两种等效益面生产函数与全要素生产率变化率的分解

本文根据规模报酬可变还是规模报酬不变，分别定义了一般等效益面生产函数和典型等效益面生产函数。由一般等效益面生产函数的离散型分解式可以测算一个生产单元的纯技术进步，以及纯技术效率变化对经济增长的贡献；而由典型等效益面生产函数可以将全要素生产率的变化率分解为典型技术进步率、纯技术效率和规模效率的变化率之和。进而由具有明确几何意义的离散型分解式分别测算典型技术进步和规模效率对经济增长的贡献。等效益面生产函数与分解式的几何意义还说明，全要素生产率的改变最终是由技术创新、制度创新和管理创新共同推动的。

Two kinds of Equal Efficiency Production Function and Decomposition of Productivity Change

The general equal efficiency production function and the typical equal efficiency production function are characterized by their variable returns to scale and constant returns to scale respectively. The algebraic decomposition based on the general equal efficiency production function can be used to estimate the shares in the economic growth contributed by the pure technical change and the change of pure technical efficiency. The change in total factor productivity is identified as the vertical shift of the typical equal efficiency production function, which can be further decomposed into the typical technological progress, the effect of scale economy, and the change in pure technical efficiency. Furthermore, the geometric illustration and the economic significance of the equal efficiency production function and its decomposition imply that the change in total factor productivity is driven by the innovation of technology, improvement of management and the renovation of regulations.