There is a large literature on the economics of accident law. Shavell (1987) and Landes and Posner (1987) are thorough book-length treatments. The analysis of the second-best negligence rule in this chapter is inspired by Polinksy (1980), who studies a slightly different situation in which the harm that is caused by injurers occurs as a lump sum, rather than as a per unit social cost. Shavell (1982) studies the interaction between liability rules and insurance markets. White and Wittman (1983) and Weitzman (1974) are the classic papers on the comparisons of tax and quantity instruments under uncertainty.

Exercises

1. In this chapter we assumed that all injurers and victims are identical. In reality, this will not be the case. To see how heterogeneity among potential injurers might alter the efficiency properties of simple negligence rules, consider a simple modification of the unilateral care model. Everything else is the same, but now assume that the injurers differ in their marginal costs of care, w.

For simplicity, suppose that there are only three types of injurers, labelled 1, 2 and 3, and suppose that there is an equal proportion of each type in the population. Assume that type 1 injurers have a marginal cost of w_{1}, type 2 injurers have a marginal cost of w_{2} , and that type 3 injurers have a marginal cost of w_{3}, with:

(a) Let w_{2} be the cost of care for a 'reasonable person', and let x* be the efficient level of care taken by a reasonable person. How does the efficient level of care taken by types 1 and 3 compare with x*?

(b) Suppose that the courts cannot observe w directly, and so decide on a 'reasonable person' negligence rule, which operates as follows:

If actual care taken a x *, then the injurer is not liable If actual care taken < x* then the injurer is liable

Will this reasonable person negligence rule induce either types 1, 2 or 3 to take an efficient level of care? (Remember, in general it will be efficient for different types to take different levels of care).

(c) Will a rule of strict liability induce either types 1, 2 or 3 to take an efficient level of care?

(d) In this context, discuss the relative benefits of strict liability versus negligence.

2. In some instances involving accidental harm, the injurer may be uncertain as to the due standard of care that actually applies. This question illustrates some of the issues that can arise when due standards in negligence rules are uncertain. Consider the following table, which describes the probability of an accident and total costs under various situations in the unilateral care model. Assume that an accident leads to a loss of $100.

Level of Care

Marginal Cost of Care

Total Cost of Care

Accident

Probability

Expected Total Loss Social Costs

1

1

0.14

2

1

0.11

3

4

0.09

4

6

0.08

5

7

0.07

Consider the unilateral care model, and suppose that there are three possible due standards that the injurer believes he might face: z_{a} = 2, z_{b} = 3 and z_{c} = 4. Let:

be the injurer's perceived probability beliefs of facing each possible due standard, with n_{a} +n_{b} +n_{c} = 1. Let x be the level of care chosen by the injurer. Assume that the injurer is risk neutral.

(a) If x < z_{a}, what is the probability that the injurer believes he will be found to be negligent?

(b) If x = z_{a}, what is the probability that the injurer believes he will be found to be negligent?

(c) If x = z_{b}, what is the probability that the injurer believes he will be found to be negligent?

(d) If x = z_{c}, what is the probability that the injurer believes he will be found to be negligent?

(e) If x = z_{:}, what is the probability that the injurer believes he will be found to be negligent?

(f) Given your answers in parts (a)-(e), what is the injurer's expected cost function? Fill in the empty cells in the table.

(g) Would the injurer ever choose the socially optimal level of care? Would the injurer ever choose an inefficiently low level of care? Would the injurer ever choose an inefficiently high level of care?

3. Consider a regulator who is considering regulating an industry in which the production of a good, x, creates a negative externality. A firm produces x, but the regulator does not know the exact shape of the firm's marginal benefit curve or the marginal social cost curve. Suppose that the firm's actual marginal benefit curve is:

where u is a random variable which takes on the values 1 and -1 with equal probability. The actual marginal social cost curve is:

where v is a random variable which takes on the values 1 and -1 with equal probability. Assume that u and v are statistically independent. The regulator knows the values B_{0} and C_{0}, but cannot observe the realisations of u or v.

Let x be the point where expected marginal private benefits equal expected marginal social costs, and consider the following three policy options that are available to the regulator:

• Quantity Regulation: Force the firm to always produce at x = x.

• Tax Regulation: Set a tax on each unit of the good that firm 1 produces, with the tax set equal to the expected social marginal cost (and expected private marginal benefit) at the point x = x.

• Strict Liability: Make firm 1 strictly liable for any 'reasonable' damages that it causes. That is, force the firm to pay the expe:ted social costs of its actions.

For each form of regulation, illustrate the expected deadweight loss diagrammatically, and compute it analytically. In each case, explain how the expected deadweight losses depend on B_{0} and C_{0}, if at all. Rank the policy options according to the expected deadweight loss that they create, and explain why your ranking makes economic sense. For the regulator to choose the efficient policy, does it need to know B_{0} and C_{0}?