows decreasing returns to scale. — Incorrect. α + β = 1.1 is greater than 1, so the function shows increasing returns to scale.
(D) With x1 = 0, output is zero whatever the amount of x2. — Correct. If x1 = 0, then x10.6 = 0, so output is zero whatever x2 is.
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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