Common Property Resource and Private Capital Accumulation

Abstract

This paper presents a differential game model of exploitation of a common property resource, when agents can also invest in private and productive capital. It is shown that in general there is a phase of capital accumulation followed by a phase of dissaving. Consumption also attains a peak before falling. When consumption reaches its peak, net saving is negative. The value function for each player is shown to be separable in the two state variables.When agents are heterogeneous, the more productive agents will accumulate more capital, but all agents follow the same consumption rule and extraction rule.