On an environmental sustainability problem

Beltratti et al proposed an environmental sustainability problem and stressed the importance of two related control problems, namely, the discounted utilitarian problem and the long-run utility problem. From the analysis of the latter, they obtained the definition of the Green Golden Rule (GGR). We discuss the optimal steady-state solutions of the first problem and provide new results, completing the known information on it. Then we tackle the second problem and its equivalent NLP problem of maximizing the steady-state utility. We obtain that the solutions to the NLP problem depend on the capital accumulation features, like those of the first problem. This corrects and completes the original analysis of the GGR.