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An economic analysis of a hybrid liability rule.

I. INTRODUCTION

In an economic model of torts, of primary concern is the efficiency of liability rules with respect to the care levels of (potential) injurers and victims. A liability rule is said to be efficient with respect to care when it provides incentives for both the injurer and victims to take due care, that is, the levels of care that minimize a social loss of accidents function that typically includes costs of care to both parties and the expected damage of the accident. It is well established in the standard tort model that a care-based rule, such as negligence, is an efficient liability rule. (1) Under the negligence rule, the injurer avoids liability by taking due care (i.e., by not being negligent), and the victim takes due care to minimize his or her personal accident loss when liable for damages. (2) It is also well established that rules that are not care-based, such as strict liability or no liability, are not efficient. With strict liability, the injurer is always liable and, therefore, the victim has no i ncentive to take any care. With no liability, the opposite is true and the injurer has no incentive to take care. Strict liability can be efficient in an accident setting in which the due care level for the victim is zero, just as no liability can be efficient in setting where the due care level for the injurer is zero.

What appears to be overlooked in the literature on liability rules is an examination of a hybrid liability rule. For the purpose of this article a hybrid liability rule is defined as a rule that incorporates properties of both a care-based and non-care-based rule, such as negligence and no liability. Fortunately, this does not have to be a completely abstract exercise. Such a hybrid rule does exist, as found in child trespassing cases.

Trespassing may present a setting in which no liability is an efficient rule. Adult trespassers are generally not owed any duty of care from landowners. If not trespassing is due care for an adult, due care for the landowner is to take no care at all. This must be so because if it is efficient for an adult not to trespass, any additional resources used to make the land safe would be wasted when the adult is taking due care. Child trespassers, however, are sometimes protected by a doctrine known as attractive nuisance. There appears to be no mention of attractive nuisance in the economics analysis of law literature, other than a passing comment by Landes and Posner (1987, 95-96):

Children frequently are attracted to dangerous conditions on land, such as railroad turntables and swimming holes. As trespassers they would under conventional tort principles be barred from recovering damages if injured by one of those conditions.... But by the virtue of the attractive nuisance doctrine, the landowner's negligence is not excused by the child's status as a trespasser. The costs to the children--more realistically, to their parents--of avoiding the lure of the attractive nuisance are often greater than the costs to the landowner of fencing out the children.

Landes and Posner (1987) correctly point out that landowners generally owe no duty of care to trespassers. But if it is the case that with respect to child trespassers it is efficient for landowners to take a positive level of care, no liability is not an efficient rule. This introduces an efficiency rationale for attractive nuisance, as they point out in their last sentence. But other than this brief mention of the doctrine, there is no discussion of whether or not attractive nuisance is in and of itself an efficient liability rule with respect to care levels.

This article examines the attractive nuisance doctrine in the context of a simple economic model of torts. Attractive nuisance is a uniquely defined and often applied legal rule. In its application, it acts as a hybrid liability rule--it applies the negligence rule to accidents involving some types of children, and the no-liability rule to accidents involving other types of children. It is shown that attractive nuisance may not always be an efficient liability rule with respect to care levels. Yet when additional factors, such as court costs, are considered, the hybrid quality of the doctrine may provide a sound economic justification for its use. The next section offers a description of the attractive nuisance doctrine.

II. ATTRACTIVE NUISANCE DOCTRINE

The attractive nuisance doctrine is stated explicitly in Section 339 of the Second Restatement of Torts: (3)

A possessor of land is subject to liability for physical harm to children trespassing thereon caused by an artificial condition upon the land if

a) the place where the condition exists is one upon which the possessor knows or has reason to know that children are likely to trespass, and

b) the condition is one in which the possessor knows or has reason to know and which he realizes or should realize will involve an unreasonable risk of death or serious bodily harm to such children, and

c) the children because of their youth do not discover the condition or realize the risk involved in intermeddling with it or coming within the area made dangerous by it, and

d) the utility to the possessor of maintaining the condition and the burden of eliminating the danger are slight as compared with the risk to children involved, and

e) the possessor fails to exercise reasonable care to eliminate the danger or otherwise to protect the children.

