Optimal harvest with multiple fishing zones, endogenous price and global uncertainty

The literature on the optimal fish harvest has concentrated on a single fishery facing multiple sources of uncertainty. In this paper we develop and implement a stochastic optimal control approach to determine the value-maximizing harvest of a fishery participating in a global market, where multiple harvesting zones sell their production. The global market is characterized by an inverse demand function, which combines a stochastic exogenous demand factor and the aggregate harvesting of all zones. Accordingly, a fishery's optimal harvest will be affected by global demand shocks and the harvesting in all the competing zones, through the global price. We consider two sources of uncertainty for the biomass, local and global biomass shocks. Through global biomass shocks, the model provides enough flexibility to incorporate the correlation between biomass shocks in multiple zones. To illustrate the implementation of the approach we apply it to the Alaska and British Columbia halibut fishery. When we compare our global competitive framework with an alternative where all zones are aggregated into a single monopolistic fishery, we find that, for the estimated parameters, competition will increase the optimal global harvest and consequently reduce the fish price without affecting the sustainability of the resource. This illustration shows that a regulator fixing total annual fish catch needs to take into consideration the structure of the market (monopolistic versus competitive) to determine the optimal level of the quotas.