In this paper, we consider four scenarios for economic optimal management of a fisheries resource by a high sea and coastal fleet segment. These scenarios differ with respect to whether a common or two separate fish stocks are considered and whether the profit from land-based processing is included. The model is parametrized using the Greenland halibut fishery on the west coast of Greenland as an empirical case. For this fishery, we show that the relative ranking of the optimal high sea industry harvest and profit compared to the coastal industry harvest and profit depends on the chosen scenario. When comparing the scenarios for optimal management and the actual situation, we find that the fish stock tends to be overexploited.