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STRICT LIABILITY VERSUS NEGLIGENCE

Hans-Bernd Schäfer and Andreas Schönenberger

Universität Hamburg - Fachbereich Rechtswissenschaft

© Copyright 1999 Hans-Bernd Schäfer and Andreas Schönenberger

Abstract
The purpose of this chapter is to compare negligence rules and strict liability
rules and to examine the allocative effects resulting from the application of
different liability regimes. It first discusses unilateral accidents, while the more
complicated bilateral cases follow afterwards. Each section starts with a
discussion of the rule of no liability before moving on to various forms of
negligence and ending with various strict liability rules. At the end of each
section, there is a discussion on how results change when relaxing specific
assumptions. The various aspects are summarised focusing on the question of
whether the outcome under a specific liability regime is efficient or not. We
also discuss a few more specific topics of interest, for example, the allocative
effects of various liability rules when agents enter into a contractual
relationship, cases of ‘joint liability’, the impact of uncertain legal standards,
and the interaction between liability law and insurance.
JEL classification: K0
Keywords: Negligence, Strict Liability

1. Introduction

The purpose of this chapter is to compare negligence rules and strict liability
rules. They are the major rules of liability used in tort law to deal with
situations where one person (the injurer) causes harm to another person (the
victim). In England, France and Germany, for instance, the usual forms of
liability are the comparative negligence rule and strict liability with the defence
of relative negligence, and in the US it is the comparative negligence rule, the
negligence rule with the defence of contributory negligence, and strict liability
with the same defence. The details of these rules will be discussed below.
Zweigert and K?tz (1996, secs. 40-43) provide a rigorous description of tort law
in England, France and Germany. For the US, a good reference is Keeton,
Dobbs, et al. (1984, chs 5, 11, 13).

Historically, it is interesting to observe the changes in the relative
importance of different liability rules. Before the nineteenth century, for
instance, strict liability was predominant in most common law jurisdictions. In
the early and mid-nineteenth century, however, this changed with negligence
and fault becoming the prevailing standard of tort liability, as Schwartz (1981)
notes. Since the twentieth century, rules of strict liability have enjoyed a
renaissance and have been applied more and more to determine who should
bear the costs of an accident and to what extent. A good example of this
phenomenon is the shift back to strict liability in products liability cases.

Moreover, tort law is much under debate because of the increasing number
of cases where compensation for losses might substantially exceed the actual
damage. In the US, for instance, damages awarded may exceed the losses
sustained in the presence of ‘punitive’ damages where parties acted with ill
will, that is the harm was intentional, whereas in Germany higher awards are
provided to give victims ‘satisfaction’ and to compensate them for
nonpecuniary losses. The scope of harm and the size of judgements have
become exceedingly expansive, and manufacturers pay extremely high
premiums for products liability insurance to protect themselves against these
awards. Many of them have withdrawn from the market entirely. This and
various other results on the issue are presented by Priest (1991). Many
economists and lawyers conclude that the tort system is in need of reform.
Again, we need to understand the basic principles of how different liability
regimes work to be able to evaluate the alternatives to reform.

Tort law is one of those areas in the law where (micro)economic models can
be successfully applied. Tort is about damages and has important economic
implications. The economic approach to tort is therefore mainly concerned with
examining the allocative effects, that is welfare effects, resulting from the
application of different liability regimes. Landes and Posner (1987, p. 6)
suggest that liability rules can be interpreted as a legal attempt to establish
incentives for parties to achieve social efficiency objectives. One of the
path-breaking studies in the development of the economic approach to tort is
Calabresi (1970). The aim of tort law, he proposes, apart from the requirement
for justice, is to minimise the social costs of a tort defined as the sum of total
accident costs, administration costs, costs of properly allocating accident losses
by means of insurance, and accident prevention costs of both the injurer and the
victim. Again, the comparison between strict liability and negligence helps to
determine which tort system is most suitable to improve welfare by, first,
encouraging individuals to engage in safer activities by providing an incentive
to do so, and second, encouraging individuals to make a given activity safer.

Throughout, we will be considering models of accidents involving two
individuals, the injurer and the victim. Both of them are engaged in some
activity, and both of them exercise a certain level of care. The decisions the
parties have to make are twofold. They have to decide how much care they want
to exercise and how much they want to engage in an activity. It is plausible to
assume that accident prevention costs increase with the amount of care taken,
and that expected damages decrease with the level of care, but increase with the
amount of activity the parties engage in.

