The Ramsey model with logistic population growth

In standard economic growth theory it is assumed that labor force follows exponential growth, a not realistic assumption. As described in Maynard Smith (1974), the growth of natural populations is more accurately depicted by a logistic growth law. In this paper we analyze how the Ramsey growth model is affected by logistic growth of population, comparing it with the classic Ramsey model. We show that there is a unique nontrivial steady state of the model and that the parameters of the logistic equation play no role in determining long run equilibrium per worker level of consumption and capital. In addition, we study the stability of the model showing that its nontrivial equilibrium is a saddle point.