This section considers some basic applications of the unilateral care model.

Punitive damages and the effects of legal errors

Punitive damages are those that are awarded to victims in excess of their actual losses; they are designed to 'punish' the injurer. How can we reconcile these kinds of damages with notions of efficiency? One justification is that injurers occasionally escape liability because judges or courts make mistakes, or because of imperfect enforcement. In the context of accident law, legal errors can be divided into two types:

• Type I error: a person who is not liable is mistakenly found liable.

• Type II error: a person who is liable is mistakenly found not liable.

We will focus on the second type of error first. Suppose that there is a rule of strict liability, and consider an injurer who only expects to face liability with probability 1 - e_{2} if an accident occurs, where e_{2} is the probability of a Type II error occurring. The injurer's expected costs are now:

A higher e_{2} lowers the injurer's expected costs, which under a rule of strict liability lowers the level of care that is taken. Now suppose that, if the injurer is found liable for damage, the injurer faces punitive damages D as well as compensatory damages of h. The injurer's expected costs are now:

The level of D that induces efficient behaviour by the injurer is the one which equates his expected costs with social costs. This means that we need to choose D to satisfy:

which implies that:
so:

The efficient level of punitive damages is increasing in the actual level of harm h, so all else being equal, those harmed by more serious tortious acts should receive higher punitive damages payouts. D* is also increasing in e_{2}, the probability of a type II error.

The effects of Type I errors can also be incorporated into this analysis. Suppose again that there is a rule of strict liability, and that the probability of a Type I error is e_{1}. In this model, a Type I error occurs when the injurer is found liable and is forced to pay damages, but in reality no actual harm has occurred. Such examples frequently arise with so- called 'frivolous' lawsuits, where plaintiffs successfully sue for damages in instances where the harm is trivial or non-existent.

Harm does not occur with probability 1 - p( x_{t}). Ordinarily the injurer would not pay damages in this instance, but if there are Type I errors, he will pay h if no harm occurs, and so this occurs with probability e_{1}[1 -p( x_{{})]. Therefore, the injurer's expected costs (assuming for the moment that there are no Type II errors) are:

which for any x_{i} exceeds w_{t}x_{t} + p(x_{t})h. The presence of Type I errors increases the injurer's expected damages, but reduces the level of care that the injurer takes. This may seem somewhat paradoxical, but is easy to understand once we think carefully about marginal versus average incentives. Type I errors increase the injurer's expected costs (thus affecting average or total incentives), but worsen the injurer's marginal incentives to take care. In the extreme case where e_{1} = 1, for example, the injurer faces damages with probability 1, irrespective of the level of care taken. In this situation there is simply no point in the injurer taking care, since he cannot reduce his liability by doing so. Combining the two kinds of errors yields the injurer's expected costs:

Both kinds of errors reduce the incentives to take care, but the combined effect (due to the presence of Type I errors) could end up increasing the expected damages paid by the injurer.