The analysis of mathematical models associated to some economic growth processes with endogenous population

摘要

The aim of this paper is to extend the study done by [5]. Here, we will analyze two mathematical models associated to some economic growth processes with endogenous population depending on the current fertility. The first model is a version of the Ramsey model in continuous and infinite time with the Cobb-Douglas production function. In the second model we consider the AK production function. The mathematical models of these economical growth processes lead to two optimal control problems with an infinite horizon. The necessary conditions for optimality are given for both economic problems. Using the optimality conditions we prove the existence, the uniqueness and the stability of the steady states.