A production function satisfies Increasing Returns to Scale (IRS) when a proportional increase in all inputs results in an increase in output by a larger proportion. This situation arises in the long run when factors are scaled up.

Mathematically, if the employment of all factors is increased by a factor $t$ (where $t > 1$), the production function exhibits IRS if the new output level is greater than $t$ times the previous output level. This is expressed as $f(tx_1, tx_2) > t.f(x_1, x_2)$. For example, if all inputs are doubled and the resulting output more than doubles, the production function satisfies increasing returns to scale.