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?

$f(tx_1, tx_2) < t.f (x_1, x_2)$ i.e decreasing returns to scale.

The correct answer is Option (3) → $f(tx_1, tx_2) < t.f (x_1, x_2)$ i.e decreasing returns to scale.

Option 1: $f(tx_1, tx_2) > t.f (x_1, x_2)$ i.e. constant returns to scale. Incorrect. It represents increasing returns to scale, not constant returns to scale.

Option 2: $f(tx_1, tx_2) < t.f (x_1, x_2)$ i.e increasing returns to scale. Incorrect. It represents decreasing returns to scale, not increasing returns to scale.

Option 3: $f(tx_1, tx_2) < t.f (x_1, x_2)$ i.e decreasing returns to scale. Correct. 

Option 4: $f(tx_1, tx_2) = t.f (x_1, x_2)$ i.e decreasing returns to scale. Incorrect. It represents constant returns to scale, not decreasing returns to scale