question D

Two firms are located along the same river. Each discharges 10 tons of waste per day at present. It is estimated that the waste causes damage downstream is known with certainty to be $100 per every ton of discharge. Thus, total damages for the two firms together currently total two thousand dollars ($2,000) per day. Unfortunately, cleanup is not cheap. The cost of cleaning up each plant is also known with certainty to be CA=50XA+5XA2CB=20XB+5XB2 where Xi(i=A,B) is the amount of cleanup for plant i, measured in tons, and Ci(i=A,B) is the cost, measured in dollars. A. [6 points] The marginal costs of cleanup for firm A is MCA=50+10XA What is the marginal cost of cleanup for firm B ? B. [8 points] An environmental group proposes a complete ban on discharges from the two firms (i.e. XA=XB=X=10 tons). It notes that the cost would only be $1,700 per day, while the benefits would be $2,000. Is the group correct? Even if they are, is this the optimal solution to this externality problem? Why or why not? C. [8 points] If separate abatement standards could be set for each firm, what should they be to maximize net benefits to society as a whole (taking the firms' costs into account)? How much would adhering to such standards cost each firm? What level of pollution would result? D. [8 points] What if a separate tax could be set for each firm, how should the tax be set to maximize net benefits to society as a whole (taking the firms' costs into account)? What level of pollution would result? How does this differ from the case of abatement standards