Stock Pollution, Child-Bearing Externalities, and the Social Discount Rate

Each generation experiences a pollution externality which is a function of the current and past production of a competitively produced good that is used for consumption, child-bearing expense, and capital bequests. Comparing the conditions for dynastic utility maximization by atomistic and representative individuals in each generation shows that Pareto optimality requires a Pigouvian pollution tax, and a parental tax per child equal to the discounted present value of all pollution taxes that the child and her descendants would pay. The social discount rate is shown to be the gross rate of return on capital times one minus the Pigouvian pollution tax rate, which itself depends upon the social discount rate.