In the remainder of this chapter, we will discuss first, in Section 2,
unilateral accidents because they describe those situations where one party, that
is the victim, has no influence on the probability and the size of damages. Also,
it is easier to understand the more complicated discussion of the bilateral case
which follows in Section 3. Each section starts with a discussion of the rule of
no liability before moving on to various forms of negligence and ending with
various strict liability rules. At the end of each section, there is also a
discussion on how results change when relaxing certain assumptions. In
Section 4, the various aspects of the comparison between liability rules are
summarised focusing on the question of whether the outcome under a specific
liability regime is efficient or not. Section 5 concentrates on a few more specific
topics of interest. First, we discuss the allocative effects of various liability rules
when agents enter into a contractual relationship, which also implies a brief
discussion on the distinction between tort law and contract law. Second, we
analyse cases of ‘joint liability’, that is situations where more than one
tortfeasor contributes to the occurrence of an accident.

2. Unilateral Accidents

The discussion here is mainly based on Sch?fer and Ott (1995) and Shavell
(1987).

In the case of unilateral accidents which we focus on in this section, it is
assumed that the victim cannot influence the amount of expected damages.
Also, to keep things simple, we further assume that the level of activity is
constant. (This assumption will be relaxed below.) Therefore, if we denote
accident prevention costs by c, the level of care by x, and if d measures the total
amount of expected damages, then, abstracting from administration costs and
assuming risk neutrality, the social objective function takes the form of:

min c (x) + d (x)                                     (1)

Setting the first derivative with respect to x equal to zero we obtain the
following solution:

c' (x) = - d' (x)                                       (2)

which simply states that the marginal cost to the injurer of taking an additional
unit of care (left-hand side of equation (2)) should equal the marginal benefit
to the victim represented by a reduction in the total amount of expected
damages (therefore the negative sign on the right-hand side of equation (2)).
It should now be clear why microeconomic models can be applied so easily in
law and economics as equation (1) is an extremely simple example of a
standard optimisation problem recurring very frequently in any area of
economic analysis.

We now consider the behaviour of the injurer under various liability rules
providing important insights as to the efficiency of these rules.

3. Rule of No Liability

If the injurer cannot be held liable for the harm she causes, and if she therefore
does not have to bear the costs of an accident, she will choose the lowest
possible level of precaution in order to minimise her costs. Since we assume
that the total amount of damages is a decreasing function of the precaution
level the accident costs will be extremely high. As a result, the outcome of this
liability rule is clearly not socially optimal.

4. Negligence

Under the negligence rule, the injurer will be held liable only if she exercised
precaution below a level usually determined by the law and/or by the court.
This level is called reasonable care or due care. Posner (1972) proposed an
economic efficiency criterion which could be used to identify the efficient
precaution level to establish it as the legal standard. It should be borne in mind
that one of the most important objectives of tort law is to give the injurer an
incentive to apply the efficient level of care fulfilling the optimality condition
(2). Interestingly enough, the first person to describe this legal standard of care
was not an economist, but a judge. Learned Hand (1947) suggested that an
injurer is liable if her burden B of adequate precautions is less than the
probability P that the accident occurs, multiplied by the size L of the injury.
Note that Judge Hand's statement of the rule is unclear as to whether it refers
to total or marginal levels of benefits and costs of caretaking, but we assume
that he had marginal values in mind. Stated in algebraic terms, an injurer is
negligent if the condition
B < PL                                  (3)
holds; and equality denotes optimality.

If the injurer exercised due care she will not be held liable for the costs of
the accident. Let us now suppose that the court or the law would set the level
of due care equal to the socially optimal level of care. Would the negligence
rule result in the socially optimal level of care being taken? The answer is yes,
as can be seen very easily by noting that a self-interested person will choose her
level of precaution to minimise her private costs. Would she therefore want to
choose a precaution level above the level of due care? No, because any care
taken in excess of the standard set by the court would be more costly without
reducing the costs of compensation since due care is enough to be non-liable.
Would she, on the other hand, want to choose a precaution level below due
care? No, because now she is running the risk of bearing the total amount of the
expected damages.

5. Relaxing Assumptions

Note that in the previous section we made a few simplifying assumptions. First,
we assumed that the court would set the level of due care equal to the socially
optimal level. Second, it was assumed that the legal sanction imposed equals
the harm actually caused and, third, the level of activity was supposed to be
constant. We will now examine how the results change if we relax these
assumptions one by one, that is, we will discuss the effects of relaxing only one
assumption at a time. Some of these issues are clearly presented by Cooter and
Ulen (1997, chs 8 and 9).

