Optimal exploitation of a renewable resource with capital limitations.

A model of interaction between a renewable natural resource with capital limitations, as exemplified by the optimal investment problem of sheep farming in a Nordic context, is analyzed. The model builds on existing studies from the fisheries literature, but the important difference is that while capital is related to harvesting effort in the fisheries, capital attributes to production capacity to keep the animal stock during the winter in our farm model. The paper provides several results where both optimal steady states and the optimal approach paths are characterized analytically. The results are further supported by a numerical example.