One element of Levari and Mirman (and all of the subsequent work) is the assumption that agents are infinitely lived. Extension to a framework where agents are finitely lived (overlapping generations models) introduces significant difficulties. In particular, the main result is one of extreme over-exploitation where the entire stock of the resource is depleted within a single generation-once completely depleted, the resource can no longer renew itself. While this may be realistic in some circumstances, this extreme over-exploitation is unappealing in many other contexts. One means for getting around this problem is to introduce capital accumulation. That is, there are two forms of capital in our model: the renewable resource which has no well defined property rights and the more traditional notion of capital which is owned by individuals. This additional realism, as it turns out, is sufficient to eliminate the extreme over-exploitation. In fact, surprisingly, this simple extension can yield both over- and under-exploitation of the renewable natural resource. In general though, if the number of interested parties is sufficient, the standard (infinite horizon) over-exploitation result still holds.
Work in progress.