Let us first examine the question of how the results of the previous section
change when the court sets a level of due care that is not equal to the socially
optimal level. Suppose, for instance, that the court does not require any
precaution at all. Under these circumstances, it is obviously cheapest for the
injurer not to exercise any care, because she will escape liability even without
taking any care at all. Taking greater care would have no advantage, but would
involve additional costs. Put more generally, the potential injurer will satisfy
the legal standard even if it is pegged below the socially efficient level. The
same applies to a legal standard above the socially efficient level, with one
important exception, though. If the amount of precaution costs at the legal
standard exceeds the total amount of precaution and expected damage costs at
the socially optimal care level, then the potential injurer will ignore the legal
standard and set her caretaking level at the lower socially optimal care level.
This result changes if the injurer is not held liable for the entire accident losses,
but only for the amount of damage in addition to the damage that would have
been caused if the injurer had exercised the level of care set by the courts
(partial liability). See, for instance, § 249 BGB under German law. For the US,
see Kahan (1989). The first authors to describe this case are Sch?fer and Ott
(1986). Here, it is optimal for the injurer to exercise socially optimal care even
if the legal standard is pegged above the socially efficient level. This is because
by exercising the efficient level of care instead of the higher legal standard,
precaution costs decrease by more than the imposed legal sanction increases.
In general, however, we can say that in order to obtain an efficient outcome the
court needs to set the due level of care equal to the socially optimal level of
care.

Note also that it is very difficult for courts, legislatures and authorities to
identify the efficient level of care in order to establish it as the legal standard.
Due or reasonable care is usually identified by comparing what a reasonable
person would have done under the circumstances with the actual precautionary
activity of the injurer. An illustration of the reasonable person standard is
provided by Posner (1992, p. 167). However, this standard is very vague and
‘flexible’. Therefore, an alternative to decide whether an injurer was negligent
or not without a specific standard of care would be, first, to ask what an injurer
could have done (alternatively or in addition) to prevent the damage or to
reduce the probability that it occurs. Then, the costs of the alternative or of the
additional precaution activity are determined. If either the difference between
the actual precaution costs and the costs of the alternative precaution activity
or the costs of the additional precaution activity are less than the reduction in
the total amount of expected damages as a result of the alternative or additional
activity, the injurer will be liable.

Another assumption we made in the previous section is that the legal
sanction imposed equals the harm actually caused. What will happen if we
relax this assumption? Endres (1991, pp. 51-87) provides a rigorous and rather
formal analysis of this question which is beyond the scope of this article. From
a rather intuitive and less formal perspective we can say that, under the
negligence rule, an equality between harm and sanction is not essential as long
as the sanction is sufficiently large so that the private costs of the injurer are
minimised by conforming to the legal standard. However, once the legal
sanction falls below a certain level, the injurer will minimise her costs by
taking less precaution than the legal standard.

Finally, we relax the assumption of a constant level of activity to study the
effects of an increase in the injurer’s level of activity that will result in a
proportional increase in the total amount of expected accident damages, given
a specific level of care. This is essential when it comes to assessing the social
utility of an activity. Finsinger and Pauly (1990) point out that the total net
utility of a risky activity ought to be positive.

The first aspect can be dealt with quite easily by slightly modifying the
optimisation problem as represented in equation (1). The social objective
function now has to take into account that various levels of activity influence
the utility u of the actor, that is the injurer. It is plausible to assume that utility
is an increasing function of activity. Those who are familiar with optimisation
problems should also note that for a unique solution to exist it is necessary to
assume further that the utility function is well-behaved. From the total amount
of utility we need, of course, to subtract the total costs of care which are
assumed to be equal to the level of activity multiplied by the level of care, x.
Eventually, we need to subtract the total amount of expected damages d. Thus
we obtain as the social objective function

max u (a) -a x -a d (x)                        (4)?

To solve this maximisation problem we first have to determine the optimal
level of care x* by minimising the total costs of taking care represented by the
second and third terms in equation (4). Substituting into (4) and differentiating
with respect to the level of activity we obtain

u' (a) = x* + d (x*)                             (5)

which is the equivalent of equation (2) in the case of a constant level of activity.
The interpretation is straightforward. The injurer should raise her activity as
long as the marginal increase in utility she derives from raising activity exceeds
the increment to total costs caused by doing so.

