In macroeconomics, the Inada conditions, named after Japanese economist Ken-Ichi Inada, are assumptions about the shape of a production function that guarantee the stability of an economic growth path in a neoclassical growth model. The conditions as such had been introduced by Hirofumi Uzawa.
The six conditions for a given function
- the value of the function
f ( x ) at 0 is 0:f ( 0 ) = 0 - the function is continuously differentiable,
- the function is strictly increasing in
x i ∂ f ( x ) / ∂ x i > 0 , - the second derivative of the function is negative in
x i ∂ 2 f ( x ) / ∂ x i 2 < 0 , - the limit of the first derivative is positive infinity as
x i lim x i → 0 ∂ f ( x ) / ∂ x i = + ∞ , - the limit of the first derivative is zero as
x i lim x i → + ∞ ∂ f ( x ) / ∂ x i = 0
All these conditions are met by a Cobb–Douglas production function.
References
Inada conditions Wikipedia(Text) CC BY-SA