Consider the production function q = f(x1, x2) where the firm produces q amout of output x1 amount of factor 1 and x2 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:

The correct option is: f (tx1, tx2) < t.f (x1, x2).

Step-by-step Explanation:

Returns to scale describes how the output of a production process changes in response to a proportional increase in all inputs (factors of production) by a common scale factor, denoted here as $t$ where $t>1$.

Let the initial production function be:
$q=f(x_1,x_2)$
where $x_1$ and $x_2$ represent the initial employment levels of factor 1 and factor 2, respectively.

When the employment levels of both inputs are scaled up by the factor $t$, the new input bundle becomes $(t{x}_1,t{x}_2)$, and the new output level is given by $f(t{x}_1,t{x}_2)$.

Decreasing returns to scale (DRS) occurs when a proportional increase in all inputs leads to a less-than-proportional increase in the output. Mathematically, this means that the new output is strictly less than $t$ times the original output:

$f(t{x}_1,t{x}_2)<t\cdot f(x_1,x_2)$

Therefore, the inequality that identifies decreasing returns to scale is indeed $f(t{x}_1,t{x}_2)<t\cdot f(x_1,x_2)$.