新古典增长模型:一个重新表述

Neoclassical Growth Models:A Reformulation

各类新古典增长模型在现有教科书中的表述形式存在很大的差异:无技术进步和外生技术进步的模型分别使用"劳均资本"和"有效劳均资本"的动态方程,内生技术进步的模型则使用"产出资本比"的动态方程。本文统一使用"产出资本比"和"消费资本比"变量对代表性的新古典增长模型,如索洛-斯旺模型、拉姆齐-卡斯-库普曼斯模型和卢卡斯模型,进行了重新表述。这种重新表述与现有教材的表述相比,具有两个明显的优点:第一,各种新古典增长模型在表述上具有数学形式上的一致性,这种一致性能够更加清晰地显示各个模型之间的继承与发展关系;第二,本文清楚地揭示新古典增长模型的核心结论是证明均衡产出资本比与消费资本比的存在且稳定,这是模型其它所有结论的基础。

Large disparities can be found in textbooks＇ treatments of different neoclassical growth models. Models without technical progress and with exogenous technical progress deliver themselves of dynamic equations of capital per labor and capital per efficient labor, respectively. Models with endogenous technical progress, however, make consistent use of dynamic equations of output-capital ratio. Employing two variables output-capital ratio and consumption ratio, we reformulate representative neoclassical growth models, including Solow-Swan model, Ramsey- Cass-Koopmans model, and Lucas model.Compared with existing expression, our reformulations have two distinct merits. First, our expressions for various models are consistent in their mathematical forms, and this consistence shows the clear-cut relationship of inheritance and development among various models. Second, our reformulation reveals distinctly that the core conclusion of neoclassical growth models is to verify the existence and stability of equilibria for output-capital ratio and consumption ratio, which form the base for all other conclusions.