Tiempo, población y modelos de crecimiento

This paper presents an analysis of the implications it has on standard growth models assume an alternative hypothesis to the exponential growth of the population and how modeling time can alter the dynamic behavior of these models. An extension (in continuous time and discrete time) of the Mankiw-Romer-Weil growth model is also studied by departing from the standard assumption of the constant population growth rate. More concretely, this rate is assumed to be decreasing over time and a general population growth law verifying this characteristic is introduced. In this setup, the model can be represented by a three dimensional dynamical system which admits a unique solution for any initial condition. It is shown that there is a unique nontrivial equilibrium which is a global attractor. In addition, the speed of convergence to the steady state is characterized, showing that in this framework this velocity is lower than in the original model.