This article proposes a network model to replicate the behaviour of the profit rate in the long run. Specifically, it accounts for the results of an empirical investigation of the profit rate in the US, which show that it has fractal properties and its complexity changes over time. The starting point of the model is Marx’s insights on the interplay between the tendency of the rate to fall and its countertendencies. It combines these insights with the persistent generation of new commodities – inventions – and a specific set of new branches of production that triggers technological revolutions. A simulation running this network model successfully replicates historical features of the system.