Arrange the following steps in the correct order to find the returns to scale of the production function q = x1α x2β:
(A) Increase both inputs t times (t > 1).
(B) Compare α + β with 1 to decide CRS, IRS or DRS.
(C) With x1 and x2 units of the inputs, write the output q0 = x1α x2β.
(D) Write the new output as q1 = tα + β q0.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (C), (A), (D), (B)
Start from the output with the given inputs, scale both inputs up, write the new output, and then compare.
(C) With x1 and x2 units of the inputs, write the output q0 = x1α x2β. — This is the starting output q0.
(A) Increase both inputs t times (t > 1). — Both inputs are now scaled up by the same number t.
(D) Write the new output as q1 = tα + β q0. — Collecting the powers of t gives the new output as tα + β times q0.
(B) Compare α + β with 1 to decide CRS, IRS or DRS. — If α + β = 1, output rises t times (CRS); more than 1 gives IRS; less than 1 gives DRS.
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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