Optimal exploitation of a renewable resource with capital limitations: Nordic sheep farming with and without grazing externalities

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 analysed. Both private and social optimality are considered; with the difference that a stock value related to the number of grazing animals is attached to the social management problem due to landscape preservation. The efficiency of alternative policy tools in terms of obtaining the socially optimal management scheme is discussed. 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 contributes 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 characterised analytically. The results are further supported by a numerical example.