Inada conditions
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 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.
It can be shown[2] that the Inada conditions imply that the production function must be asymptotically Cobb–Douglas.
In stochastic neoclassical growth model if the production function does not satisfy the Inada condition at zero, any feasible path converges to zero with probability one provided that the shocks are sufficiently volatile.[3]
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
- ^ Barelli, Paulo and Samuel de Abreu Pessoa (2003) "Inada Conditions Imply That Production Function Must Be Asymptotically Cobb-Douglas" Economics Letters 81(3) 361-63
- ^ Takashi Kamihigashi (2006) "Almost sure convergence to zero in stochastic growth models", Economic Theory (Springer), 29(1), 231-237