If the control authority does not know the marginal damage function, it will not be able to identify the economically efficient level of pollution abatement, nor the efficient tax or subsidy level. Demonstrate that

(a) knowledge of the pollution abatement cost schedule alone means that it can calculate the required rate of tax to achieve any target level it wishes;

(b) if the regulator knew neither the marginal damage nor the marginal abatement cost schedules, then it could arbitrarily set a tax rate, confident in the knowledge that whatever level of abatement this would generate would be attained at minimum feasible cost.