A Marxian Optimal Growth Model for Economies with Minimum Subsistence Wages

This study constructs a two-sector two-class economic growth model to analyze an economy described in Marx's Capital, where only the capitalist owns the means of production and maximizes the surplus value, while the worker provides labor in exchange for the minimum subsistence wage. Unlimited labor supply is the critical factor for the wage to be at the minimum subsistence level. In contrast to the Marxian optimal growth model, which indicates that the growth path in the capitalist economy follows a stable path to a steady state and is appropriate for analyzing the developed capitalist economy, our model demonstrates that, except in some rare cases, there is no stable path to a steady state in the economy and it is valid for analyzing an economy with an excessive labor supply. The results further indicate that it is common for capital to follow the process of unlimited self-growth, which causes the capitalist economy to be unstable.