Resource leasing and optimal periodic capital investments

In this paper we analyse a fishery resource exploitation model in which a single firm or a cartel has leased the rights to manage the resources independently. Two variables, resource level and the capital level, determine the dynamics of the resource system. The leasing contract includes an incentive for the agent to maintain the resource level high. The main result is that sole-agent resource management and efficiency of the resource use do not necessarily imply that the fishery is stabilized at a unique steady state level. Instead, the optimal resource exploitation may lead to periodic capital investments in fishing vessels and gear which in turn causes cycles in the resource economy. We show analytically that nonzero discount rate and low capital depreciation rate both favor the conditions under which periodic optimal solutions may occur. Simulation results related to a Baltic herring fishery are used to illustrate the results.This research was partly supported by the Austrian Science Foundation under contract number P7783. The support of the Academy of Finland and Yrjö Jahnsson Foundation to V. K. is greatly appreciated. We thank Carl Folke, Mikael Hildén and Steffen Jørgensen and three anonymous referees for helpful comments. V. K. thanks the Beijer Institute of the Royal Swedish Academy of Science for its hospitality.