We can now move on to discussing whether the negligence rule can
guarantee that an activity is socially useful. A simple example might illustrate
this point. Assume that the utility of an activity is 100. The costs of the optimal
level of precaution are 80, and the amount of total damages is 30. Since the
victim has to bear the costs of the accident when the injurer exercises due care
and, therefore, is not liable, the injurer has a benefit of 20 by engaging in her
activity. However, the net utility of the activity is clearly negative meaning that
the injurer should not engage in the activity in the first place. Since injurers
will escape liability by taking due care they have no reason to consider the
effect that their activities have on accident damages. As a result, the rule of
negligence can create incentives to exercise an optimal level of precaution, but
it is not able to make sure that the social utility of an activity is positive.

Yet, there are exceptions where it can be easy for courts to observe the (lack
of) social utility of an activity. In these cases, courts can set legal standards for
both the optimal level of care and the optimal level of activity. However,
because of information costs it is generally difficult for courts to set both
standards of caretaking and/or activity levels. Shavell (1987), and Landes and
Posner (1987) focus on this issue.

6. Strict Liability

We will now turn the discussion to the major alternative of the rule of
negligence: the rule of strict liability. Again, we start off by assuming that the
legal sanction equals the actual damage and that the activity level is constant.
Under strict liability, the courts do not have to set any level of due care because
the injurer has to bear the costs of the accident regardless of the extent of her
precaution. In this case, the expected amount of costs to the injurer of taking
care x is
c (x) + d (x)                              (6)
that is, the injurer faces the total amount of costs caused by the accident. Since
it is the self-interested injurer’s objective to minimise her private costs and
since, under strict liability, the total social costs just equal her private costs, the
injurer will have an interest to minimise total accident costs. In other words,
the social objective function (1) and the private objective function resulting
from minimising equation (6) are obviously identical. Therefore, under the rule
of strict liability in the case of unilateral accidents, the injurer will choose the
socially optimal level of care.

As a result, both the rule of strict liability and the rule of negligence achieve
the socially optimal level of care. There are, however, also quite a few
differences. For instance, the division of costs under each rule is different.
Under strict liability, the injurer has to bear the total amount of expected
damages, whereas under the negligence rule, the victim has to bear the accident
costs if the injurer exercised due care. Further differences appear when relaxing
the assumptions we made.

7. Relaxing Assumptions

As mentioned in the previous section, the courts do not have to set a level of
due care. Under strict liability, all the courts need to do is to determine the size
of the damage, whereas, under the negligence rule, the courts also need to
determine the level of due care as a legal standard for the socially optimal level,
and they have to determine the level of care actually taken in order to see
whether the injurer was negligent or not. Proving negligence, however, can be
difficult and costly.

Shavell (1987, p. 264) argues that under strict liability the number of claims
is likely to be higher than under negligence because the victim has an incentive
to make a claim whenever her damages exceed the costs of making the claim.
Under negligence, on the other hand, the injurer can escape liability by
demonstrating that she has not violated the legal standard of care. Since under
the rule of strict liability it is not necessary to establish that the injurer was
negligent, the probability of trial should be less, because it is easier to predict
who is likely to win the case. Consequently, voluntary payments made in the
shadow of the law should be much more probable. There is not only more
potential for disagreement leading to trial under the negligence rule, it is also
plausible to assume that the average administrative cost per claim is higher
under negligence because the issue of negligence must be adjudicated, as was
mentioned above. As a result, one can expect the average costs of resolving
claims to be higher under negligence because of both a higher probability of
trial and higher costs per trial.

Another advantage of the rule of strict liability is that it is the injurer who
has to bear the cost of searching for the optimal level of care, as Finsinger and
von Randow (1991, p. 89) suggest. In many cases, he is better at deciding what
precautions to exercise and to what extent he should do so because he is likely
to be familiar with the activity that can cause an accident.

Another assumption we made is that the legal sanction equals the damage
actually caused. In the previous section we saw that equality is not essential as
long as the sanction is sufficiently large for the injurer to conform to the legal
standard. Under strict liability, this result changes quite drastically. Whenever
damages are not perfectly compensatory, that is, compensation is below the
level that would make the victim indifferent between no accident and an
accident with compensation, the potential injurer does not have an efficient
incentive to exercise the socially optimal level of care.

