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一个评价单元的等效益面生产函数是这个单元的技术效率与前沿面生产函数之积。在这一定义之下,本文证明了全要素生产率的改变就是等效益面生产函数的相对垂直移动。由此,在假设规模效益不变的情况下,可将一个评价单元的经济增长量分解为三个要素的代数和。这三个要素分别是:技术进步、技术效率的改善和投入量增加的贡献。在此时间离散型分解式的基础上,根据这些要素的不同变化情况,进一步给出了技术进步贡献率的测算方法。这种测算方法既可以评价各生产单元的单期技术进步贡献率,也可以测算它们在一个周期上的技术进步贡献率。基于等效益面生产函数上的关于经济增长的代数分解式与技术进步贡献率的定义均具有明显的几何意义。
The equivalent benefit surface production function of an evaluation unit is the product of the technical efficiency of this unit and the frontier production function. Under this definition, this paper proves that the change of total factor productivity is the relative vertical movement of the equivalent benefit surface production function. As a result, the economic growth of one evaluation unit can be decomposed into the algebraic sum of the three elements under the assumption of the same economies of scale. The three elements are: technological progress, improvement of technical efficiency and contribution of increased input. Based on the discrete decomposition of this time, the method of calculating the contribution rate of technological progress is given according to the different changes of these factors. This measurement method can not only evaluate the contribution rate of single-phase technological progress of each production unit, but also measure their contribution rate of technological progress in one cycle. The definitions of the algebraic decomposition of economic growth and the contribution rate of technological progress based on the equivalence benefit production function all have obvious geometric meanings.