稻田条件

在宏观经济学中， 稻田条件 (根据日本经济学家稻田献一命名)^[1] 是关于生产方程形状的假设。如果满足稻田条件，就在新古典经济增长模型中满足了经济增长稳定。

对于函数${\displaystyle f(x)}$，六个条件是:

1. 函数 ${\displaystyle f(x)}$ 在x为0时的值为0: ${\displaystyle f(0)=0}$
2. 函数连续可导,
3. 函数对任何自变量${\displaystyle x_{i}}$都严格递增: ${\displaystyle \partial f(x)/\partial x_{i}>0}$,
4. 函数的一阶导数对自变量${\displaystyle x_{i}}$严格递减 (也就是说函数是凹函数): ${\displaystyle \partial ^{2}f(x)/\partial x_{i}^{2}<0}$,
5. 一阶导函数在任一自变量${\displaystyle x_{i}}$趋于0时极限为正无穷大：${\displaystyle \lim _{x_{i}\to 0}\partial f(x)/\partial x_{i}=+\infty }$,
6. 一阶导函数在任一自变量${\displaystyle x_{i}}$趋于正无穷大时极限为0：${\displaystyle \lim _{x_{i}\to +\infty }\partial f(x)/\partial x_{i}=0}$

可以证明^[2] 稻田条件决定了生产方程一定渐进于Cobb–Douglas函数。

参考

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