The easiest way to see this is by recalling optimality condition (2) which
states that the marginal cost to the injurer of taking an additional unit of care
should equal the marginal benefit to the victim represented by a reduction in
the total amount of expected damages. Let us assume that the costs of taking
care is a linear and increasing function of the level of care, that is any increase
in the level of care leads to a proportional increase in accident prevention costs.
We also assume that the functional relationship between the level of care and
the reduction in accident damages is such that the exercise of precaution
reduces expected damages, but at a decreasing rate. Expressed in more
mathematical terms, the first derivative of this function is positive and the
second derivative is negative. We now assume that the potential injurer knows
and expects that the legal sanction generally does not equal the total amount of
the accident damages, but that it equals a fraction of them only, because the
tortfeasor remains anonymous, damages are higher than her personal wealth,
victims are fully insured by first party or social insurance, or the damage is
dispersed, which leaves the victim little incentive to litigate. This leads to a
proportional downward shift of the damage reduction function. The crucial
impact of the proportional shift is that, holding the level of care constant, the
marginal reduction in damage and thus the marginal benefit of taking an
additional unit of care is less than in the case of perfect compensation. Since,
on the other hand, the cost function of taking care is assumed to be linear, the
marginal cost of taking care remains constant. As a result, the optimality
condition is not met any longer under the circumstances given. In order for the
cost minimising condition to be satisfied again, the potential injurer will reduce
her level of care which leads to an increase in the marginal reduction in
damage by taking care. As a result, the potential injurer does not exercise the
socially optimal level of care when damages are not perfectly compensatory.

Suppose that the tort-liability system works imperfectly in the sense that
only a fraction of all victims actually brings suit and recovers. Let us call the
ratio of compensated victims to the total number of victims the enforcement
error. The efficiency loss due to enforcement errors can be offset by augmenting
compensatory damages with punitive damages. In order to restore efficient
incentives for the potential injurer to exercise optimal care we need a punitive
multiple (multiplicative factor by which compensatory damages are adjusted to
offset the enforcement error) that equals the inverse of the enforcement error.
If, for instance, only half of the total number of victims actually bring suit then
the courts should double compensatory damages when calculating total
damages. Thus, compensatory damages and punitive damages add up to total
damages. References for issues related to punitive damages and their allocative
effects are Cooter (1982) and Kolstad, Ulen and Johnson (1990).

Finally, we relax the assumption of a constant level of activity. Recall that
under negligence the net utility of an activity could be negative because the
injurer had no reason to consider the effect that her activity had on others as
she can escape liability by taking due care. Under strict liability, however, the
injurer has to bear the total social costs of an accident, that is the sum of the
total precaution costs and the total accident damages, regardless of the level of
precaution she takes. She cannot escape liability, and the effects of activity on
risk and accident costs are fully internalised. Therefore, the injurer will engage
in an activity if and only if the net utility of that activity is positive.

Put more generally, given the possibility of escaping liability, the injurer
will not be motivated to consider the effect on the total amount of harm of the
level at which she engages in her activity. She will consider her private benefits
only. Any increase in activity, however, will raise the total amount of expected
accident damages given the level of care. Thus, the injurer will choose too high
a level of activity (see for example Polinsky, 1980). Under strict liability, the
injurer internalises the total amount of social costs and reduces the level of
activity to the socially optimal level. This conclusion was first clearly stated by
Shavell (1980).

8. Bilateral Accidents

We now extend the analysis made above to cases where both parties in an
accident may contribute to the accident costs. Again, this section is based
mainly on Sch?fer and Ott (1995), Shavell (1987), but also on Adams (1985),
and Cooter and Ulen (1997). One of the first economists to study these issues
was Brown (1973) who introduced the use of the assumption that the
probability that an accident will not occur is a function of the caretaking of both
the tortfeasor and the victim. In fact, it is rare that an accident is due to one
party (that is the injurer) only. It is much more common that the victim can
also exercise some precaution to prevent an accident. What makes bilateral
accidents quite a complicated issue to look at is the interdependence of the
parties' behaviour. We will see that in many cases the choice of one party in
terms of levels of activity and care essentially depends on the other party’s
choice.

Since we now also have to take into account the victim’s ability to reduce
the probability or size of an accident, we need to modify the social objective
function given above. If we denote the level of care taken by the injurer by x,
as before, and if y measures the level of care taken by the victim, the social
objective function now becomes

min c (x) + c (y) + d (x,y)                       (7)

where d(x,y) denotes the total amount of expected damages which, of course,
depends on the level of care exercised by both parties. Let x* and y* denote the
socially optimal values of x and y.

