Two very different commercial sectors produce a common airborne pollutant located in two different geographic regions. One has marginal benefits of pollution of 100-2e1 while the other has marginal benefits of 80-e2.

a. Write the equation for the total demand for emissions across both sectors. Does one sector have uniformly lower marginal abatement costs than the other? What is the total amount of emissions in the absence of regulation?

b. A cap and trade program is created with an initial allocation of 100 permits. After trading occurs, what will be the market price of a unit of quota? How much will each sector emit?

c. Assuming that the initial allocation of quota was proportional to the historical shares of pollution in the previously unregulated market, who is a buyer and a seller in part b and how much quota changes hands? 

d. It is later found that the marginal damage function from emissions is MD=(e1+e2)=E. How does the efficient level of emissions compare to the level achieved under the cap and trade policy above? Graphically, depict the net loss to society (the deadweight loss in econ-speak) from over/under abatement of pollution.