A firm triples all its inputs, and its output becomes four times the earlier output. For its production function q = f(x1, x2), which of the following holds?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → f(3x1, 3x2) > 3.f(x1, x2), so it shows increasing returns to scale
Inputs are tripled, so t = 3. The new output is 4 times the old one, which is more than 3 times.
\( \displaystyle f(3x_1, 3x_2) = 4\,f(x_1, x_2) \gt 3\,f(x_1, x_2) \)
Output rises by a larger proportion than the inputs, so this is increasing returns to scale.
Option (3) f(3x1, 3x2) > 4.f(x1, x2), so it shows increasing returns to scale — f(3x1, 3x2) equals 4 f(x1, x2), so it is not greater than it. The comparison is with t times the old output, here 3 times.
NCERT (2026-27): “Returns to Scale Consider a production function q = f (x1, x2) where the firm produces q amount of output using x1 amount of factor 1 and x2 amount of factor 2. Now suppose the firm decides to increase the employment level of both the factors t (t > 1) times. Mathematically, we can say that the production function exhibits constant returns to scale if we have, f (tx1, tx2) = t.f (x1, x2) ie the new output level f (tx1, tx2) is exactly t times the previous output level f (x1, x2). Similarly, the production function exhibits increasing returns to scale if, f (tx1, tx2) > t.f (x1, x2). …” |