稻田條件

在宏觀經濟學中， 稻田條件 (根據日本經濟學家稻田獻一命名)^[1] 是關於生產方程形狀的假設。如果滿足稻田條件，就在新古典經濟增長模型中滿足了經濟增長穩定。

對於函數${\displaystyle f(x)}$，六個條件是:

1. 函數 ${\displaystyle f(x)}$ 在x為0時的值為0: ${\displaystyle f(0)=0}$
2. 函數連續可導,
3. 函數對任何自變量${\displaystyle x_{i}}$都嚴格遞增: ${\displaystyle \partial f(x)/\partial x_{i}>0}$,
4. 函數的一階導數對自變量${\displaystyle x_{i}}$嚴格遞減 (也就是說函數是凹函數): ${\displaystyle \partial ^{2}f(x)/\partial x_{i}^{2}<0}$,
5. 一階導函數在任一自變量${\displaystyle x_{i}}$趨於0時極限為正無窮大：${\displaystyle \lim _{x_{i}\to 0}\partial f(x)/\partial x_{i}=+\infty }$,
6. 一階導函數在任一自變量${\displaystyle x_{i}}$趨於正無窮大時極限為0：${\displaystyle \lim _{x_{i}\to +\infty }\partial f(x)/\partial x_{i}=0}$

可以證明^[2] 稻田條件決定了生產方程一定漸進於Cobb–Douglas函數。

參考

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
2. 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