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) = d2   /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) = k2  /2, where k is the amount of emission reduction per year in a region, in  millions of tons. 
1.1. Write total damages in terms of the amount emissions are reduced in each of  the two regions. 
1.2.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. 
1.3. Find the efficient amount of emissions reduction from each region. 
1.4. What emission fee, applied in each region, would support this efficient level of  emissions? 
2. [40 points, 3 parts]. Consider a pollution problem invo