Inada conditions
Appearance
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 are:
- the value of the function at 0 is 0:
- the function is continuously differentiable,
- the function is strictly increasing in : ,
- the second derivative of the function is negative in (thus the function is concave): ,
- the limit of the first derivative is positive infinity as approaches 0: ,
- the limit of the first derivative is zero as approaches positive infinity:
All these conditions are met by a Cobb–Douglas production function.
References
Further reading
- Barro, Robert J.; Sala-i-Martin, Xavier (2004). Economic Growth (Second ed.). London: MIT Press. pp. 26–30. ISBN 0-262-02553-1.
- Gandolfo, Giancarlo (1996). Economic Dynamics (Third ed.). Berlin: Springer. pp. 176–178. ISBN 3-540-60988-1.
- Romer, David (2011). "The Solow Growth Model". Advanced Macroeconomics (Fourth ed.). New York: McGraw-Hill. pp. 6–48. ISBN 978-0-07-351137-5.