Population dynamics and economic growth. Co-evolution and complexity

In the section Dynamics due to changes in the population structure, Pantaleoni (1909) underlined the influence that population dynamics might have on growth and other economic variables. Pantaleoni anticipates a number of issues that need to be addressed in studies of economic dynamics, such as static and dynamic conditions, equilibrium, and different forms of dynamic phenomena. These issues can be traced back to modern mathematical concepts developed in the field of dynamical systems theory, i.e. states of the system, asymptotic behaviours, coexistence of attractors and complex basins. The present work aims at proposing an example confirming that endogenous population dynamics play a role in simple economic models. With this aim in mind, this work investigates the qualitative and quantitative dynamics of a Solow–Swan growth model (Solow, 1956; Swan, 1956) with differential savings as proposed by B¨ohm and Kaas (2000) by assuming the shifted Cobb–Douglas (SCD) production function (Capasso et al., 2010) and endogenous population growth described by the modified κ-logistic law (Baldi, Mammana and Michetti, 2024) able to take into account rare events. The richness of dynamic phenomena hypothesized in Pantaleoni (1909) emerges.