Using a simple analytical model incorporating costs and benefits, stock decay, time discounting, and uncertainty, we uncover several important principles governing the choice of price-based policies (e.g., taxes) relative to quantity-based policies (e.g., tradeable permits) for controlling stock externalities. As in Weitzman (1974), the relative slopes of the marginal benefits and costs of controlling the externality continue to be critical determinants of the efficiency of prices relative to quantities, with flatter marginal benefits and steeper marginal costs favoring prices. But we can say more. The relative slopes also help determine the optimal control path, with convergence to a steady state proceeding slowly as long as marginal benefits are relatively flat. On this basis we conclude that the conditions typically characterizing long-lived stock externalities—in particular, that the optimal control path involves long-term changes in the stock level—tend to favor price-based policies. While this result holds over a wide range of conditions, it depends on several key variables. Positive correlation of cost shocks across time, in particular, as well as low rates of time discounting and stock decay, will tilt the balance back toward quantity controls.
These results are potentially applicable to a wide range of market failures involving stock externalities. In addition to the obvious application to stock pollutants, one can view species preservation, land-use policy, education, and research as areas where policymakers wish to regulate a stock-like externality. This analysis provides a useful framework for comparing alternative policy instruments for regulating such problems. Regarding climate change, for example, these results suggest that the use of tradeable emission permits rather than emission fees to slow growth in the stock of greenhouse gases is probably inefficient. Optimal policy would involve either tradeable permits that quickly stabilize the stock, or emission fees that gradually slow its growth.