马克思两大部类再生产的冯·诺依曼产出比——通过生产资料优先增长获得冯·诺依曼产出比  

von Neumann Output Ratio in Marx's Social Reproduction with the Two Major Categories——Obtaining von Neumann Output Ratio through Preferential Growth of the Means of Production

作　　者：陶为群[1] TAO Weiqun(Jiangsu Branch,The People's Bank of China,Nanjing,Jiangsu,China)

机构地区：[1]中国人民银行江苏省分行

出　　处：《政治经济学季刊》2024年第3期61-79,共19页Political Economy Quarterly

摘　　要：冯·诺依曼产出比是数理经济学中一个具有广泛影响的概念和术语。在马克思社会资本再生产理论的数量关系与冯·诺依曼产出比之间建立联系,辨识并且明晰马克思两大部类再生产的冯·诺依曼产出比,具有理论意义。本文运用马克思社会再生产理论,围绕两大部类再生产的冯·诺依曼产出比与资本家的个人消费的对立统一关系,将两大部类社会再生产公式与两大部类再生产的产出增长方程组贯通。通过找到并确定由两大部类当年产出列向量到下年产出列向量的平衡增长传递矩阵,本文证实了两大部类产出保持原有结构的发展速度是平衡增长传递矩阵的特征值;以两大部类的不变资本增长率作为中介,确定了“生产资料优先增长”是两大部类再生产获得冯·诺依曼产出比的路径。接下来,本文运用马克思两大部类社会再生产能够通过生产资料优先增长使两大部类之间比率收敛的研究结果,获得以马克思社会再生产理论中的几个基本概念和术语为形式化表达的冯·诺依曼产出比;验证了冯·诺依曼产出比、最高平衡增长率、资本家的个人消费最小值满足两大部类再生产的产出增长方程组。von Neumann Output Ratio is a widely influential concept and term in mathematical economics.von Neumann Output Ratio of Marx's reproduction with two major categories is the ratio between the total output of the means of production category and the total output of the consumption category while the two major categories obtain the maximum equilibrium growth rate.It can most centrally formalize the social structure in the state of the highest equilibrium growth.It is of theoretical significance to establish the relationship between the quantity relation of Marx's theory of social capital reproduction and von Neumann Output Ratio,and to identify and clarify von Neumann Output Ratio of Marx's reproduction with two major categories.Based on Marx's theory of social reproduction,following the stand,viewpoint,basic model and analysis method of this scientific theory,this paper focuses on the unity of opposites between von Neumann Output Ratio of Marx's reproduction with two major categories and personal consumption of capitalists,and connects Marx's social reproduction formula and the equation system of output growth of the two major categories.By finding and determining the equilibrium growth transfer matrix of output column vector of the two major categories from this term to next term,the paper proved just the development rate of the output of the two major categories which maintains original output structure is the eigenvalue of the transfer matrix.Then,by using the constant capital growth rate of the whole society of social reproduction as an intermediary,it is determined that the equilibrium growth rate of output of the two major categories is a monotone increasing function of the ratio of output of categoryⅠto output of categoryⅡ,so as to determine that“preferential growth of means of production”is the path to obtain von Neumann Output Ratio of Marx's reproduction.By use of the research result that the ratio between the two major categories in Marx's social reproduction can be convergent through the prefere

关 键 词：两大部类 社会再生产 冯·诺依曼产出比 最优平衡增长 资本家的个人消费 

分 类 号：A81[哲学宗教—马克思主义哲学]