Optimal conditions for the control problem associated to a Ramsey model with endogenous population

摘要

In this paper, we will analyze the mathematical model associated to an economic growth process with endogenous population depending on current fertility. The model is a version of the Ramsey model in continuous and infinite time with the Cobb-Douglas production function. Mathematical modeling of this economical growth process leads to an optimal control problem with an infinite horizon. The necessary conditions for optimality are given. Using the optimality conditions we prove the existence, uniqueness and stability of the steady state for a differential equations system.