Renewable resource and harvesting cost in a simple monetary overlapping generation economy

The literature has pointed out that renewable resource preservation in the long run is ensured in two situations: (1) when resource can serve as a store of value and (2) when households are altruistic. The following paper shows that a third situation also implies resource preservation, that is, when harvesting is costly. To do so, a simple monetary overlapping generation economy is developed in which a renewable resource is privately owned by a representative household who lives for two periods. During her youth, she inherits the resource from her parents and decides how much to harvest. Income obtained from the resource selling is fully saved in fiat money to finance old age consumption. Harvesting is assumed to take time (harvesting cost) and then, the young household has to arbitrate between leisure or harvesting. In this simple context, we show that the resource level can be non zero in the long run (resource preservation). In particular, we observe that two steady states can coexist: one with a low resource level (overexploitation) and the other with a high resource level (underexploitation). Moreover, under a sufficiently productive harvesting technology, two-period cycles can emerge around each steady state through a flip bifurcation as well as local indeterminacy around the higher steady state. In this sense, costly harvesting appears to be both a source of resource preservation and a source of resource fluctuations.