Karl Marx’s economic theory, despite being one of the most comprehensive critiques of capitalism, has often been criticized for lacking the mathematical rigor associated with modern economic analysis. One of the persistent critiques is that Marx failed to employ marginal analysis, a fundamental tool in neoclassical economics that focuses on incremental changes in economic variables. Some assert that Marx’s use of averages, rather than marginal techniques, reflects a primitive approach compared to the marginal revolution that began with Jevons, Walras, and Menger. John Maynard Keynes dismissed Capital as “an obsolete economic textbook” that was not only scientifically flawed but also irrelevant to the modern world. Paul Samuelson’s critique was even more belittling, as he characterized Karl Marx as a “minor post-Ricardian” in economic theory. Considering that Samuelson viewed Ricardo himself to be “the most overrated of economists,” this judgment is particularly dismissive, implying that Marx’s contributions were even less significant by comparison. More recently, Sandmo claimed that Marx is of “little direct importance” to modern economic theory, “even if there still are economists who find inspiration in Marx’s works.”
Being one of those economists, to whom Sandmo condescendingly refers, I intend to counter these critiques by demonstrating that Marx’s writings reveal a deep understanding of the dynamics that marginal analysis later formalized, while also arguing that his use of averages better captures economic reality, particularly in the context of crises and systemic trends.
Marx’s interest in the philosophical implications of calculus
Marx’s lack of formal marginal analysis was not due to ignorance of calculus or its utility. In his Mathematical Manuscripts, Marx explored the philosophical implications of calculus, particularly the nature of continuous change and infinitesimals. He was deeply interested in how these mathematical concepts could be applied to his broader understanding of capitalist dynamics, but he was more concerned with the social relations and class structures underlying economic processes than with mathematical formalism.
As noted by Jon Elster, “political bias apart, Marx’s economic theory fell on deaf ears because it came at the wrong time,” coinciding with the rise of marginalism. Nevertheless, as John Roemer and other scholars have shown, Marx’s concepts of exploitation and accumulation can be formalized using marginal analysis tools, demonstrating his underlying grasp of these ideas
Marx and the use of marginal techniques
Though Marx did not explicitly adopt the formal apparatus of marginal analysis, his economic thought clearly reveals an intuitive grasp of the principles behind it. In Das Kapital, Marx often refers to rates of change, marginal effects, and diminishing returns—concepts that modern economists would describe using marginal analysis.
For instance, in Das Kapital (Volume III, Chapter 15), Marx discusses the falling rate of profit and capital accumulation:
“We have seen… that the rate of profit expresses the rate of surplus-value always lower than it actually is. We have just seen that even a rising rate of surplus-value has a tendency to express itself in a falling rate of profit… The rate of profit would equal the rate of surplus-value only if c = 0, i.e., if the total capital were paid out in wages.”
Here, Marx is clearly discussing the rate of change of capital, which mirrors the kind of marginal thinking that neoclassical economists later formalized. The diminishing marginal returns on capital investment are implicit in his description of the falling rate of profit as the organic composition of capital rises. This can be formalized as a profit maximization problem, where capitalists accumulate capital until the marginal return on investment no longer justifies further accumulation:
This equation represents the condition at which capitalists stop investing—when the marginal profit (П) on additional capital (К) becomes zero or negative. Marx’s description shows a clear anticipation of the ideas that later became central to marginalist thought.
In another passage, Marx touches upon what modern economists would call the marginal product of labor:
“In the same measure in which production is cheapened – i.e., in the same measure in which more can be produced with the same amount of labour – it compels by a law which is irresistible a still greater cheapening of production, the sale of ever greater masses of product for smaller prices.”
Marx is describing a situation in which technological innovation or division of labor leads to an increase in the marginal product of labor—more output with the same input. This concept, while not labeled as such, aligns with what later became formalized as the marginal productivity theory in neoclassical economics.
The relationship between labor and output, in this context, could be captured by a marginal productivity function f(L), where L is the amount of labor. The marginal product of labor MPL is the derivative of the output function with respect to labor:
Marx’s discussion shows a clear awareness of how changes in labor efficiency (through mechanization or labor division) affect overall output, though he focuses on the broader implications for capitalist competition and profit.
Averages vs. marginal products: A matter of economic reality
More importantly, neoclassical explanations based on marginal analysis are not necessarily superior in describing economic reality. For example, Anwar Shaikh argues in Capitalism: Competition, Conflict, Crisis that Marxist treatment of production is quite consistent with the empirical evidence, and that the theoretical cost curves derived in this basis are similar to empirically observed curves and consistent with business experience. On the other hand, the ubiquitous neoclassical U-shaped cost curve is neither empirically grounded nor of much practical use.
Critics often claim that Marx’s use of averages, rather than marginal products, shows a lack of sophistication. However, Marx’s focus on averages is more reflective of economic reality than marginalist approaches. For example, crises in capitalism occur not because individual capitalists stop investing when their marginal product of capital declines but because the national average rate of profit falls. Given the tendency for profit rates to equalize across sectors, as Marx highlighted, it is the dynamic of the average rate of profit that defines boom and bust cycles in capitalist economies, as Carchedi and Roberts convincingly demonstrate using the US data for the past 60 years.
Consider Marx’s theory of the falling rate of profit, which argues that as the organic composition of capital (constant capital to variable capital) increases, the rate of profit tends to decline, leading to crises:
Here, r is the rate of profit, s is surplus value, c is constant capital, and v is variable capital. As c rises relative to v, r falls. Marx was not concerned with the marginal product of capital for an individual firm but with how systemic trends in the average rate of profit lead to crises. This systemic view is crucial for understanding the broader dynamics of capitalism, where crises are triggered by declines in average profitability, not the marginal decisions of individual capitalists.