Parts (a) and (b) establish a tort setting in which the landowner knows (or should know) that a serious accident involving a child may occur on his or her property. Part (c) suggests that the defense of attractive nuisance is only available to a certain type of child. Part (d) suggests that the due care level for the landowner must be positive, and part (e) places liability on the landowner only if he or she takes less than due care. Thus, when the attractive nuisance doctrine is accepted by the court, it changes the no-liability rule into the negligence rule. (4)

In interpreting the attractive nuisance doctrine in the context of the model presented in the following section, condition (c) is key. More specifically, condition (c) is interpreted as applying to a high-cost-of-care child whose due care level is zero, but not to a low-cost-of-care child whose due care level may be positive. (5) In this sense, the no-liability rule is applied to a trespassing low-cost child, but with a trespassing high-cost child, conditions (d) and (e) impose the negligence rule on the landowner.

III. TRESPASS MODEL

Consider a simple trespass tort model with a landowner and a child. The landowner has two care levels to choose from--Care and No Care, with the cost of Care denoted by B. The child also has two care levels to choose from--Care (i.e., no trespass) and No Care (i.e., trespass). It is assumed, however, that the child can have one of two types of cost of Care: a low cost of [A.sub.1] with probability [alpha], and a high cost of [A.sub.2] with probability (1 - [alpha]), with 0 [less than or equal to] [alpha] [less than or equal to] 1. (6)

When both the low-cost and high-cost child choose Care, there is no trespass and no probability that an accident will occur. When the landowner chooses Care, the probability that an accident occurs is [p.sub.C] [greater than or equal to] 0 when neither type of child chooses Care, (1 - [alpha])[p.sub.C] when only the low-cost child chooses Care, and [alpha][p.sub.C] when only the high-cost child chooses Care. (7) When the landowner chooses No Care, the probability that an accident occurs is [p.sub.N] > [p.sub.C] when neither type of child chooses Care, (1 - [alpha])[p.sub.N] when only the low-cost child chooses Care, and [alpha][p.sub.N] when only the high-cost child chooses Care. If an accident occurs, the damage created is denoted by D.

To find the due care levels, the social loss of the accident across eight different combinations of care levels are compared, with the low-cost child's care level listed first, the high-cost child's care level listed second, and the landowner's care level listed third:

(1) L(C, NC, C) = [alpha][A.sub.1] + B + (1 - [alpha])[p.sub.C]D

(2) L(C, NC, NC) = [alpha][A.sub.1] + (1 - [alpha])[p.sub.N]D

(3) L(NC, NC, C) = B + [p.sub.C]D

(4) L(C, C, C) = [alpha][A.sub.1] + (1 - [alpha])[A.sub.2] + B

(5) L(C, C, NC) = [alpha][A.sub.1] + (1 - [alpha])[A.sub.2]

(6) L(NC, C, C) = (1 - [alpha])[A.sub.2] + B + [alpha][p.sub.C]D

(7) L(NC, C, NC) = (1 - [alpha])[A.sub.2] + [alpha][p.sub.N]D

(8) L(NC, NC, NC) = [p.sub.N]D.

To rule out some of the care level combinations as possible social loss minima, it is assumed that [A.sub.1] < B + [p.sub.C]D < [p.sub.N]D < [A.sub.2]. The first inequality implies that if the model only considers accidents with a low-cost child ([alpha] = 1), the child would be in the best position to prevent an accident. The second inequality implies that if the landowner chooses Care, the cost of care and the expected damage are less than the expected damage when the landowner chooses No Care. Finally, the third inequality implies that if the model only considers accidents with a high-cost child ([alpha] = 0), the landowner would be in the best position to prevent an accident.

In this framework, it is never efficient for all three parties to choose Care. If both the low-cost and high-cost child choose Care there is no trespass, and the landowner choosing Care over No Care increases the social loss by B. Also, by assuming that [A.sub.1] < [A.sub.2], the possibility that due care for the low-cost child can be No Care, while due care for the high-cost child can be care, is ruled out. Furthermore, with [p.sub.N]D < [A.sub.2], it is assumed that it is never efficient for the high-cost child to choose Care. Finally, with B + [p.sub.C]D < [p.sub.N]D, if each type of child chooses No Care, it is efficient for the landowner to choose Care over No Care. Taken together, these assumptions leave three possible social loss values to consider: expressions (1), (2), and (3).

