No.494245
Someone years ago on here said that if Marx had understood calculus he would have see more patterns in capitalism. Does anyone know what those additional insights would have been. I asked Gemini and here's what I got:
If Marx had mastered calculus, he likely would have gained deeper, more precise insights into the following areas of capitalist mechanics: 1. Marginal Analysis of Exploitation and Profit Marx believed that value was created by labor and that capitalists maximize profits by increasing the rate of exploitation (\(s/v\), where \(s\) is surplus value and \(v\) is variable capital). The Insight: Instead of static ratios, calculus would have enabled Marx to treat the rate of exploitation as a derivative (\(ds/dv\)), allowing him to model how an infinitesimal change in labor hours or wage rates affects surplus value.Marginal Labor Power: He could have analyzed the marginal utility of labor—the exact point at which adding one more worker ceases to be profitable, rather than relying on average productivity. 2. Precise Modeling of the Falling Rate of Profit A central pillar of Marx’s theory is the tendency of the rate of profit to fall as the "organic composition of capital" (\(C/V\) — constant capital to variable capital) rises. The Insight: Marx could have used differential calculus to analyze the rate of change of the profit rate (\(dP/dt\)) as a function of technological investment. This would have provided a rigorous, dynamic, rather than just conceptual, understanding of when the rate of profit would fall, and how quickly, as constant capital (machines) grows faster than variable capital (labor). 3. A Dynamic Theory of Capital Accumulation and Crises Marx observed that capitalist accumulation is not linear but cyclic and prone to crises, partly due to the "industrial reserve army" (unemployment). The Insight: Using differential equations, Marx could have modeled the interaction between the growth of capital (\(dK/dt\)) and the rate of wages (\(dW/dt\)). He could have created a mathematical model for the business cycle, showing how the "reserve army" of unemployed acts as a dampener, restricting wage growth at certain points in the cycle.Prediction of Crisis Timing: Rather than relying on observing past events, he might have predicted that the frequency or intensity of crises depends on the speed of capital accumulation (second-order derivatives). 4. Mathematical Definition of "Socially Necessary Labor Time" Marx's theory hinges on "socially necessary labor time"—the average time required to produce a commodity. The Insight: Instead of a simple average, calculus would allow for treating this as a weighted probability distribution or a continuous, integral-based average, which better reflects how competitive markets continuously update the value of goods as technology advances. 5. Rejection of Marginalism through Superior Tools Interestingly, had Marx known calculus, he might have used it to attack the emerging Marginalist school (Jevons, Menger, Walras), which used calculus to focus on utility and demand. The Insight: Marx could have used calculus to show that marginal utility (marginalism) is merely a "phenomenal form"—a result of the deeper underlying production relations (labor theory of value)—using advanced mathematics to support a structuralist rather than individualist approach to economics. 6. The "Derivative" as a Dialectical Process In his Mathematical Manuscripts, Marx showed interest in the "rational" calculus of d'Alembert and the "algebraic" calculus of Lagrange. He sought to define the derivative (\(dy/dx\)) as a process of continuous change, viewing it as a mathematical representation of dialectical change ("becoming"). The Insight: He would likely have attempted to model the transition from simple commodity production to capitalist production, or from free competition to monopoly, as a "phase change" or an accumulation of small changes (\(dx\)) resulting in a structural break in the economic system (\(dy\)). In short, if Marx had known calculus, Das Kapital would have been far more technically rigorous, transforming his "tendencies" and "laws" into precise, dynamic, time-based mathematical model