Common property resource and private capital accumulation with random jump


In [6], 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

Masatoshi FUJISAKI
University of Hyogo

Research Institute for Economics and Business Administration
Kobe University
Rokkodai-cho, Nada-ku, Kobe
657-8501 Japan
Phone: (81) 78 803 7036
Fax: (81) 78 803 7012

Hiroshi OHTA
Kobe University, GSICS