Suppose there are two factories that emit a certain pollutant into the air. When a factory reduces emission, there is a "marginal abatement cost" (MAC) for each unit of pollution abatement (reduced emission). The marginal abatement costs for the two factories are given by MAC1 and MAC2 respectively. Let MAC1 = 100 - 10E1 and MAC2 = 50-10E2, where E is the level of emission. Now assume each unit of emission causes a damage to the society given by the marginal damage function MD=30.

a) Calculate the level of emission without any government regulation. Suppose the owners and workers are not directly affected by the pollutant.

b) What is the marginal benefit function of emission produced by factory 1, and what is the marginal benefit of emission by factory 2?

c) Compute the socially efficient level of emission and the socially efficient level of abatement from each factory. Derive the solution algebraically and illustrate graphically. d) Now suppose the marginal damage of emission is 60 instead, compute the socially efficient level of emission and the socially efficient level of abatement from each factory.