Optimal investment in enhancing social concern on biodiversity conservation: a dynamic approach.
For maintaining biodiversity conservation areas, we need to invest in various activities, such as monitoring the condition of the area, preventing illegal exploitation, and removing harmful foreign species. But we also need to invest in activities to enhance the concern of the society on biodiversity reservation because the level of support by the community should critically depend on its concern on the biodiversity conservation. In this paper, we study the optimal fraction of the resources to invest in activities for enhancing the social concern y(t) by environmental education, museum display, publications, and media exposure. We search for the strategy that maximizes the time-integral of the quality of the conservation area x(t) with temporal discounting. The optimal allocation schedule is analyzed by dynamic programming and by Pontryagin's maximum principle. The optimal control consists of two phases:  in the first phase, the social concern level approaches to the final optimal level ,  in the second phase, resources are allocated to both activities, and the social concern level is kept constant y(t)=y*. If the social concern starts from a low level, the optimal path might include a period in which the quality of the conservation area declines temporarily, because all the resources are invested to enhance the concern. When the support rate increases with the quality of the conservation area itself x(t) as well as with the level of social concern y(t), both variables may increase simultaneously in the second phase. We discuss the implication of the results to good management of biodiversity conservation areas.
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