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

本研究考察了拥有可耗尽或可再生资源的经济是否能够在不同的世代中保持其消费水平不变，如果是这样，在什么规则下挖掘资源。该研究方法是利用最优控制理论的理论分析方法之一，自20世纪70年代以来，最优控制理论被用于资源经济分析。然而，与现有文献相反，本研究借助最优随机控制来处理不确定性。由于我们对资源经济的广泛调查，我们已经开始相信，当不确定性对形式化理论模型很重要时，资源价格应该是最合适的随机变量。因此，本研究采用遵循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越来越明显。通过这两年的研究，我们获得了以下新发现：2000学年的研究表明，如果资源价格的方差是时间的递增函数，无论资源是可耗尽的还是可再生的，Hartwick关于消费可持续性的规则应该被修改，以包括调整过去时期的资本收益（或损失）的条款。2001学年的研究表明，从Hartwick规则出发，为了使挖掘资源获得的利润的折现总额最大化，仅限于可再生资源，稳态下的最优资源库存水平可能大于或小于资源最大可再生率所对应的库存水平，但在资源库存不影响挖掘成本的情况下，该水平会变小。如果时间折现率为零，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.