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.

中文翻译：

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关于环境可持续性问题

Beltratti等人提出了环境可持续性问题，并强调了两个相关控制问题的重要性，即贴现功利主义问题和长期效用问题。通过对后者的分析，他们获得了绿色黄金法则（GGR）的定义。我们讨论了第一个问题的最佳稳态解，并提供了新的结果，并完成了有关该问题的已知信息。然后，我们解决第二个问题及其等效的最大化稳态效用的NLP问题。我们发现，对NLP问题的解决方案取决于资本积累特征，就像第一个问题一样。这将纠正并完成对GGR的原始分析。