A firm’s production function is q = x1x2, and input prices are given. To double its output in the long run, by what factor must the firm raise both inputs, and what happens to its LRAC?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → By a factor of about 1.41; LRAC falls
If both inputs are raised t times, output becomes t × t = t2 times.
\( \displaystyle t^2 = 2 \;\Rightarrow\; t = \sqrt{2} \approx 1.41 \)
With input prices fixed, cost also rises about 1.41 times, while output doubles. Cost per unit falls, so LRAC falls. This is increasing returns to scale (the exponents add up to 2).
NCERT (2026-27): “3.7.2 Long Run Costs … IRS implies that if we increase all the inputs by a certain proportion, output increases by more than that proportion. In other words, to increase output by a certain proportion, inputs need to be increased by less than that proportion. With the input prices given, cost also increases by a lesser proportion. For example, suppose we want to double the output. To do that, inputs need to be increased, but less than double. The cost that the firm incurs to hire those inputs therefore also need to be increased by less than double. What is happening to the average cost here? It must be the case that as long as IRS operates, average cost falls as the firm increases output. …” |