For a liability rule to be efficient with respect to care levels, the rule must provide each type of child and the landowner with the incentives to take due care for every possible combination of care levels that may minimize social loss. The attractive nuisance doctrine acts as a hybrid rule, applying a no-liability rule with accidents involving a low-cost child, and a negligence rule with accidents involving a high-cost child. On its own, a no-liability rule is not an efficient rule when due care for the landowner is positive, as is the case when (1) or (3) minimizes social loss. A negligence rule, on the other hand, is well known in the literature on the economics of torts to always be efficient with respect to care. (8) What remains is to examine the conditions under which the attractive nuisance doctrine is an efficient liability rule.

IV. ATTRACTIVE NUISANCE AND DUE CARE

First consider the conditions under which expression (1) minimizes social loss. The difference between (1) and (2) is the landowner's care level. If (1) < (2), it must be the case that B < (1 - [alpha])([p.sub.N] - [p.sub.C])D. With the low-cost child choosing Care, when the landowner chooses Care social loss is increased by B, but the probability of an accident occurring with the high-cost child is lowered by the amount ([p.sub.N] - [p.sub.C]). Also, it must be the case that B < (1 - [alpha])[p.sub.N]D. (9) That is, the landowner's cost of Care must be less than the expected damages of the accident when the low-cost child chooses Care, the high-cost child chooses No Care, and the landowner chooses No Care. The difference between (1) and (3) is the low-cost child's care level. With (1) < (3), it must be the case that [A.sub.1] < [p.sub.C]D. (10) This means that by taking Care, the low-cost child incurs a cost of [A.sub.1] but avoids an expected damage of [p.sub.C]D when the landowner is also choosing Care. In all, when (1) minimizes social loss, the low-cost child is in the best position to avoid an accident involving him- or herself, but the landowner is in the best position to avoid an accident involving the high-cost child.

With due care positive for the low-cost child and the landowner but zero for the high-cost child, the attractive nuisance doctrine is efficient with respect to care. If attractive nuisance is allowed as a defense for the high-cost child but not the low-cost child, the landowner chooses Care at a cost of B to avoid the higher expected liability of (1 - [alpha])[p.sub.N]D when taking No Care. Furthermore, without the defense of attractive nuisance, the low-cost child chooses Care at a cost of [A.sub.1], to avoid the higher expected damages of [p.sub.C]D Finally, even without being able to shift liability to a nonnegligent landowner, the high-cost child chooses No Care because the expected damage of [p.sub.C]D is less than the cost of Care of [A.sub.2]. (11)

When (2) minimizes social loss, the due care level for the landowner is No Care. If the attractive nuisance doctrine is applied in this setting to protect the high-cost child, the courts will find the landowner nonnegligent and therefore not liable. Furthermore, the low-cost child chooses Care because [A.sub.1] < [p.sub.N]D, and the high-cost child chooses No Care because [A.sub.2] > [p.sub.N]D Attractive nuisance, then, is efficient when (2) minimizes social loss.

When (3) minimizes social loss, it is efficient for each type of child to choose No Care and for the landowner to choose Care because B + [p.sub.C]D < [p.sub.N]D By taking Care, the landowner avoids liability and incurs a personal loss of B, and the damage if an accident occurs is borne by the child. But if attractive nuisance is used as a defense for the high-cost child only, the landowner's expected liability is (1 - [alpha])[p.sub.N]D when he chooses No Care, even though the expected damage is [p.sub.N]D Taking Care imposes a cost of B on the landowner, but if this is greater than his expected liability of taking No Care, (1 - [alpha])[p.sub.N]D), the landowner will choose No Care. Only if B < (1 - [alpha])[p.sub.N]D will the landowner take due care. Thus, the attractive nuisance doctrine may not provide the landowner with the incentive to take due care when (3) minimizes social loss.

