Long Cycles Versus Time Delays in a Modified Solow Growth Model

In this work, we study the dynamics of Solow’s economic growth model assuming that the labor force growth rate function, n(t), is a solution of a delay differential equation. This approach is motivated by the fact that there are delays in entering and retiring an individual from the labor force, relative to its birth date. Maintaining the fundamental equation of the Solow model, which describes the dynamics of capital accumulation over time, and changing the hypothesis about the evolution of labor force growth rate, we intend to evaluate the effects on capital accumulation when taking into account labor life cycles. This means that we assume n(t) does not respond instantaneously to variations, but it is a function of previous states. For this, we introduce a time delay pattern in the labor force growth rate, by considering that a normalized labor force growth rate is a solution of a delay differential equation. We show that a cyclic behavior of n(t) can be generated endogenously by an economic model. Although in a previous work, we have already observed that if n(t) is assumed to be a T-periodic function then the solution of Solow equation is also T-periodic, the truth is that these two functions present a phase difference. Note that, this lag can readily be generated in a regular ordinary differential equation model, since it is a necessary consequence of the slow adjustment rates. In this present work, we show that the introduction of time delays in modelling n(t) generates endogenous cycles for the economy.