This chapter focuses on renewable resources and studies the interaction of economic agents, extracting renewable resources, and the resource dynamics as well as the fate of the resources in the long run. The chapter is organized as follows. Section 15.2 introduces the model and various specifications of the model as well as two theorems. The theorems reveal the relation between zero horizon optimization where the discount rate tends to infinity, and infinite time horizon optimization, where the discount rate is finite. In Section 15.3, analytical results for the open access regime — in the literature typically viewed as a zero horizon optimization problem — are gathered concerning the systems of predator-prey and competitive interactions. Both interactions allow for limit cycles in the optimal trajectories. Section 15.4 presents numerical results for the monopoly problem.
Keywords: economic model, economic growth, open access, demand elasticity, predatory-prey system, monopoly,