On the existence and uniqueness of solution to the Lucas-Uzawa model

In this paper we define the concept of admissible solution and then provide closed-form solutions for all variables of the model along the transitional dynamics path. We present numerical simulations and compare our results with those obtained through the methods developed by Boucekkine and Ruiz-Tamarit and, Barro and Sala-I-Martin.

Research Highlights►The concept of the admissible solution, necessary to determine the conditions of the existence of the transitional dynamic process was defined. ►Closed-form solutions for the original variables along the transitional dynamics path are derived. ►Numerical simulations are presented to compare our results with those obtained by Boucekkine and Ruiz-Tamarit, Barro and Sala-I-Martin.