Resource extraction and recycling with environmental costs

Extraction and use of a natural resource is assumed to affect the environment adversely. A perfect substitute for the resource can be supplied through a recycling process. Recycling may also have harmful effects on the environment, but to a smaller extent than extraction. The optimal path of extraction and recycling is studied under various assumptions about the environmental effects of recycling and the assimilative capacity of the environment. In particular, it is shown how the cost of recycling will affect initial resource extraction as well as the environmental quality at the time of resource exhaustion and in the long-run stationary state.