Historical materialism, dynamic optimization and economic growth: comments on the mathematization of Marxist political economy

QIAO Xiaonan1,2 HE Zili1,2

(1.School of Economics, Nankai University)
(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;

【Funds】 General Program of the National Social Science Fund of China (14BJL048) Key Program of the National Social Science Fund of China (ZX20150046) General Program of the National Social Science Fund of China (13BKS047)

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    [1]. ① [France] LaFargue, P. Souvenirs personnelssur Karl Marx. Beijing: People’s Publishing House, 73 (1973).

    [2]. ① The Complete Works of Marx and Engels (马克思恩格斯全集) 33. Beijing: People’s Publishing House, 87 (1995).

    [3]. ② The typical foreign scholars include the school of analytical Marxism represented by John Roemer, and the related Chinese literature includes Ding (1999), Ding and Li (2007), Zhang (2006), Ma (2011), Fujimori and Li (2014), Wu and Bai (2015), as well as Meng and Feng (2015 and 2016). Due to space limitations, not all of the research is fully listed here.

    [4]. ③ Selected Works of Marx and Engels (马克思恩格斯选集), Vol. 4. Beijing: People’s Publishing House, 742–743 (1995).

    [5]. ④ Selected Works of Marx and Engels (马克思恩格斯选集), Vol. 2. Beijing: People’s Publishing House, 32–33 (1995).

    [6]. ① Labor capital goods refer to the stock of capital goods corresponding to unit labor or labor time. If the labor time that the unit labor can provide is standardized as 1, the two are completely equivalent in the mathematical expression.

    [7]. ① Superscript ** here indicates the equilibrium of common decision model to distinguish it from the equilibrium of capitalist decision model.

    [8]. ① A series of research by Kanae analyzed the problem of price and value determination under different welfare functions, but to maintain the consistency of the model, this paper followed the above logarithm function form.

    [9]. ① See Piketty (2014).

    [10]. ② The existing literature shows that Piketty’s data can be used for research. Meanwhile, the declining trend of profit margin emphasized by Marx can be obtained (Maito, 2014).

    [11]. 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.

    [12]. 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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This Article


CN: 11-1081/F

Vol 52, No. 08, Pages 17-32

August 2017


Article Outline


  • 1 Introduction
  • 2 Productivity: industrial revolution and economic growth
  • 3 Production relations: class and exploitation
  • 4 The labor theory of value: from the production system to the value system
  • 5 Social reproduction: a perspective of understanding the economic structure and its proportionality
  • 6 Organic composition of capital and profit margin: re-examination based on the value dimension
  • 7 Economic cycle: random shocks and economic fluctuations
  • 8 Root of wealth inequality: an explanation of the Piketty experience
  • 9 Conclusions
  • Footnote