Consider the production function $q = f(x_1, x_2)$ where the firm produces q amout of output $x_1$ amount of factor 1 and $x_2$ amount of factor 2. The firm decides to increase the employment level of both the factors t (t > 1). Identify the equation for decreasing returns to scale from the following.

Option 1 -> This is simply the production function definition, not a returns to scale condition.

Option 2 -> This equation represents constant returns to scale, where scaling inputs by t scales output by exactly t.

Option 3 -> This represents decreasing returns to scale, where scaling inputs by t (t > 1) results in output increasing by less than t.

Option 4 -> This represents increasing returns to scale, where scaling inputs by t results in output increasing by more than t.

Hence, Option 3 -> Decreasing returns to scale occurs when proportionate increase in all inputs results in a less than proportionate increase in output. Mathematically, when all inputs are multiplied by t (where t > 1), if f(tx₁, tx₂) < tf(x₁, x₂), it means the output increases by a factor less than t, which is the defining characteristic of decreasing returns to scale. For example, if inputs double (t=2) but output less than doubles, the firm experiences decreasing returns to scale. -> correct