A solution to the Lucas-Uzawa model with increasing returns to scale: Note

Chilarescu [2008, An analytical solutions for a model of endogenous growth, Economic Modelling.] claims that he determines a solution path to the Lucas-Uzawa model with increasing returns to scale. However, the path is not a closed-form since it depends on the initial consumption and the initial time for goods production, that are unknown. Moreover, the production function is nonconcave and then the first order conditions and the transversality conditions are not sufficient for the optimality. This note converts the model to a problem in which the Hamiltonian is available and derives a fully-closed form solution.