***Avoid hand written solution

One town is concerned about recent findings that local smoothie firms are polluting the air with sulfur dioxide, which leads to acid rain,? The town estimates the marginal damage as a function of pollution reduction to be MD= - 300 - 2R. Further, there are two types of smoothie firms in this town. The relatively aged historic (A) smoothie firms with the additional cost of polluton reduction of MCA = 10RA and the recently built contemporary (B) smoothie firms with the additional cost of pollution reduction of MC = 5Rp. Here, R is the amount of (i.e., quantity) of pollution reduction.

(a) (5 points) Absent any intervention from the town government, what is the equilibrium (total) amount of pollution reduction?

(b) (5 points) This town is deliberating on how to split up the pollution reduction among the suppliers. One option would be to have both plants split the reduction evenly. Show whether this is the most efficient solution. If not, find (or calculate) what would be the most efficient allocation among the plants.

(c) (5 points) Consider our discussion of private solutions to externalities. Is there a likely Coasian solution between the citizens and the smoothie firms? If so, describe a potential solution. If not, briefly explain why not