Long cycles in a modified Solow growth model
In this paper we analyze the dynamics of the Solow growth model with a generic production function. For this purpose, we consider that the labor growth rate, \(L^{\prime }(t)/L(t)\), is a \(T\)-periodic function, for a fixed positive real number \(T\). We obtain the closed form solutions for the fundamental Solow equation with the new description of \(L(t)\), using a CobbDouglas production function. Using notions of the qualitative theory of ordinary differential equations and nonlinear functional analysis, we prove that there exists a \(T\)-periodic solution for the Solow equation with a generic production function. From the macroeconomic point of view this is a refined Solow model, which exhibits a smooth cyclic behavior in the economy with long period and relatively small amplitude.
long cycles solow growth model periodic solutions