Precisely why the attractive nuisance doctrine fails when (3) minimizes social loss can best be illustrated with a specific setting in which by choosing Care, the landowner can completely prevent an accident (i.e., [p.sub.C] = 0) with either a low-cost or high-cost child.(12) When the landowner's cost of care is less than the expected damage to the high-cost child (i.e., B < [1 - [alpha]][p.sub.N]D), attractive nuisance provides the landowner with the incentive to take Care, and this also protects the low-cost child. When the landowner's cost of care is greater than the expected damage to the high-cost child but is less than the expected cost of care to the low-cost child ([alpha][A.sub.1]) and the expected damage to the high-cost child ([1 - [alpha]][p.sub.N]D), it is efficient for the landowner to choose Care (i.e., [3] < [2] with [p.sub.C] = 0). But in this latter case, the landowner inefficiently chooses No Care and accepts the expected liability of (1 - [alpha])[p.sub.N]D instead of the more expensive co st of care, B.

Attractive nuisance fails, then, when (3) is the social loss minimum and B > (1- [alpha])[p.sub.N]D Though it is unlikely that (3) never minimizes social loss, as the low-cost child's expected cost of care approaches zero either because [A.sub.1] [right arrow] 0 and/or [alpha] [right arrow] 0, the possibility of (3) minimizing social loss approaches zero. Thus it may be reasonable to believe that in the type of setting that the attractive nuisance doctrine will most often be applied, the cost of care to the low-cost child is likely to be small and the probability of having an accident involving a high-cost child, (1 - [alpha]), is likely to be large. Still, especially with avoidable accidents, a landowner efficiently choosing Care may not only protect the high-cost child but provide an additional benefit of saving any cost of care the low-cost child would incur to avoid trespassing.

V. COURT COSTS

In addition to efficiency with respect to care levels, economists are often concerned with the issue of court costs. Two types of court costs of using liability rules are usually identified--information costs and claims costs. (13) Information costs involve the costs of applying a liability rule, such as assessing care levels for care-based rules. Claims costs involve the costs of processing and collecting a legal claim (other than the information costs). No liability is clearly the most efficient of all liability rules with respect to all court costs. In theory, with a no-liability rule, victims have no reason to bring claims against injurers. Also, the rule is not care-based, so there is no information needed to apply the rule. The negligence rule, on the other hand, involves information costs when claims are made as the court must determine the due care level and the actual care level of the injurer. Again in theory, because negligence is efficient with respect to care, the injurer avoids liability by taki ng due care and the victim has no incentive to bring a claim. Thus, with perfect information for victims, injurers, and the courts, the no-liability and negligence rules involve no court costs.

Attractive nuisance, however, will involve some court costs even if all the parties and the courts have perfect information. When (3) minimizes social loss and the injurer prefers to accept the expected liability rather than the higher cost of care, the high-cost child has a potential successful claim to make against the injurer. Thus when the hybrid rule fails to provide the injurer with the incentive to take due care, it also leads to court costs.

Based on the discussion to this point, the negligence rule appears to dominate both the no-liability and the hybrid rule. No liability and the hybrid rule are not always efficient with respect to care, but the negligence rule is efficient. The hybrid rule involves court costs, but with perfect information no liability and negligence involve no court costs. To provide a justification for the hybrid rule, then, the assumption of perfect information must be relaxed. (14) For example, individuals may not have a good understanding of how a liability rule works, or they may simply be misinformed about which liability rule is governing their actions. Furthermore, any care-based rule involves determinations of due care and actual care levels, and these can be miscalculated by individuals and by the courts. A non-negligent injurer may ultimately be found to be negligent, whereas a negligent injurer may escape liability. (15)

For a brief comparison of the negligence and hybrid rule with respect to court costs, consider the following scenario. To put the hybrid rule in its worst light, assume that social loss (3) is the minimum and that the hybrid rule is inefficient because the cost of due care outweighs the landowner's expected liability. In this case, the low-cost child has no claim because of the no-liability part of the rule, but the high-cost child does have a claim leading to court costs of K per claim. With the injurer taking No Care, the total social loss including court costs can be written as [p.sub.N][D+(1-[alpha])K]. (16) With the negligence rule, the landowner takes Care and avoids liability. But assume because of errors in the application of the negligence rule, each type of child brings a claim with probability t. The total social loss including court costs can be written as [p.sub.C] [D + tK]+B. Thus, the hybrid rule leads to a lower social loss than does the negligence rule when

(9) [p.sub.N][D + (1 - [alpha])K] < [p.sub.C][D + tK] + B.