There are now two conditions determining the optimal levels of care. First,

c' (x) = - dx (x,y*)                              (8)

with dx being the partial derivative of d with respect to x and with y assumed
to be optimal. What it says is that the marginal cost to the injurer of taking an
additional unit of care should equal the marginal benefit of the reduction in the
expected cost of the accident, provided that the victim chooses the socially
optimal level of care. Second,

c' (y) = - dy (x*,y)                            (9)

which says that the marginal cost to the victim of increasing her level of care
should equal the marginal benefit of the expected reduction in accident costs,
provided that the injurer chooses the socially optimal level of care.

The fact that the socially optimal solution requires that both parties exercise
optimal care will be crucial in the analysis that follows.

9. The ‘Cheapest Cost Avoider’

Before discussing and comparing the various liability rules in the case of
bilateral accidents we want to examine cases which exhibit properties of both
unilateral and bilateral accidents. This version can emerge when either the
injurer or the victim (or a third person) are able to prevent the accident. Note
the distinction: unlike in the case of unilateral accidents, it is now not only the
injurer, but also the victim who can prevent the accident. And unlike in the
case of bilateral accidents where typically both parties need to exercise care to
achieve the socially optimal and efficient outcome, it is now either the injurer
or the victim who has to take care to achieve the socially optimal result.

As Calabresi (1970) argues, in these cases, the person should be held liable
who could have prevented the accident with the least cost of taking care
(cheapest cost avoider). The idea is quite simple: We know that as long as
property rights are well-defined and there are no transaction costs, trade
between agents would result in an efficient allocation of resources when there
is an externality, a conclusion commonly known as the Coase Theorem (see
Coase, 1960). Furthermore, note that what is known as causation in tort law
can be reinterpreted as an externality in economics. An externality can be
defined as a cost that the action of a person imposes on others without their
consent. The prevention of an accident would therefore be undertaken by the
party who could do so with the least cost (cheapest cost avoider). However, this
solution will not be achieved because of prohibitive ex ante costs of bargaining
about who should be held liable for possible accident damages. In this case, the
courts should place the burden of covering the costs of the accident on the
individual who can avoid the accident at the lowest cost no matter whether it
is the injurer, the victim, or a third party.

10. Rule of No Liability

As before, if the injurer cannot be held liable for the harm she causes, she will
choose the lowest possible level of care, that is zero, to minimise her cost. This
may also lead the victim to exercise excessive care. As we have seen in the
previous section, this is clearly not optimal because accident costs will be
excessively high.

11. Negligence

Recall that the rule of negligence imposes the obligation to satisfy a legal
standard of care usually defined as due care. The injurer is therefore liable
unless he can prove that he has exercised due care. We now continue our
analysis by introducing, discussing, and comparing several forms of the
negligence rule (see for example Wittmann, 1986; Haddock and Curran, 1985).
Let us begin with the simplest form of negligence.

Simple Negligence
The properties of this rule are basically the same as in the unilateral case, that
is, the injurer is liable if and only if her level of precaution is below the legal
standard regardless of the precaution level exercised by the victim. Assume now
that the level of due care chosen by the courts equals the socially optimal level.
Injurers will therefore have an incentive to exercise due care in order to escape
liability. Hence, the victim faces the costs

c (y) + d (x*,y)                                  (10)

and will choose the level of care that minimises this expression. Setting the first
derivative with respect to y equal to zero we obtain equation (9), one of the two
optimality conditions in the bilateral case.

If the injurer expects that the self-interested victim will exercise due care,
the same arguments as in the unilateral case apply. The injurer faces the costs

c (x) + d (x,y*)                                   (11)

and will choose the level of care that minimises this expression. Again, setting
the first derivative with respect to x equal to zero we obtain equation (8), the
other optimality condition in the bilateral case.

Therefore, we can conclude that the simple negligence rule leads to socially
optimal levels of care. The outcome is a Nash equilibrium which can be
expected to emerge straightaway because a rationally self-interested person will
assume that another equally self-interested person has decided to exercise
efficient precaution and, that being so, it is reasonable for that person also to
exercise efficient precaution. Generally, a pair of strategies is said to be a Nash
equilibrium if player A’s choice is optimal given B’s choice, and player B’s
choice is optimal given A’s choice. It is standard in the literature to assume the
existence of a Nash equilibrium. However, there might be problems of
existence, even in the case of well-behaved functions (see, for example, Endres
and Querner, 1995). It is also standard to discuss bilateral accidents in the
context of a Nash framework (for a reference that points to alternative
approaches (see Endres, 1992). Finally, note that under the rule of simple
negligence there is no need to establish a legal standard of care for the victim.
This conclusion changes under the following rules.

