Inada Condition

Macro

The intuition behind the Inada Condition mainly concerns about marginal product of capital, ie, $MPK$. It is the first order derivative of the production function with respect to capital, mathematically, we denoted by $F_k(k,h)$ or $f^{\prime }(k)$.

$h$ here means the labor input, and $k$ means the capital input.

The two key Inada Condition are:

1. ${\lim }_{k\to 0}{F}_k(k,h)=\infty$: As the amount of capital of input is closed to $0$, the marginal product of capital would be extremely high, ie, $MPK\to \infty$. It means that if a country has very little capital, then investing in capital would bring a very high return.
2. ${\lim }_{k\to \infty }{F}_k(k,h)=0$: This one is also very intuitive, as the amount of capital of input is extremely high, the marginal product of capital would be very low, ie, $MPK\to 0$. It means that if a country has a lot of capital, then investing in capital would bring a very low return.