A Study of Resource and Environment Policy and Dynamic Gains from Trade

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The purpose of this research is to theoretically analyze whether or not an economy being only endowed with a natural resource as the source of income can survive over the long time. Developing countries may not secure their sustainability if they try to live solely on selling excavated natural resources to industrial countries. They would naturally think of any method of self dependence. Is it really viable?The analytical model used in this three year research period has the following characteristics. 1. Two types of stock variables, a renewable resource and other physical capital, are considered. 2. A composite commodity produced by using these two stocks is utilized for consumption and investment. 3. The magnitude of changes in stock levels is subject to uncertainty. The first characteristic is the device for theoretically expressing the requirement of transforming natural resource to other physical capital before the resource completely depletes, since it seems meaningless as an eco … More nomic problem if the resource, though renewable, can be assumed ultimately non-exhaustible (if the probability of exhaustion is zero for sure, sustainability does not constitute an economic problem apart from actual levels of instantaneous excavation of the resource). The second characteristic is to secure the mechanism of optimally allocating the produced commodity into consumption and investment for physical capital accumulation in order to examine the sustainability under the assumption that the economy is optimally managed. Finally, two types of uncertainty are considered in the last characteristic. One addresses for continuous changes in the level of stock as time elapses and the other for jumps in stock with discrete time interval. The former case is modeled by using a Brownian motion and the latter by Poison process. Brownian motion is the best device to express the situation in which the variance of stock level changes will be continuously wider as time goes by even if the present size of stock is certainly observed and the immediately next time period will show a very little change. We consider, on the other hand, a compound Poison distribution for treating various lengths of intervals between changes with meaningful sizes occurring randomly rather than with infinitesimally small sizes happening continuously over time.The main results are that (1) we have proved the existence of steady state in this economy under certainty, namely without the first characteristic of the model, (2) the optimal excavation level of the resource under uncertainty is smaller than that under certainty but the optimal level of resource consumption survives the introduction of uncertainty, and (3) we have establish several propositions on the ruin and surviving probabilities of this economy. Less