Long cycles in a modified Solow growth model

Abstract

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 Cobb–Douglas 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.