Pollution Abatement Under Learning by Doing with Heterogeneous Costs

Many environmental policies including the Kyoto Protocol, the Acid Rain Program, the Montreal Protocol and the phase-out of leaded gas are designed to achieve a target level of abatement within a specified period of time. This paper examines how pollution abatement should be allocated over time using heterogeneous technologies characterized by learning by doing. In the presence of learning by doing, conventional economic wisdom regarding the allocation of pollution abatement must be modified. This paper derives the appropriate generalization of the principle that marginal abatement costs are equalized and shows how learning by doing alters the optimal allocation of abatement. The paper considers three classes of abatement cost functions: linear costs, convex costs and constant elasticity costs. The optimal solution is derived for linear and constant elasticity costs. In the case of convex costs sufficient conditions are given for abatement to be shared across all technologies and a bound is placed on the optimal cumulative abatement that occurs over any interval [0,t]. The results are used to provide insight into the effects of technological learning on pollution abatement policy, the tradeoffs involved in allocating abatement between mature and infant technologies, and the role played by abatement costs and discounting in determining how pollution abatement should be allocated over time and across technologies