The Optimal Investment Rule for Substainability of Resource Economies, Efficiency and Equity

这项研究考察了被赋予可耗尽或可再生资源的经济学是否能够在不同的世代保持其消费水平不变，如果能够，这些资源将在什么规则下被挖掘。该研究方法是利用20世纪70年代以来发展起来的最优控制理论进行资源经济分析的理论分析方法之一。然而，与现有文献相反，本研究借助于最优随机控制来处理不确定性。作为我们对资源经济的广泛调查的结果，我们已经确信，当不确定性重要时，资源价格应该是最合适的随机化变量，从而使理论模型形式化。因此，本研究使用一个服从布朗运动的随机过程来表示资源价格。与现有的研究相比，随着时间的推移，价格对未来的不确定性变得更加明确。通过两年的研究，我们得到了以下新的发现。2000学年的研究表明，如果资源价格的变化是时间的递增函数，无论资源是可耗尽的还是可再生的，哈特威克关于消费可持续性的规则都应该修改为包括一个术语，用于调整过去时期的资本收益(或损失)。2001学年的研究表明，从哈特威克规则出发，对于可再生资源而言，为了最大化开采资源的利润贴现和，稳态下的最优资源存量水平可以大于或小于资源的最大再生率对应的存量水平，但如果资源存量不影响开采成本，则最优存量水平变小，如果时间折扣率为零，则等于后者。

This Research has examined if or not economics endowed with exhaustible or renewable resources are able to keep their consumption levels constant throughout different generations and if so, under what rule the resources are to be excavated. The research method is one of the theoretical analyses utilizing optimal control theory that has been exploited since the 1970s for economic analysis of resources. However, contrary to the existing literature, this research treats uncertainty with an aid of optimal stochastic control. As the result of our broad investigation on resource economies, we have come to convince that the resource price should be the most appropriate variable to be randomized when uncertainly matters to formalize theoretical models. Thus, a stochastic process following a Brownian motion has been used in this research to express the resource price. Compared with existing studies, it has been made clearer that the price becomes more uncertain toward future as time goes by. We have obtained the following new findings by our research for the two years.1. The research in the 2000 academic year has shown that, if the variance of resource price is an increasing function of time, regardless of whether the resource is exhaustible or renewable, Hartwick's rule on consumption sustainability should be modified to include a term for adjusting capital gains (or losses) over past periods.2. The research in the 2001 academic year has shown that departing from the Hartwick rule, for maximizing the discounted sum of profits derived from excavated resources, confined to renewable resource, the optimal resource stock level at steady state may be larger or smaller than the stock level corresponding to the maximum renewable rate of the resource, but it becomes smaller if the resource stock does not affect excavating costs, and it is equal to the latter if the rate of time discount is zero.