Negligence with the Defence of Contributory Negligence
Under this rule, the injurer will be held liable if she does not take due care, and
if, in contrast to this, the victim does take due care. The injurer will not be held
liable if she either takes due care or if the victim does not take care. In other
words, in comparison to simple negligence, the injurer now has, apart from the
exercising of due care, an additional possibility to escape liability by showing
that the victim failed to take due care.

To see whether this rule leads to a socially optimal outcome, we can use the
same line of argument as before. If the injurer assumes that the victim takes due
care to avoid liability, she will also have an incentive to do so for the same
reason. This, in turn, leads the victim to take due care because she now has to
bear the total amount of damages. She can minimise these costs by taking due
care. Since the injurer is aware of this, it is reasonable for her to take due care
herself and so on. Again, we have a stable and unique equilibrium, and a
socially optimal result will be achieved.

Comparative Negligence Rule
The difference between this rule and the two previous ones is that, when both
parties are negligent, the accident costs are divided between them in proportion
to the extent of their negligence. One way of doing this is to calculate the ratio
of the differences between the due level of care and the actual level of care.
If the courts choose optimal levels of due care, then both the injurer and the
victim will exercise due care. The rationale is precisely the same as before.
Again, we can conclude that the outcome under this rule is socially optimal.
When comparing the various versions of the negligence rule we come to the
conclusion that none of these versions is more or less efficient than the others
(efficiency equivalence theorem, see Orr, 1991; Rubinfeld, 1987). They all lead
to socially optimal outcomes, provided that the courts set the legal standard of
precaution at the efficient level, because self-interested agents have an incentive
to choose the legal standard of care. The reason for this is, in essence, that
whenever one party exercises due care, then it is entirely upon the other party
to decide whether it alone will be held liable by failing to take due care.

However, as White (1989) argues, there is empirical evidence that, in contrast
to the equivalence theorem, contributory negligence provides better incentives
to avoid accidents.

An analysis of how these results change when relaxing and modifying some
of the underlying assumptions will be given later. First we will examine various
forms of strict liability.

12. Strict Liability

As in the previous section, there are several forms of the strict liability rule to
consider. We begin with the simplest form of strict liability.

Simple Strict Liability
In this case, the injurer has to bear the total amount of accident costs regardless
of the extent of her precaution. Conversely, the victim will be compensated for
all costs imposed on her which implies that the marginal benefit to the victim
of taking an additional unit of care is zero for any level of care. Thus, it is
optimal for the victim to choose a zero level of care because at zero level the
marginal cost of taking care equals zero, and her private optimality condition
is satisfied. Of course, optimality condition (9) is not met and the outcome is
not socially optimal because the marginal benefit of increasing the level of care
exceeds the marginal cost to the victim.

Strict Division of Losses
Under this liability rule, the injurer has to pay a fraction f of the accident costs.
Hence, the injurer faces the costs

c (x) + f . d (x,y)                                 (12)

and the victim faces the costs

c (y) + (1- f) . d (x,y)                        (13)

It is crucial to note that the size of the fraction is assumed to be independent
of their levels of care. Thus, the first order conditions are

c' (x) = - f . dx (x,y)                               (14)

and

c' (y) = - ( 1-f ) . dy (x,y)                           (15)

Comparing these optimality conditions with conditions (8) and (9) it is clear
that, at any level of care, the marginal benefit of taking care is less under strict
division. Since parties save only a fraction of the true reduction in accident
losses by taking care, they have too little incentive to exercise a socially optimal
level of care.

Strict Liability with the Defence of Contributory Negligence
Under this rule, the injurer is liable for the accident losses unless the victim's
level of care was less than her due level of care. It is straightforward to show
that under this rule the outcome is socially optimal, provided that the courts
choose the level of care for victims equal to the socially optimal level of care.
The rationale is the same as under the various versions of the negligence rule.
Since injurers will be liable for accident damages if victims take due care and
therefore will not bear the accident costs, injurers will exercise due care to
minimise accident costs. On the other hand, victims will exercise due care
because they do not want to be found contributorily negligent. Again, we obtain
a socially optimal Nash equilibrium as a result.

