Historical materialism, dynamic optimization and economic growth: comments on the mathematization of Marxist political economy
(2.Collaborative Innovation Center for China Economy, Nankai University 300071)
【Abstract】Nowadays, how to innovate and develop the Marxist political economy and further build a socialist political economy with Chinese characteristics remains a major theoretical issue for China’s economic academy. How to promote the mathematization of Marxist political economy is a question worthy of further study. Due to a lack of understanding of the Marxist political economy, there has long been a misunderstanding that it rejects mathematical methods and that compared with current western economics its degree of mathematization is not high and thus lacks scientificity. Scholars engaged in Marxist political economy have two views on its mathematization. Some scholars have fully affirmed the advantages of mathematical methods and have actively promoted the mathematization of Marxist political economy. Others have demonstrated cautious attitudes toward the mathematization of Marxist political economy and advocate insisting on its essence in the process of theoretical development. They want to avoid the western economics problem of excessive mathematics. However, they are cautious of vulgarization due to the pursuit of a mathematical form. If our aim is to innovate and develop the Marxist political economy, it is necessary to analyze and respond to the above views. We take the Marxist theory of optimal economic growth as a clue, systematically reviewing the characteristics of its theoretical modeling in seven aspects: productivity, production relations, the labor theory of value, social reproduction, capital organic composition and profitability, economic fluctuations, and inequality between the rich and poor. Furthermore, through the comparative analysis of the Marxist theory of optimal economic growth and the mathematical model of Western economics, we provide a preliminary discussion of the basic principles and modeling ideas of the mathematization of Marxist political economy. Our research indicates that Marxist political economy does not exclude mathematical methods. However, the process of mathematical modeling must adhere to historical materialism as a basic principle, which means seizing the contradictory relationship between productivity and production relations and their movement to analyze the law of economic and social operation. It is a viable modeling idea to construct a dynamic model based on the labor theory of value, which involves two kinds of behavior subjects ( workers and capitalists), distinguishes production goods and consumption goods, and includes the exploitative relationship and the characteristics of circuitous production. Specifically, at the productivity level, along with technological progress and industrial revolution, we focus on the impact of the combination of labor and means of production on the mode of production, using the dynamic changes in the number of capital goods per unit labor to examine the proportion of labor allocation and economic growth between two categories. At the level of production relations, based on the theory of labor creating value, we translate the economic production system into a value system by calculating the value per unit of goods in two categories. Furthermore, based on the specific productivity development stage ( i.e., the extent to which the production of goods limits human labor in terms of physical strength, endurance, and precision in the production process), we examine the relationship between the particular ownership and the exploitation of the capitalist class to the working class. The income distribution relationship as a flow affects the ownership of production goods as a stock, which makes production relations feeding back to productivity and promotes economic and social development. As western economics mainly solves the problem of resource allocation and focuses on describing the “invisible hand” of the market mechanism, it hardly deals with the problem of production relations and the translation from a production system to a value system. Therefore, this determines the complexity and innovation of Marxist political economy modeling.
【Keywords】 Marxist political economy; mathematical method; historical materialism;
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. ① Superscript ** here indicates the equilibrium of common decision model to distinguish it from the equilibrium of capitalist decision model.
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. ① See Piketty (2014).
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. ③ The expansion of the theory includes the study of Liu (2008) on government taxation and study of Ohnishi and Kanae (2015) on populous countries.
. ① The optimization model also involves economic philosophy issues. Accordingly, some scholars opposed using optimization technology modeling. This paper also maintains that it is necessary to dialectically view the relationship between finiteness and completeness of rationality and that between the economic individual and the whole. However, it can be tried at least in the discussions about the benchmark model.
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