Mathematical analysis in Marxist political economy
Mathematical analysis offers opportunities for innovating Marxist political economy. Photo: TUCHONG
Mathematical political economy is a paradigm that employs mathematical analysis methods to conduct research on Marxist political economy. To clarify why and how mathematical analysis methods are used in the study of Marxist political economy, it is necessary to understand the theoretical contributions and development directions of mathematical political economy.
Origins of mathematical analysis in political economy
The use of mathematical analysis in Marxist political economy is by no means a novelty. In Das Kapital, Marx paid close attention to uncovering quantitative relationships as a way to clearly and precisely reveal the underlying laws of capital movement. He left behind a large volume of mathematical manuscripts, many of which are temporally or conceptually connected to his economic writings. Marxist political economy has never lacked nor rejected mathematical methods; on the contrary, the scientificity and revolutionary nature of its theory partly stem from employing what were, at the time, the most advanced analytical techniques. As Paul Lafargue recounted in Reminiscences of Marx, Marx believed that a science only reaches true perfection when it successfully applies mathematics. Therefore, the proper use of mathematical analysis is both an inevitable requirement and a key means of enhancing the scientific validity and epochal significance of Marxist political economy.
More specifically, mathematical analysis offers three distinct advantages for the development of Marxist political economy. First, mathematical language surpasses natural language in its capacity to articulate theoretical content with clarity and precision. Second, it provides a structured framework for critically engaging with specific theories through targeted discussions using concrete mathematical models. Third, Marxist political economy adheres to historical materialism. The integration of logic and history is fundamental to its methodology. Mathematical models enhance the compatibility between theory and empirical data, making it easier to test the consistency between theoretical propositions and real-world facts. In short, employing mathematical analysis methods significantly strengthens both the normative foundation and practical relevance of Marxist political economy.
Developing mathematical analysis
The feasibility of applying mathematical analysis to Marxist political economy rests on solid ground. On one hand, Marxist political economy offers a systematic theoretical framework accompanied by a coherent, self-consistent set of concepts, which provides a natural basis for formalized expression. Marxist scholars have already demonstrated the potential of employing mathematical analysis, influencing fields such as the post-Keynesian school and modern growth theory. On the other hand, as mathematical tools have become increasingly sophisticated, there is now greater opportunity to develop and employ analytical tools better suited to the theoretical framework of Marxist political economy—tools capable of tackling problems that Marx “could not solve at least temporarily,” due to methodological constraints. Consequently, the future development of mathematical political economy requires maintaining fidelity to the basic methods and principles of Marxist political economy, while selectively incorporating useful insights from mathematical economics.
Mathematical analysis serves economic thought. While certain insights can be rigorously argued using natural language alone, economists nevertheless value the catalytic role that well-constructed mathematical models play in refining theoretical arguments. Good models possess both “retrospective” and “prospective” qualities, which demands higher standards in their application. Model assumptions should be simple—akin to “Occam’s razor”—while every step of the solution process should carry explicit and coherent economic meaning. In terms of the positioning of mathematical analysis methods and requirements for mathematical models, Marxist political economy largely aligns with Western economics. The fundamental difference lies not in the tools themselves, but in the underlying economic philosophy. Divergent economic thought leads to different applications of mathematical analysis. Comparatively speaking, mathematical political economy exhibits three distinct characteristics.
First, it emphasizes that economic agents are the embodiment of specific production relations. Neoclassical economics focuses on the decision-making behavior of representative economic agents, assuming they are rational individuals with the freedom to weigh all trade-offs. By contrast, Marxist political economy stresses production relations: economic agents are not atomized individuals but are embedded in interdependent production processes of goods and services. Capitalists, who own the means of production, earn what they spend, while workers, as the labor force, spend what they earn. These relationships between people shape real, antagonistic economic positions and manifest in differences in income sources, consumption patterns, and other behaviors—relationships that cannot be reduced to mere transactions between people and objects.
Second, it views economic operation as a cyclical process linked by extensive, roundabout production. Neoclassical economics typically adopts a “linear flow” framework, progressing from production factors to final output. In contrast, Marxist political economy stresses a “circular flow” perspective, viewing economic operation as the integration of production and circulation processes. Surplus value aside, outputs of one production stage become production factors for the next. The growth and distribution of national wealth are two sides of the same coin. Accordingly, mathematical political economy places particular emphasis on input-output data, understanding the national economic cycle as a circulation of value and use value with the carrier of capital cycle.
Third, beyond the two main differences in model setup, mathematical political economy also requires a return to the methodological approach of historical materialism during model resolution. Neoclassical economics tends to focus on observable phenomena and assumes stable equilibrium conditions. Marxist political economy, however, posits that equilibrium is only occasionally achieved and is often subject to disruption. It focuses instead on underlying economic structures. Marx’s concept of “commodity fetishism” reminds us to distinguish between surface appearances and internal laws. While identifying equilibrium conditions has its place, it is more crucial to reveal the forces leading to disequilibrium—namely, deep-seated structural contradictions—in order to truly return to the methodology of historical materialism.
Enriching Chinese Marxist political economy
Since the reform and opening up, under the guidance of seasoned political economists and with the efforts of younger scholars, research in mathematical political economy has steadily advanced, achieving notable breakthroughs in specialized areas. In the new era, China’s development of mathematical political economy has greatly enriched research in socialist political economy with Chinese characteristics and has contributed to the ongoing adaptation of Marxism to the Chinese context and the needs of the times. In recent years, increasing numbers of young scholars have entered the field, producing a series of original achievements that can broadly be categorized as either “By Marx” or “For Marx.”
Research “By Marx” is problem-oriented empirical work that uses the foundational theories of Marxist political economy to quantitatively assess China’s current economic development, aiming to elevate China’s experience into systematic Chinese theories. One focus is on structural factors, using the “technical structure of reproduction” as a key variable to systematically summarize and accurately grasp the structural features underpinning China’s high-quality development. Another line of inquiry leverages the analytical strength of Marx’s department classification framework, systematically analyzing the interactions among distinct yet interconnected economic sectors to explore structural contradictions and long-term dynamics. A third focus expands the research scope to better understand new phenomena, trends, and contradictions, developing new models and metrics to address major economic challenges facing China.
Research “For Marx,” on the other hand, seeks to refine and advance the core theories of Marxist political economy through innovations in mathematical analysis. One approach revisits classic propositions, emphasizing the mathematical reconstruction of these ideas through matrix-based and dynamic modeling. By applying modern analytical methods to reexamine foundational theories, scholars can not only offer more standardized interpretations, but also uncover new dimensions and nuances, thereby advancing the theoretical framework of Marxist political economy. Another valuable avenue involves proposing systematic frameworks that, while sometimes carrying ontological implications and generating debate, facilitate comparisons and dialogue across different schools of thought and modeling approaches. Such efforts are particularly useful in clarifying common distortions and misunderstandings of Marxist political economy, both domestically and internationally.
Standing at the forefront of innovation in Marxist political economy, mathematical analysis offers vast potential for application in the study of socialist political economy with Chinese characteristics. More pioneering, high-impact research should be pursued to further enrich and develop this field.
Li Bangxi is an associate professor from the School of Social Sciences at Tsinghua University. Liu Chong is an independent postdoctoral researcher from the Department of Land Economy at the University of Cambridge.
Edited by ZHAO YUAN