Common property resource and private capital accumulation with random jump
In , Long and Katayama presented a model of exploitation of a common property resource, when agents can also invest in private and productive capital. They considered the case where the resource extracted from a common pool is non-renewable. In this paper, we try to extend their result to the case where the common pool is under uncertainty in the sense that it could have a sudden increase or decrease in the process of extraction and moreover we shall calculate the exhaustion probability.
Keywords: common property resource, private capital accumulation, pure jump process, exhaustion probability, HJB (Hamilton-Jacobi-Bellman) equation
JEL Classification: Q32
AMS Classification: 91B32, 91B38, 60G57, 49L20