SOME REFLECTIONS ON MARX'S PRICES OF PRODUCTION: Historicity of the Law of Value, Dialectical-Materialist Foundation, and a Dynamic Formalization Under Uncertainty

This research develops a comprehensive study of the process of transformation of labour values into prices of production in Karl Marx's economic theory, by means of an interdisciplinary approach that integrates Marxist political economy, the philosophy of historical and dialectical materialism, historiography, econometrics and Bayesian statistical modelling. Its principal aim is to reassess the so-called transformation problem, maintaining that it does not represent an internal inconsistency of Marxist theory, but a consequence of having interpreted Marx's analysis through simultaneist models incompatible with the temporal and historical nature of capitalism.

The work establishes the law of value as a historically determined law and develops a philosophical grounding based upon the distinction between the ontological and the epistemological planes, the relation between totality and contingency, and the dynamic character of economic laws. On that conceptual basis, it analyses the historical evolution running from pre-capitalist socio-economic formations to modern capitalism, the genesis of the prices of production, capitalist competition, the formation of the average rate of profit and the transformation of values into prices of production, and incorporates in addition a critical review of the principal contemporary debates in Marxist political economy, including the controversies between the simultaneist and temporalist schools, the Brenner Debate and the literature on the temporal single system.

As a methodological contribution, the research proposes a dynamic formalization under uncertainty of the process of transformation, replacing the static formulations of the simultaneist school and the difference equations of the temporalist school with an explicitly temporal, probabilistic and stochastic model. Measurement uncertainty is incorporated directly within the mathematical structure of the model by means of the tools of Bayesian inference, which makes it possible to represent the process of convergence of market prices towards prices of production as a dynamic and observable phenomenon.

The empirical validation uses sectoral data on the economy of the United States for the period 1960–2020 and integrates the construction of Marxist variables, the classification of productive and unproductive activities, the Bayesian disaggregation of market prices, hierarchical models based on Ornstein–Uhlenbeck processes, simulations, internal and external validation procedures, robustness analysis, cointegration tests and multiple statistical tests. The work distinguishes explicitly between the philosophical, historical, conceptual and statistical scope of each result, and reports both the evidence that is favourable and that which turns out to be unfavourable to the hypotheses under evaluation.

Taken as a whole, this research proposes a unified framework for the study of the law of value, the prices of production and the dynamics of capitalism, integrating philosophical, historiographical and econometric evidence within a single scientific programme. The work contributes simultaneously to Marxist economic theory, economic history, the philosophy of science, the methodology of the social sciences and applied econometrics, offering a temporal and empirically testable formulation of one of the most debated problems in political economy since the publication of Volume Three of Capital.