Inada conditions

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 six conditions are:

#the value of the function at 0 is 0,
#the function is continuously differentiable,
#the function is strictly increasing in x,
#the derivative of the function is decreasing (thus the function is concave),
#the limit of the derivative towards 0 is positive infinity,
#the limit of the derivative towards positive infinity is 0.

References

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