Harman Patil (Editor)

Inada conditions

Updated on
Edit
Like
Comment
Share on FacebookTweet on TwitterShare on LinkedInShare on Reddit

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 f ( x ) are:

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

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

References

Inada conditions Wikipedia