生产函数形式与技术替代率

Production Function From and Related Rate of Technical substitution

本文用数学方法推证出两个重要结论:1.生产函数之间存在单增变换式的充要条件是它们的技术替代率相同([1]中定理1):2.生产函数的技术替代率相同的充要条件是它们的替代弹性和生产扩张线均相同([2]中定理2)。在此基础上,文中阐述了生产函数形式完全由技术替代率决定。最后,以常用的C—D、CES和近几年提出的新CES和VES等生产函数为例进行了说明。

In this paper, two signifcant conclusions are obtained. They are 1、Necessary and sufficient conditions for the exist of a monotonic increasing transformation between two production fumctions is that they have the same rate of thchnical substitution(Theoreml in partⅠ); 2、 Necessary and sufficient conditions for the same rate of technical substitution is that their elasticities of substitution and output expansion paths are equal (Theorem 2 in part Ⅱ). In this paper, We also infer that production function form is determined by their rate of technical substitution. In the last the C-D. CES functions and new CES、VESfunctions, Which are described in recent papers, are studied.