# 1 polluter has total abatement cost tac 10a2 where amount it abates relative

1. A polluter has total abatement cost of TAC = 10A^2, where A is the amount it abates relative to uncontrolled emissions of 200 pounds. A performance standard requires it to abate As = 100. The polluter faces a fi ne of $20,000 if any non-compliance is detected. (a) Initially, suppose any noncompliance is detected with certainty. Will the polluter comply with the performance standard? What A does the polluter choose? Explain with numbers. (b) Now suppose the probability of detection increases with the amount of the violation, where the violation is the diff erence between the standard and actual abatement, i.e. v = As – A. If the probability of detection p(v) = .02v, what is the expected marginal cost to the polluter of violating the standard? Does the polluter comply? What level of A does the polluter choose? (c) Now suppose the detection returns to being certain. How much will the polluter violate the standard with a fi ne of $200 per ton of violation? (d) With the $200 per ton fi ne, what is the violation with 50% probability of detection? 2. People from diff erent towns would travel to fi sh at a reservoir if a dam were built. Travel costs $1 per mile. Assume we know demand to be linear and the that the two people share the same demand curve. Person One way distance Visits A 10 miles 40 B 20 miles 30 (a) Illustrate and label the individual demand curve for visits to the reservoir. What is the price intercept for the demand line? (b) What are the consumer surpluses for A and B from the reservoir? 3. Suppose the government is trying to decide whether to build a water treatment plant on the Raritan River. The plant will cost $90 million to build in the first period. It will begin operating in the second period, at which point its operating costs will be $50 million each period. It will not yield any bene fits until it starts operating, at which point the benefi ts of clean water will be $100 million per year. Suppose the project will only operate for two periods (after the initial period in which it is constructed). (a) Would this project be admissible if the real discount rate between the periods were 5%? What if it were 10%? (b) Explain verbally why you get the result you do. What does it tell you about the value of deferred bene fits at di fferent interest rates? 4. Consider a policy that would reduce urban air pollution concentrations. A study of the health bene fits of the program finds that marginal social bene fits are MSB = 200 – 10q, where q is the number of parts per million (ppm) by which air pollution concentrations are reduced. The marginal social cost of reducing pollution is constant at $50. (a) What would be the allocatively effi cient reduction in air pollution concentration? What would the net benefi ts of this policy be? (b) Suppose the government chose to reduce pollution by 20 ppm. Would this policy be admissible using a cost-bene fit analysis? Illustrate and explain.