Stagnation and cycles in Marx’s Circuit of Capital

Marx’ circuit of capital describes the circular process of transformation of money to commodities and of commodities to money, the unified process of capital turnover from production to exchange. It becomes the prime tool Marx used to analyze the process of labor, the reproduction and accumulation of capital, and the possibility and actuality of crises in the capitalist mode of production. In a paper in 1982 and two books is 1986, Foley formulated a mathematical model for the circuit of capital. In the present work, we reformulate this model into a closed and autonomous dynamical system and we proceed to analyze its phase space; not surprisingly, this model resembles the famous epidemiological models, used to describe a similar circular process for the spread of a disease. The equilibrium points of the system reveal the cases for a ‘normal’ phase of expansion, as well as for an ‘excess capital’ crisis; the shift of stability from the one to the other reveals a possibility theory of crisis as a secular stagnation process, while the shift from stability to cycles reveals an actuality theory of short-run fluctuations due to ‘excess commodities’ and ‘excess money’.