1. An oceanfront town is considering ways to reduce littering on its beaches. It currently has a fine for littering of 100. It does not currently patrol the beaches to try to catch anyone littering so it estimates the probability of someone littering is caught is .001.

Suppose that anyone who is caught is convicted. Further, assume that the reason people litter is they don't want to walk to a trash can on the beach, which costs 2 in effort. Additionally, assume that potential litterers are rational and respond to expected costs and benefits.

(a) If the town leaves the fine unchanged, to what value does it need to raise the probability of someone who litters being caught?

(b) If the town does not change the probability that someone who litters is caught, how large must the fine be to deter littering?

(c) Suppose the town assigns police officers to patrol the beaches and estimates that the probability that someone who litters is caught is now .04. Will this deter littering? Explain.

(d) Suppose the mayor is opposed to new expenditures and to have police officers patrol the beaches will require paying overtime. Based on this, would she prefer to impose the fine found in part b)? Explain.

2. A university currently fines unauthorized parking in faculty/staff parking spaces 50. The university currently employs five parking enforcement officers and estimates that the probability that a parking violator is ticketed is .4. Assume that all ticketed violations result in payment of the fine. Adding a sixth parking enforcement officer is expected to increase the probability that a parking violator is ticketed to .5.

(a) The university is considering adding another parking enforcement of- ficer to better address this parking issue. A faculty member suggests that instead of adding another parking enforcement officer the university should simply raise the fine to 80. Assuming that potential parking violators rationally weight the costs and benefits of parking illegally, which policy will have a bigger impact? Explain.

(b) Suppose the cost of the additional officer is a factor. Which policy, as described in part a) above, would be preferred? Explain.

3. Suppose a village is concerned about graffiti and wishes to deter it. The probability that someone illegally painting graffiti is caught and convicted is given by p = [1 [1/(1 + n)]], where n denotes the number of police officers who attempt to catch graffiti offenders, and assume this must be a whole number. This is costly. Assume the benefit to the criminal of committing the crime is 200 and the harm it causes is 350. The village imposes a fine f on anyone found guilty of graffiti. Assume the village wishes to deter the crime, regardless of the cost, but wishes to minimize its cost.

(a) Suppose the village is free to select both the fine f and n. What is its optimal choice of f and n? Explain.

(b) Now suppose that the state law imposes a limitation on the size of the fine, and requires that the fine be no larger than the harm imposed. What are the optimal values of f and n now?