A MARXIAN MATHEMATICAL MODEL OF CAPITAL ACCUMULATION IN A TWO-SECTOR ECONOMY

The purpose of this paper is to construct a macroeconomic model of capital accumulation of a two-sector economy, building upon the Marxian model of expanded reproduction with which the factors of economic crises can be derived. Its methodology involved the simple generalization and formalization of the relations between the two economic sectors laid out by Marx in Capital, Vol. 2. On top of that, a time variable was added to make the system dynamic and so that it would evolve over time. The model has succeeded in covering some of the gaps in both Goodwin’s and Foley’s models by accounting for various parameters which Foley and Goodwin assumed to be constant. After the model was developed mathematically, a sensitivity analysis was run on it in which technical changes, wage fluctuations and other variables were introduced. Not only was the model found to be consistent with Marxist theory, but four causes of crises were also found following a sensitivity analysis. The model has its limitations, which are discussed in the conclusion, yet it can certainly be built upon in the future.