Harvesting natural resources: management and conflicts

It is reasonable to consider the stock of any renewable resource as a capital stock and treat the exploitation of that resource in much the same way as one would treat accumulation of a capital stock. This has been done to some extent in earlier papers containing a discussion of this point of view. However, the analysis is much simpler than it appears in the literature especially since the interaction between markets and the natural biology dynamics has not been made clear. Moreover renewable resources are commonly analyzed in the context of models where the growth of the renewable resource under consideration is affected by two factors: the size of the resource itself and the rate of harvesting. This specification does not take into account that human activities other than harvesting can have an impact on the growth of the natural resource. Furthermore, natural resource harvesting are not productive factories. Fishery economic literature (based on the foundations of Gordon, 1954; Scott, 1955; and Smith, 1963) suggests particular properties of the ocean fishery which requires tools of analysis beyond those supplied by elementary economic theory. An analysis of the fishery must take into account the biological nature of fundamental capital, the fish and it must recognize the common property feature of the open sea fishery, so it must allow that the fundamental capital is the subject of exploitation. The purpose of this paper is the presentation of renewable resources dynamic models in the form of differential games aiming to extract the optimal equilibrium trajectories of the state and control variables for the optimal control economic problem. We show how methods of infinite horizon optimal control theory may be developed for renewable resources models.