Inada conditions

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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 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}: \partial f(x)/\partial x_{i}>0,
  4. the second derivative of the function is negative in x_{i} (thus the function is concave): \partial^{2} f(x)/\partial x_{i}^{2}<0,
  5. the limit of the first derivative is positive infinity as x_{i} approaches 0: \lim_{x_{i} \to 0} \partial f(x)/\partial x_i =+\infty,
  6. the limit of the first derivative is zero as x_{i} approaches positive infinity: \lim_{x_{i} \to +\infty} \partial f(x)/\partial x_i =0


References[edit]

  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. 

Further reading[edit]