With (3) as the social loss minimum, B + [p.sub.C]D < [p.sub.N]D. (17) For (9) to hold, then, it is necessary but not sufficient that [p.sub.N](1 - [alpha])K < [p.sub.C]tK, that is, the expected court costs must be lower with the hybrid rule compared to the negligence rule. This is more likely to be the case the lower the probability of a high-cost child (1 - [alpha]), the higher the probability of a child bringing a claim under the negligence rule (t), and the smaller the effect of the landowner's care on reducing the probability of an accident. (18) When (9) holds, the hybrid rule's efficiency with respect to court costs outweighs the negligence rule's efficiency with respect to due care.

VI. CONCLUDING COMMENTS

It has been argued in this article that attractive nuisance acts as a hybrid liability rule--the landowner faces no liability with accidents involving a low-cost child but faces the negligence rule with accidents involving a high-cost child. The primary rationale for the defense of attractive nuisance to a rule of no liability is that it provides the landowner some incentive to protect the high-cost child. Without the defense of attractive nuisance, a rule of no liability is only efficient when (2) minimizes social loss. Attractive nuisance is efficient with respect to care when (1) or (2) minimizes social loss, but is not always efficient when (3) minimizes social loss because if the landowner chooses No Care, his expected liability is (1 - [alpha])[p.sub.N]D instead of the true expected damages of [p.sub.N]D. The negligence rule, however, improves on attractive nuisance by providing the incentive for the landowner to take due care regardless of the due care level of the low-cost or high-cost child.

It is always easy to justify the no-liability rule by arguing that in its application, very few court costs are incurred. But this is true for all torts, not just trespassing, yet there are obvious advantages to liability rules that may be costly to administer but provide incentives for individuals to take due care. If in general, as with adult trespassers, it is likely that the due care level for the potential trespasser is Care (i.e., no trespass), there is economic sense to a rule of no liability even with respect to due care. But with child trespassers, especially young children, it may be reasonable to believe that a landowner's due care level is positive. If this is true, the advantages of no liability with respect to court costs must be weighed against the disadvantages of no liability with respect to due care.

Similarly, it is always easy to justify the negligence rule as being efficient with respect to due care. But the negligence rule involves court costs, especially in terms of information costs. Attractive nuisance also involves information costs, but to the extent that it is easy to distinguish between low-cost and high-cost children, further information costs of using attractive nuisance are only incurred with accidents involving a high-cost child. The attractive nuisance doctrine, then, incorporates one of the best properties of a negligence rule in terms of providing the landowner with incentives to choose Care, and one of the best properties of no liability in terms of minimizing the court costs of an accident involving a low-cost child.

Where attractive nuisance fails is when it is efficient for the landowner to choose Care and it is efficient for both the low-cost and high-cost child to choose No Care. In the case, for example, where the landowner can efficiently choose Care and eliminate the possibility of an accident occurring, the low-cost child is no longer in the best position to protect him- or herself. But in this setting, if the landowner's cost of care exceeds the expected liability (B > [1 - [alpha]][p.sub.N]D), the landowner lacks the incentive to take due care. It may very well be that this setting is not empirically relevant for two reasons: (3) may not be the minimum social loss; or, even if it is, the landowner's cost of care may not exceed the expected liability. But even with its shortcomings, attractive nuisance clearly improves on no liability, the current benchmark liability rule in trespass cases, in providing incentives for landowners to protect young children. Furthermore, the advantage of the negligence rule in impro ving on attractive nuisance with respect to due care may be outweighed by the additional information costs of negligence in trying to determine liability in all child trespass cases that lead to claims.

The trespassing setting provides an excellent example of the legal system's implicit understanding of the efficiency of liability rules. For adults, no liability appears to be a sound way to deal with trespassing. For children, especially young ones, no liability may not provide the proper incentives for the landowner to take due care, but negligence may impose too many court costs on the system. The attractive nuisance doctrine appears to be a sound example of the legal system trading off between due care and court costs; this is exactly what a hybrid liability rule has as its advantage over strictly non-care-based or strictly care-based rules. It remains to be seen what other legal settings may provide good examples for the efficient use of hybrid liability rules.

