马克思的社会扩大再生产的动态投入产出分析

The Dynamic Input-Output Analysis of Marx’s Social Reproduction Expansion

建立马克思的社会扩大再生产的动态投入产出模型。本文基于社会扩大再生产持续进行的可行路径和充分必要条件,推导社会扩大再生产的动态投入产出传递矩阵和一般求解方法。推导传递矩阵的特征值与相应的特征向量,给出动态投入产出优化的结果。借助马克思《资本论》中的一个举例,计算验证了社会扩大再生产动态投入产出的特征值和优化。

The model of dynamic input-output analysis of Marx’s social reproduction expansion was established. Based on the feasible path of continuous social reproduction expansion with corresponding sufficient and necessary conditions,this paper deduced a transfer matrix and a common method of seeking solution of the dynamic input-output model. The paper deduced the eigenvalue of the transfer matrix and the corresponding eigenvectors. The results of dynamic input-output optimization were also given. An example of Marx’s Das Kapital was drawn upon to verify the eigenvalue and the optimization of dynamic input-output of the reproduction expansion,in a calculative way.