As the population dynamics and economic growth could be treated as a dynamic system described by a set of ordinary differential equiations in a general form of competing species, it is feasible to apply Lotka-Volterra Relation on the study of the complex feedbacks among economy, population, labor and capital.
Incorporating a logistic growth function for one of the spcies, a carrying capacity could be considered the idea of an upper limit to that logistic growth.
Anyone would be interested in this analysis methods? In fact it has been applied by some scholars of Argentina. Still interesting to make a further development.
Simply for your reference, wish it could inspire your ideas.