Cumulative pollution with a backstop

Environmental policymakers must address the adverse effects of a number of pollutants that accumulate in the environment. For these substances, whose damages depend on the accumulation of nondegraded emissions, policy must do more than simply address the current emissions flow. In this paper we examine optimal time paths of consumption and production in a simple model encompassing production and consumption of a "dirty" and costlier "clean" good and a pollution stock that can decline over time with degradation or assimilation. A key element of our analysis is the consideration of several alternative specifications of the assimilation function, including the assumption that assimilation decreases with accumulation of pollution. This specification is especially interesting since it gives rise to nonconvexities that lead to multiple possible equilibria. With positive assimilative capacity, the optimal path often (though not always) settles into a steady state that involves some continued use of the polluting commodity at a rate consistent with assimilative capacity. In such cases, permanently banning the polluting commodity may not be present value maximizing in that it ignores the valuable services provided by assimilative capacity, though banning may be the best feasible policy or provide a desired margin of safety. Temporary banning of the polluting commodity is indicated if the initial pollution stock is large, the commodity if highly polluting, and the rate of assimilative capacity is low to give degraded ecosystems a chance to recover. Permanent banning also arises along an optimal path when assimilative capacity decreases with pollution. However, banning in this case may occur under two very different situations: when the environment is close to pristine and when it is highly degraded. Complex time-varying policies would be needed to realize these outcomes.