Dynamic optimization in natural resources management

Dynamic modeling is general and recently the most interesting perspective to solve a dynamic economic problem based on Pontryagin’s maximum principle. Moreover traditional economic theory, up to the middle of twentieth century, builds up the production functions regardless the inputs’ scarcity. Nowadays it is clear that both the inputs are depletable quantities and a lot of constraints are imposed in their usage in order to ensure economic sustainability. For example the input “oil” used in the production is a non renewable resource so it can be exhausted. In a same way every biomass resides in ecosystems is a resource that can be used in a generalized production function for capital accumulation purposes but the latter resource is a renewable one. The purpose of this paper is the presentation of some natural resources dynamic models in order to extract the optimal trajectories of the state and control variables for the optimal control economic problem. We show how methods of infinite horizon optimal control theory developed for natural resources models.