Solving Macroeconomic Models with Homogenous Technology and Logarithmic Preferences - A Note

In a recent published paper, Bethmann analyzed a stylised Robinson Crusoe economy, defining the state-like and control-like variables and then introducing the value-function-like function. He claims in the final section, that even if the model can be solved explicitly, but with complicated numerical analyses, he focuses instead on illustrating some dynamic programing techniques. In our opinion there are no complicated mathematical procedures to solve explicitly the model and we present here a closed-form solution of the model, only for the continuous case.