A Tail-Payoff Puzzle in Dynamic Pollution Control

We analyze dynamic models with negative externalities occurring from production capital and input use. We uncover a puzzle related to such models: evaluated with a social welfare function, the steady-state outcome of a socially optimal policy, and thus the tail of the corresponding payoff sequence, may yield a smaller social payoff than a market outcome. The main questions we address are under what conditions this phenomenon arises and how general it is. We show that there are always Pareto-optimal policies which lead to the puzzle when the discount rate is fixed. In addition to discounting, the driving force of our results is that the periodic pollution and profits are linked to production capital. We demonstrate the puzzle with a model for controlling phosphorus losses from crop production. We argue that the puzzle should be taken into account in the policy analysis of dynamic problems, including negative externalities.