(1.) For a thorough discussion of the economic analysis of tort law, see Landes and Posner (1987) or Shavell (1987).

(2.) Other efficient care-based rules include strict liability plus contributory negligence, negligence plus contributory negligence, and comparative negligence. For definitions and discussions of these rules, see Landes and Posner (1987, chap. 3).

(3.) This description is found in Keeton et al. (1984, 402 n. 24).

(4.) Although the actual application of the attractive nuisance doctrine differs from state to state, most state courts use the Second Restatement's basic outline in dealing with child trespasser cases in which the issue of attractive nuisance is raised. A precise discussion of the subtle differences in the application of the attractive nuisance doctrine across states is well beyond the scope of this article. Keeton et al. (1984, 402-11) offers a more detailed discussion of the application of the attractive nuisance doctrine.

(5.) In considering condition (c), the courts often look at the age of the child, but not exclusively. Other facts surrounding the accident are often taken into account.

(6.) Part of the cost of not trespassing can include parental monitoring costs of the child's behavior, especially for the high-cost child who may be too young to know better. Also, there may be a cost of not trespassing that includes the lost utility of not being able to play in a specific area.

(7.) When [p.sub.C] = 0, if it is efficient for the landowner to choose Care, an alternative care setting exists, and due care for each type of child is No Care. When [p.sub.C] > 0, an accident may still occur if the landowner chooses Care. For example, if it is efficient for the landowner to remove an attractive nuisance from his property, [p.sub.C] will be zero. If it is efficient for the landowner to fence an attractive nuisance, it may still be possible for a trespassing child to climb over the fence and be involved in an accident.

(8.) In a trespass setting, the negligence rule differs from the attractive nuisance doctrine in that negligence holds the landowner to due care for all accidents, not just those involving a high-cost child.

(9.) With (1) < (2), B + (1-[alpha])[p.sub.C]D < (1 - [alpha]) [p.sub.N]D [right arrow] B < (1 - [alpha]) [p.sub.N]D.

(10.) With (1) < (3), [alpha][A.sub.1] < [alpha][p.sub.C]D [right arrow] [A.sub.1] < [p.sub.C]D.

(11.) B + [p.sub.C]D < [A.sub.2] [right arrow] [p.sub.C]D < [A.sub.2].

(12.) With [p.sub.C] = 0, if it is efficient for the landowner to choose Care, it cannot be efficient for the low-cost child to choose Care. This rules out expression (1) as a possible minimum social loss in this setting.

(13.) See Landes and Posner (1987, 65).

(14.) See Landes and Posner (1987, 72-73) for a succinct discussion of how the negligence rule may lead to claims and information costs.

(15.) It is important to note that to the extent that errors in the courts' application of the negligence rule may be anticipated, the rule may no longer provide the incentive for the individuals to take due care. See Shavell (1987, 79-83).

(16.) With (3) as the social loss minimum, each type of child can be in an accident. Therefore, the expected damage is [p.sub.N]D when the injurer takes No Care, and [p.sub.C]D when the injurer takes Care.

(17.) Expression (3) < (8).

(18.) By assumption, [p.sub.C] < [p.sub.N]. If the landowner can greatly reduce the probability of an accident occurring, there may be fewer expected court costs when the landowner takes Care.

REFERENCES

Keeton, W. Page, D. B. Dobbs, R. E. Keeton, and D. G. Owen. Prosser and Keeton on the Law of Torts, 5th ed. St. Paul, MN: West Publishing, 1984.

Landes, W. M., and R. A. Posner. The Economic Structure of Tort Law. Cambridge: Harvard University Press, 1987.

Shavell, S. Economic Analysis of Accident Law. Cambridge: Harvard University Press, 1987.

HAROLD WINTER *

* I would like to thank William Neilson, Jeffrey Baird, and two anonymous referees for helpful comments. I also benefited from the research assistance of Michael Melander.

Winter: Associate Professor, Department of Economics, Ohio University, Athens, OH 45701. Phone 1-740-593-2048, Fax 1-740-593-0181, E-mail winter@ohio.edu
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