A paper mill discharges chemicals into a river which washes the shores of a downstream resort area. The private cost, social cost, and marginal benefit associated with the production of paper are given by the following equations: PMC = 5 + Q, SMC = 10 + 2Q, and MB = 35 - 0.5Q. What level of emissions tax (per unit of output produced) would provide the paper mill with the incentive to produce at the allocatively efficient level of output?

Question

Quizplus · Accepted Answer

The allocatively efficient level of output occurs where the social marginal cost (SMC) equals the marginal benefit (MB). Setting SMC = MB gives 10 + 2Q = 35 - 0.5Q, solving for Q gives Q = 10. The private marginal cost (PMC) at this output level is 5 + 10 = 15. The emissions tax needed is the difference between SMC and PMC at Q = 10, which is 15.

A Paper Mill Discharges Chemicals into a River Which Washes