Dynamic systems modeling and analysis of the Marx’s law of profit rates

Abstract

In this study, a dynamic system model is developed to analyze the Marx’s law stating that profit rate tends to decrease in the long term. Based on the proposed model, it is demonstrated that profit rate may increase or decrease according to the initial values of variable and constant capitals. That is, the Marx’s law is a conditionally true statement. In addition, for the Marx’s argument that an increase in the surplus-value rate to counteract a decrease in profit rate may decrease the profit rate, it is demonstrated that the argument holds only under certain conditions. Moreover, an advanced model of profit rate is presented to capture the behaviors of employment and wage. Furthermore, it is shown that the proposed model appropriately captures the long-term trend of declining profit rate from 1945 to 2015 in the United States.