The Optimal Management of Environmental Quality with Stock and Flow Controls

We characterize environmental quality as a stock, and its rate of deterioration as a flow. 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 resource stock. Abatement (curbing the flow) and restoration (restoring the stock) are interdependent tools in such problems. Under the optimal policy, periodic restoration complements positive but variable abatement that partly stems the quality decline. The preferred balance between the two strategies depends on environmental and economic factors. If flows are low enough, or if abatement is sufficiently inexpensive relative to restoration, optimal abatement may be sufficiently intense to offset the expected deterioration and produce an equilibrium in expectation. When deterioration is more rapid or more variable, when abatement is more expensive, or when restoration is less costly, the optimal policy relies more on restoration. We apply the analysis to the restoration of an endangered species, and show how it could illuminate a range of other problems in the environmental arena. But the lessons are general, and we briefly discuss how they apply to the management of both physical and human capital stocks.