Emission Fees and Damages

1. Consider the problem of regulating acid rain in the eastern US. Assume emissions are generated in the Midwest and the Northeast but acid rain damage only occurs in the Northeast. One million tons of emissions in the Midwest results in 1 microgram per square meter of deposition; one million tons of emissions in the Northeast results in 2 micrograms per square meter of deposition. Damage (in millions of dollars per year) from deposition (d) is given by: D(d) = d^2/2, where d is measured in micrograms per square meter of deposition. Prior to any imposition of emission controls, the Midwest was emitting only 3 million tons per year, whereas the Northeast was emitting 5 million tons per year. Pollution control costs in either region are given by: C(k) = k^2/2, where k is the amount of emission reduction per year in a region, in millions of tons. 

A. Write total damages in terms of the amount emissions are reduced in each of the two regions. 

B. Write an expression for the total social costs, consisting of pollution damage and emission control costs. Write this expression in terms of the amount emissions are  reduced in each of the two regions. 

C. Find the efficient amount of emissions reduction from each region. 

D. What emission fee, applied in each region, would support this efficient level of emissions?