Présentation sur YouTube.

We consider the model of economic growth with a renewable environmental good, introduced by Beltratti, Chichilnisky, and Heal (1993-1995), and discuss the connections among solutions of different problems related to that model. The cited authors were concerned with a rather general 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.

We discuss the first problem under the catching up optimality criterion and provide new results from the analysis of the necessary conditions for this optimal control problem. Then we tackle the second problem and its proposed 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 discounted utilitarian problem. Furthermore, the solutions to the NLP problem coincide with the steady-state solutions of the infinite horizon undiscounted problem. This corrects and completes the original analysis of the Green Golden Rule.