MarxKapital: A Computational Framework for Marxian Value Theory with Real Empirical Calibration

MarxKapital is an open-source Julia package for the mathematical modeling of Marxian value theory: capital accumulation, the tendency of the rate of profit, the transformation of labor values into prices of production, and the sectoral dynamics of expanded reproduction. Beyond the classical two-department and generalized N-department reproduction schemes, it implements three complementary mechanisms for coupling sectoral accumulation through the technical matrix A — capital mobility, an aggregate realization-pressure heuristic, and an exact per-sector quantity-rationing scheme solved by fixed-point iteration — without recourse to differential-algebraic equation (DAE) solvers. This paper presents both the methodological framework and a live, reproducible empirical pipeline that calibrates the model directly from official European statistical sources (Eurostat and AMECO, via their SDMX REST APIs), replacing the synthetic or ad hoc calibration common in the computational Marxian literature. The pipeline is applied to Portugal: a 2022 sectoral national-accounts profile (19 sectors), a coherent 2020 production-structure calibration, and an aggregate profit-rate series for 1996–2022. The paper also documents, transparently and in detail, four defects found by auditing the model and pipeline — a stock-flow conflation, a depreciation-term invariance bug, a technical-matrix construction that was reading the wrong Eurostat dataflow, and a supply-side flow omitting circulating constant capital — each disclosed alongside its fix and quantified consequence. The paper treats this progression as a contribution in its own right, on the view that a live statistical pipeline's value lies as much in surfacing and fixing this kind of error as in the numbers it ultimately reports. Source code, tests, and the reproduction scripts for every figure and table in this paper are available at https://github.com/randsley/MarxKapital.