Law and Economics Problems

Question 1: Punitive Damages

Suppose that an injurer escapes liability in three out of four accidents that he causes. Let the damages per accident be $100,000.

Questions:

a) In order for the injurer to face the correct incentives to take care, what should his punitive damages be? What should his total damages be (punitive damages + compensatory damages)?

Question 2: Torts and the Amount of Activity

Suppose the harm caused by the accident is A = 1. Consider a situation in which precaution doesn't have much influence on the probability of an accident. Rather, the amount of time spent in the activity by both the victim (a_v) and the injurer (a_i) are more important determinants. Suppose the utility that the victim obtains from his activity (not including harm from the accident) is u_v(a_v) = a_v - a_v² and the injurer obtains from his activity (not including damage payments) is u_i(a_i) = a_i - a_i².

Questions:

a) Suppose that the level of activity does not influence the probability of an accident. Compute the activity levels for both the injurer and the victim. Hint: Each player will maximize his utility.

b) Assume the probability of accident is influenced by activity levels. Specifically, p(a_v, a_i) = a_va_i. Compute the socially-optimal activity levels. Hint: Maximize the total social welfare, which is equal to the two player's utility levels minus the expected harm from the accident. (You will have to take 2 derivatives, and set each one equal to 0. This will give you 2 equations with 2 unknowns).

c) Again, assume p(a_v, a_i) = a_va_i. Compute the equilibrium levels of activity if there is no liability. Hint: If the injurer is not liable for any damages, he will simply maximize his utility (as in part a). Once you have determined the injurer's activity level, create an equation for the victim's welfare (his utility minus the expected cost of the accident).

d) Again, assume p(a_v, a_i) = a_va_i. Compute the equilibrium level of activity if there is strict liability. Hint: Under strict liability, the victim is never liable, he will simply maximize his utility (as in part a). Once you have determined the victim's activity level, create an equation for the injurer's welfare (his utility minus the expected cost of the accident).

Question 3: Optimal Fine and Imprisonment

Suppose that optimal deterrence of a particular crime requires setting the expected punishment equal to $2,000. Assume that the probability of apprehension is fixed at .2.

Questions:

a) Suppose an offender has wealth of $5,000 and incurs a cost of $1,000 per month spent in prison. What combination of a fine and prison term achieves optimal deterrence at the lowest cost?

b) What combination of a fine and prison term is optimal for an offender with wealth of $7,000? (Assume he incurs the same monthly cost of imprisonment)

c) Suppose considerations of fairness dictate that the prison term and fine for offenders who commit the same crime must be the same. What fine and prison term must be imposed on the two offenders to maintain optimal deterrence? Explain the sense in which this policy reflects a trade-off between fairness and efficiency.

Question 4: Irrational Criminals

Begin by assuming that all potential criminals are alike. Each has a benefit B of committing a crime, where B = $10,000. Let p be the probability the criminal is caught and punished. The criminal's punishment is S (i.e. the sentence) years in prison. (Notice, there is no fine, just prison time.) The cost of prison (to the criminal) is T = $1,000 for each year spent in prison. Therefore, the condition for a rational criminal to commit a crime is B > pTS. Since all potential criminals are identical, if this condition holds, all potential criminals will commit a crime.

Suppose there are 100 potential criminals. Each chooses whether to commit this crime which has a social harm cost of $100,000. Suppose criminals are caught with a 15% probability. The prison cost is $5,000 per prisoner, per year. The social cost of crime is: prison costs plus the social harm from crimes less the benefit to the criminal.

Questions:

a) What is the optimal choice of sentence, S? What are the total costs associated with this choice?

b) Now suppose that there are an additional 50 criminals who are irrational and therefore, always commit crimes. What is the optimal choice of sentence, S?

c) Suppose the police force costs $250,000. The social cost of crime is now: prison costs plus social harm plus police costs less the benefit to the criminal. In a world with 100 rational criminals and 50 irrational criminals, what is the social cost of crime?

d) Suppose you can instead hire a police force that costs $500,000 but catches criminals with a probability of 0.25. What is the new optimal choice of sentence, S? What is the social cost of crime with this police force?

e) Which of these police forces would you choose (the one in part c or d)? Describe the intuition for your answer.