In macroeconomics, the Inada conditions, named after Japanese economist Ken-Ichi Inada,[1] 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.[2]

The six conditions for a given function ${\displaystyle f(x)}$ are:

1. the value of the function ${\displaystyle f(x)}$ at 0 is 0: ${\displaystyle f(0)=0}$
2. the function is continuously differentiable,
3. the function is strictly increasing in ${\displaystyle x_{i}}$: ${\displaystyle \partial f(x)/\partial x_{i}>0}$,
4. the second derivative of the function is negative in ${\displaystyle x_{i}}$ (thus the function is concave): ${\displaystyle \partial ^{2}f(x)/\partial x_{i}^{2}<0}$,
5. the limit of the first derivative is positive infinity as ${\displaystyle x_{i}}$ approaches 0: ${\displaystyle \lim _{x_{i}\to 0}\partial f(x)/\partial x_{i}=+\infty }$,
6. the limit of the first derivative is zero as ${\displaystyle x_{i}}$ approaches positive infinity: ${\displaystyle \lim _{x_{i}\to +\infty }\partial f(x)/\partial x_{i}=0}$

All these conditions are met by a Cobb–Douglas production function.

## References

1. ^ Inada, Ken-Ichi (1963). "On a Two-Sector Model of Economic Growth: Comments and a Generalization". The Review of Economic Studies 30 (2): 119–127. JSTOR 2295809.
2. ^ Uzawa, H. (1963). "On a Two-Sector Model of Economic Growth II". The Review of Economic Studies 30 (2): 105–118. JSTOR 2295808.