Managing the quality of a resource with stock and flow controls

We consider a class of problems, which we call “SFQ” problems, in which both stocks and flows can be controlled to promote the quality of a valued resource, such as environmental quality or public infrastructure. Under the optimal policy, periodic restoration of the stock of quality complements positive but variable abatement of the flow of damages. When deterioration is more rapid or highly variable, or when abatement is more expensive relative to restoration, the optimal policy relies relatively more on restoration.When deterioration is due to private firms or individuals, a flow tax equal to the present value of marginal damages provides efficient incentives for abatement. This tax rises at first as quality worsens, but eventually falls as restoration nears. The revenues raised by such a tax approximates the cost of restoration, with the two quantities converging as the variance of flows goes to zero.We discuss the implications of the SFQ model for a range of real-world problems in the environmental arena, and for the management of public infrastructure. But the lessons are general, and we briefly discuss how they apply to private stocks of physical and human capital.