A firm’s production function is q = K × L. It now uses 4 units of capital and 4 units of labour, and wants to produce 64 units. Which of the following is correct?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Both doubling the two inputs and raising only labour four times give 64 units; doubling shows IRS.
Given:
q = K × L
K = 4, L = 4, target q = 64
Now:
\( q = 4 \times 4 = 16 \)
Doubling both inputs:
\( q = 8 \times 8 = 64 \)
Raising only labour four times:
\( q = 4 \times 16 = 64 \)
Both routes give 64. When inputs double, output becomes four times (16 to 64), more than double. So the function shows increasing returns to scale.
NCERT (2026-27): “3.1 Production Function … Consider the farmer we mentioned above. For simplicity, we assume that the farmer uses only two inputs to produce wheat: land and labour. A production function tells us the maximum amount of wheat he can produce for a given amount of land that he uses, and a given number of hours of labour that he performs. Suppose that he uses 2 hours of labour/ day and 1 hectare of land to produce a maximum of 2 tonnes of wheat. Then, a function that describes this relation is called a production function. One possible example of the form this could take is: q = K × L, Where, q is the amount of wheat produced, K is the area of land in hectares, L is the number of hours of work done in a day. Describing a production function in this manner tells us the exact relation between inputs and output. If either K or L increase, q will also increase.” “3.6 Returns to Scale The law of variable proportions arises because factor proportions change as long as one factor is held constant and the other is increased. … Remember that this can happen only in the long run. One special case in the long run occurs when both factors are increased by the same proportion, or factors are scaled up. When a proportional increase in all inputs results in an increase in output by the same proportion, the production function is said to display Constant returns to scale (CRS). When a proportional increase in all inputs results in an increase in output by a larger proportion, the production function is said to display Increasing Returns to Scale (IRS) Decreasing Returns to Scale (DRS) holds when a proportional increase in all inputs results in an increase in output by a smaller proportion. For example, suppose in a production process, all inputs get doubled. As a result, if the output gets doubled, the production function exhibits CRS. If output is less than doubled, then DRS holds, and if it is more than doubled, then IRS holds.” |