Question

If we have constant returns to scale and we increase the quantity of labour ($X_1$) used per unit of time by 20% but keep the amount of capital ($X_2$) constant, the output will:

• A. Increase by 20%.
• B. Decrease by 20%.
• C. Increase by more than 20%.
• D. Increase by less than 20%.

Hint:

Under CRS, if only one input increases by $x$%, output will always increase by less than $x$% because of the law of diminishing marginal productivity of the variable input.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question tests the distinction between returns to scale (where all inputs are changed proportionally) and returns to a variable factor (where one input is changed while others are held constant).

Step 3: Detailed Explanation:
Let us analyze the differences:
Returns to Scale: Under Constant Returns to Scale (CRS), if we increase all inputs by a certain percentage, output increases by that exact same percentage. For example, if we increased both labour ($X_1$) and capital ($X_2$) by 20%, output would increase by exactly 20%.
Returns to a Variable Input: Here, we increase only one input (labour $X_1$ by 20%) while keeping the other input (capital $X_2$) fixed.
Because capital is fixed, the ratio of labour to capital increases, which triggers the law of diminishing marginal returns.
Since the variable input (labour) is not supported by a proportional increase in capital, each additional unit of labour becomes less productive than the previous units.
Therefore, although total output increases, the percentage increase in output must be less than the percentage increase in the variable input (i.e., less than 20%).

Step 4: Final Answer:
The output will increase by less than 20%.