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:

$f (tx_1, tx_2) < t.f (x_1, x_2)$

The correct answer is Option (3) → $f (tx_1, tx_2) < t.f (x_1, x_2)$

In the production function q = f(x₁, x₂), if the firm increases all inputs by a factor t (where t > 1), then:

• If f(tx₁, tx₂) = t·f(x₁, x₂) → Constant Returns to Scale

• If f(tx₁, tx₂) > t·f(x₁, x₂) → Increasing Returns to Scale

• If f(tx₁, tx₂) < t·f(x₁, x₂) → Decreasing Returns to Scale

So, under decreasing returns to scale, output increases less than proportionately to the increase in inputs.