An optimal strategy to control mining and recycling of non-renewable resources

The current debate on non-renewable resources has been increasingly recognizing their critical role over time, since natural reserves are dramatically decreasing. We aim at studying non-renewable resource management when extraction from natural reserves and recycling are considered, as well as the impact of technological progress on consumption and welfare in the short-run term. Mathematical modelling may provide significant help to policymakers in devising suitable strategies for social welfare optimization and environmental conservation. In this direction, we introduce an optimal control model for allocating labor between mining and recycling over a finite time horizon; specifically, we aim at optimally manage virgin resource depletion and waste accumulation. Actually, a suitable scrap value function is involved in the optimization process, in order to account for the issue of reducing waste accumulation and preserving natural stock in the forthcoming future. We analyze the problem and provide the necessary optimality conditions.