Is the Theory of a Falling Profit Rate Valid?

Marx's theory of the falling rate of profit makes two main appearances in his work. The first is in Chapter 25 of Capital Volume 1, entitled “The General Law of Capitalist Accumulation.” It is further developed in Part III of Volume 3 of Capital, entitled “The Law of the Tendency of the Rate of Profit to Fall.” In this article I will outline the structure of the theory presented in these two volumes of Capital. Following that I will look at some criticisms that have been leveled at it. I will go on to argue that the criticisms are based on a misunderstanding of some of the dynamic causal mechanisms that Marx assumed. Following on from this I shall present a dynamic solution to the equations of accumulation and show under what circumstances these lead to a falling rate of profit. The dynamic model will then be used to analyze the trajectories of some contemporary capitalist economies and to help understand the current structure of the world economy.