In this paper I propose a time‐consistent method of discounting hyperbolically and apply it to three canonical environmental problems: (i) optimal renewable resource use, (ii) the tragedy of the commons, and (iii) economic growth and pollution. I show that, irrespective of potentially high initial discount rates, time‐consistent hyperbolic discounting leads always to a steady state of maximum yield, or, if the environment enters the utility function, a steady state where the Green Golden Rule applies. While (asymptotic) extinction is a real threat under exponential discounting it is impossible under time‐consistent hyperbolic discounting. This result is also confirmed for open‐access resources. In a model of economic growth and pollution, hyperbolic discounting establishes the Golden Rule of capital accumulation and the modified Green Golden Rule.

中文翻译：

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双曲线贴现和三个典型环境问题的时间一致解

在本文中，我提出了一种时间一致的双曲线贴现方法，并将其应用于三个典型的环境问题：（i）最佳可再生资源利用，（ii）公地悲剧，以及（iii）经济增长和污染。我证明了，不管潜在的初始贴现率是多少，时间一致的双曲线贴现总是导致最大收益率的稳定状态，或者，如果环境进入效用函数，则适用绿色黄金法则的稳定状态。虽然（渐近）灭绝是指数折现下的真正威胁，但在时间一致的双曲线折现下是不可能的。对于开放访问资源，也确认了此结果。在经济增长和污染的模型中，双曲线贴现建立了资本积累的黄金法则和修改后的绿色黄金法则。