In a production function $q = f(x_1, x_2)$ where the firm produces q output using $x_1$ of factor 1 and $x_2$ of factor 2. Now suppose the firm decides to increase the employment level of both the factors t (t > 1) times. then which among the following is correct?

Option 1 -> $f(tx_1, tx_2) > t f(x_1, x_2)$ indicates output increases MORE than proportionally, which is increasing returns to scale, not constant.

Option 2 -> $f(tx_1, tx_2) < t f(x_1, x_2)$ indicates output increases LESS than proportionally, but it's incorrectly labeled as increasing returns to scale.

Option 3 -> $f(tx_1, tx_2) < t f(x_1, x_2)$ correctly shows output increases LESS than proportionally AND is correctly identified as decreasing returns to scale.

Option 4 -> $f(tx_1, tx_2) = t f(x_1, x_2)$ indicates proportional increase (constant returns to scale), but is incorrectly labeled as decreasing returns to scale.

Hence, Option 3: $f(tx_1, tx_2) < t f(x_1, x_2)$ i.e decreasing returns to scale -> In decreasing returns to scale, when all inputs are scaled up by factor t (t > 1), the output increases by less than t times. This means if you double all inputs, output less than doubles. This typically occurs due to coordination difficulties, management inefficiencies, or resource constraints as the scale of production grows. Option 3 correctly matches the mathematical condition with its economic interpretation -> correct