Inada Terms

Inada conditions in the macroeconomics are called assumptions about the nature of the production function , which guarantee the stability of economic growth in the neoclassical model . In its current form, Hirofumi Uzawa was introduced ^[1] , named after another Japanese economist, ^[2] .

Six conditions are given:

function value $f(\mathbf {x} )$ ${\ displaystyle f (\ mathbf {x})}$ $f (\ mathbf {x})$ at $\mathbf {x} =\mathbf {0}$ ${\ displaystyle \ mathbf {x} = \ mathbf {0}}$ ${\ displaystyle \ mathbf {x} = \ mathbf {0}}$ equals 0: $f(\mathbf {0} )=0$ ${\ displaystyle f (\ mathbf {0}) = 0}$ ${\ displaystyle f (\ mathbf {0}) = 0}$ ;
the function is continuously differentiable ;
function strictly increases in $x_{i}$ ${\ displaystyle x_ {i}}$ $x_ {i}$ : $\partial f(\mathbf {x} )/\partial x_{i}>0$ ${\ displaystyle \ partial f (\ mathbf {x}) / \ partial x_ {i}> 0}$ ${\ displaystyle \ partial f (\ mathbf {x}) / \ partial x_ {i}> 0}$ ;
the second derivative of the function is negative with respect to $x_{i}$ ${\ displaystyle x_ {i}}$ $x_ {i}$ (i.e. the function is concave ): $\partial ^{2}f(\mathbf {x} )/\partial x_{i}^{2}<0$ ${\ displaystyle \ partial ^ {2} f (\ mathbf {x}) / \ partial x_ {i} ^ {2} <0}$ ${\ displaystyle \ partial ^ {2} f (\ mathbf {x}) / \ partial x_ {i} ^ {2} <0}$ ;
first derivative limit $f(\mathbf {x} )$ ${\ displaystyle f (\ mathbf {x})}$ $f (\ mathbf {x})$ equal to infinity for $x_{i}$ ${\ displaystyle x_ {i}}$ $x_ {i}$ tending to 0: $\lim _{x_{i}\to 0}\partial f(\mathbf {x} )/\partial x_{i}=+\infty$ ${\ displaystyle \ lim _ {x_ {i} \ to 0} \ partial f (\ mathbf {x}) / \ partial x_ {i} = + \ infty}$ ${\ displaystyle \ lim _ {x_ {i} \ to 0} \ partial f (\ mathbf {x}) / \ partial x_ {i} = + \ infty}$ ;
first derivative limit $f(\mathbf {x} )$ ${\ displaystyle f (\ mathbf {x})}$ $f (\ mathbf {x})$ equal to 0 for $x_{i}$ ${\ displaystyle x_ {i}}$ $x_ {i}$ tending to infinity: $\lim _{x_{i}\to +\infty }\partial f(\mathbf {x} )/\partial x_{i}=0$ ${\ displaystyle \ lim _ {x_ {i} \ to + \ infty} \ partial f (\ mathbf {x}) / \ partial x_ {i} = 0}$ ${\ displaystyle \ lim _ {x_ {i} \ to + \ infty} \ partial f (\ mathbf {x}) / \ partial x_ {i} = 0}$ .

Of the class of CES functions, all these conditions are satisfied only by the Cobb – Douglas function .

Notes

↑ Uzawa , H. On a Two-Sector Model of Economic Growth II (Eng.) // The Review of Economic Studies : journal. - 1963. - Vol. 30 , no. 2 . - P. 105-118 .
↑ On a Two-Sector Model of Economic Growth: Comments and a Generalization (English) // The Review of Economic Studies : journal. - 1963. - Vol. 30 , no. 2 . - P. 119-127 .

Literature

Barro R.J. , Sala-i-Martin H. Economic growth. - M .: BINOM. Knowledge laboratory. - 2010 .-- S. 41 - 824s. - ISBN 978-5-94774-790-4 .
Romer D. Higher Macroeconomics. - M.: Publishing. HSE House, 2014 - p. 28—29 —855s. - ISBN 978-5-7568-0406-2
Gandolfo, Giancarlo. [ [1] in Google Books Economic Dynamics]. - Third. - Berlin: Springer, 1996. - P. 176-178. - ISBN 3-540-60988-1 .

[1] Uzawa , H. On a Two-Sector Model of Economic Growth II (Eng.) // The Review of Economic Studies : journal. - 1963. - Vol. 30 , no. 2 . - P. 105-118 .

[2] On a Two-Sector Model of Economic Growth: Comments and a Generalization (English) // The Review of Economic Studies : journal. - 1963. - Vol. 30 , no. 2 . - P. 119-127 .

Inada Terms

Notes

Literature

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