Moreover, Marx’s use of averages is particularly relevant when analyzing labor exploitation. While marginal productivity theory focuses on the productivity of individual workers, Marx’s concern was with the average rate of surplus value extracted from the working class as a whole. Marx argued that capitalism tends to obscure the socially necessary labor time involved in producing commodities. The average rate of surplus value, which aggregates the exploitation of labor across different sectors and firms, provides a better understanding of the systemic exploitation embedded in capitalist production. This is important because it is the aggregate or average rate of exploitation that drives overall capital accumulation, not the marginal decisions of individual firms. The systemic exploitation of labor can only be understood through an analysis of averages, as the profit generated from labor in one firm impacts the overall exploitation rate across the economy.
In his discussion of the law of value and the equalization of profit rates, Marx again shows why averages are more applicable than marginal values. The average rate of profit becomes the gravitational center around which individual profit rates fluctuate. Capitalists, by seeking higher returns, move capital between sectors, causing profit rates to equalize across the economy. Thus, it is the average rate of profit that determines long-term investment behavior, not the marginal profit rate of any one sector at a given moment.
This explains why Marx was focused on the general tendencies of capitalism, such as the falling rate of profit, rather than the decisions of individual capitalists optimizing marginal returns. The systemic outcome of these individual actions leads to the equalization of profit rates over time, which can only be understood through the lens of average profit rates.
Marx’s grasp of marginalism compared to his predecessors
In this respect, Marx showed a greater understanding of economic reality than his classical predecessors, Adam Smith and David Ricardo, who focused on long-term averages without engaging deeply with marginal effects. Smith’s theory of value, for instance, is based on the amount of labor required to produce goods over time, while Ricardo’s focus on rent and wages similarly lacks a consideration of marginal productivity.
In contrast, Marx’s work demonstrated a dynamic understanding of how capital accumulation, labor productivity, and profit rates evolve in response to competitive pressures. As David Harvey notes in A Companion to Marx’s Capital, Marx’s focus on the falling rate of profit and its systemic effects shows a deeper grasp of the dynamics of capitalism than either Smith or Ricardo
Marx’s approach predated the marginalist revolution by several decades, and while he did not adopt the formal tools of marginal analysis, his theory nonetheless reflected the underlying dynamics of incremental change. Moreover, Marx’s critique of capitalism retained a class-oriented focus, distinguishing his work from the individualistic orientation of marginalist economics. This class focus allows Marx’s theory to address the systemic exploitation and crises that arise from capitalist production, which marginalist theory often ignores.
The ideological nature of criticizing Marx
While critics accuse Marx of lacking the formal rigor of marginal analysis, it is telling that the same critique is rarely applied to Adam Smith or David Ricardo. Both of these economists, whose works Marx heavily relied on (while also critiquing their limitations), developed their theories without the benefit of formal marginalist tools, yet their contributions are celebrated as foundational. But Smith’s “invisible hand,” which implies social harmony, obviously suits the capitalist class much better than Marx’s call for “changing the world.” This double standard reflects an ideological bias: Marx’s radical critique of capitalism invites scrutiny that is often harsher than what is applied to other classical economists.
In reality, Marx’s understanding of economic dynamics predated the marginalist revolution by several decades. His insights into how rates of profit, capital accumulation, and labor productivity interact show a keen understanding of marginal changes and the forces of competition. While Marx didn’t use the formal tools of calculus in his expositions, the substance of his analysis is undeniably aligned with the concepts that marginalism later formalized. At the same time, his insights into capital accumulation, profit rates, and labor exploitation offer a deeper understanding of capitalism’s systemic crises—insights that marginalism often overlooks.
Conclusion: Marx’s relevance in the modern economic discourse
Marx’s economic theory remains one of the most comprehensive critiques of capitalism, and the accusations that it lacks mathematical rigor or marginal analysis miss the mark. While Marx did not use the formal tools of marginalism, his writings clearly demonstrate an understanding of marginal dynamics, particularly in the context of the falling rate of profit, capital accumulation, and labor exploitation. Moreover, Marx’s use of averages offers a more realistic account of systemic trends in capitalist economies, particularly when analyzing crises and profit rates.
Far from being outdated, Marx’s insights remain highly relevant to contemporary economic discussions. As Michael Heinrich and Anwar Shaikh have noted, Marx’s analysis of capitalism continues to provide valuable tools for understanding the systemic crises that characterize modern economies. By focusing on class dynamics and the average behavior of economic variables, Marx offers a broader perspective that complements and, in many ways, surpasses the individualistic focus of marginalist economics.
In the aftermath of the events in the Soviet Union and Eastern Europe from 1989 to 1991, many in academic and media circles declared that “communism had died,” asserting that Marx and Marxism were now irrelevant and disproven. However, as Hunt and Lautzenheiser argue, Marx’s work was fundamentally a critique of capitalism, not of the systems that called themselves “communist.” These developments in Eastern Europe do not diminish Marx’s profound insights into the nature and dynamics of capitalist economies. If Marx had written about economies like those in Eastern Europe, perhaps these events could challenge his ideas. But since his focus was on understanding capitalism, only developments within capitalist systems can truly test or disprove his theories. According to Hunt and Lautzenheiser, those events have yet to occur, and Marx’s ideas will continue to remain relevant as long as capitalism operates as he described.
Marx’s economic theory, when understood in its proper context, demonstrates both mathematical sophistication and a deeper grasp of capitalist dynamics than is often acknowledged. It is time to reassess Marx’s contributions and recognize the enduring relevance of his work in light of modern economic challenges.