Qualitative Dynamics and Numerical Evidences in a Business‐cycle Model with Non‐concave Production Function and Variable Population Growth Rate

We analyze the dynamics produced by the neoclassical one-sector growth model with differential savings as in [3] while assuming a sigmoidal production function as in [8] and the labor force dynamics described by the Beverton Holt equation, as proposed in [2]. The resulting discrete time dynamic system is bidimensional, autonomous and triangular: we determine its invariant sets and study their local stability. We also perform a mainly numerical analysis to show that complex features are exhibited, related both to the structure of the coexixting attractors and to their basins. The study presented shows that complexity emerges if the elasticity of substitution between production factors is low enough and shareholders save more than workers, thus confirming the results obtained with concave production functions (see [6], [7] and [9]).