Strict Liability with the Defence of Relative Negligence
This rule is basically the same as the previous one with the following
difference: if the victim is found negligent because she failed to take due care,
she will have to bear only a fraction of her losses. If the fraction depends on the
victim's actual level of care relative to due care, if it is sufficiently large, and
if the courts choose the legal level of care equal to the socially optimal level of
care, then the outcome is socially efficient. The rationale is the same as before.

13. Relaxing Assumptions

Recall the first simplifying assumption that the court sets the level of due care
equal to the socially optimal level. In the section on unilateral accidents, we
conclude that under strict liability the courts need only determine the size of the
damage, whereas under negligence the courts must in addition calculate the
socially optimal level of due care, and they have to determine the level of care
actually taken in order to see whether the injurer was negligent or not.

In bilateral accidents, however, this result holds true only for the rule of
simple strict liability which, as we saw in the previous section, does not achieve
socially efficient results. Those forms of strict liability that lead to socially
optimal outcomes have the same requirements with respect to their ease of
application as the various rules of negligence. The only difference affecting the
ease of application of the two rules is that under strict liability the courts do not
need to determine the actual level of care of the injurer.

The second assumption concerns the equality between the legal sanction and
the damage actually caused. In the case of unilateral accidents we see that,
whenever damages are not perfectly compensatory, the potential injurer does
not have an efficient incentive to exercise the socially optimal level of care. In
the case of bilateral accidents, this result holds true only for, first, the potential
injurer, and second, under the rule of simple strict liability.

For instance, it is important to note that, under simple strict liability,
undercompensation would tend to create an incentive for the victim to exercise
precaution by creating some residual liability. This is also how insurance
companies deal with the problem of moral hazard. Since, however, the
incentive problem of the potential injurer remains unsolved,
undercompensation cannot lead to socially optimal results.

Also, we should note that, under the rules of strict liability with the defence
of contributory or relative negligence, equality between the legal sanction and
the harm does not matter as long as the sanction is sufficiently large so that the
private costs of the parties are minimised by conforming to the legal standard.
These are, of course, the same results as under the rules of negligence.

Finally, the third assumption eventually refers to the constant level of
activity. Recall that in the case of unilateral accidents the rule of strict liability
and the rule of negligence produced different results. Under negligence, the
injurer had no reason to consider the effect that her activity has on others and
would therefore choose too high a level of activity. Under strict liability, on the
other hand, the injurer internalises the total amount of social costs and
therefore reduces the activity level to the socially optimal level. The crucial
condition in order for any liability rule to lead to a socially efficient level of
activity is that the parties engaging in some activity must bear the total amount
of accident losses. Otherwise only a fraction of the activity’s costs are
internalised, and the level of activity will be too high. As a matter of fact,
though, it is impossible for both parties to bear the accident losses.

Therefore, results change quite drastically in the case of bilateral accidents
as compared to unilateral accidents. As Shavell (1987, p. 29) puts it, the reason,
in essence, is that for injurers to choose the correct level of activity they must
bear accident losses, but for victims to choose the correct level of activity they,
too, must bear accident losses. Yet, of course, injurers and victims cannot both
bear accident losses under a liability regime, but the problem can be nicely
solved by using Pigou taxes, which has led Baumol and Oates (1988) to prefer
a system of Pigou taxes to liability as a matter of principle.

As a result, in bilateral accidents no liability rule leads to socially optimal
levels of activity. This implies that the net utility of an activity can be negative,
as the following example illustrates. In bilateral accidents, an activity is socially
useful if the utility to the injurer less the precaution costs to both the injurer and
the victim less the costs of the accident is positive. Assume now that the utility
is 100, optimal precaution cost to the injurer is 40, optimal precaution cost to
the victim is 30, and the expected accident cost is 50. Obviously, the activity is
not socially useful because its net utility is negative. Note, however, that under
both the rule of negligence and the rule of strict liability the injurer will engage
in the activity. Under negligence, his private utility is 100 - 40 = 60, and under
strict liability, his private utility is 100 - 40 - 50 = 10. This is because, as noted
above, the injurer does not take into consideration the precaution cost of the
victim.

A theoretical possibility to achieve a socially optimal outcome would be to
establish the legal obligation for the injurer to bear her own precaution cost, the
accident cost, and also the precaution cost of the victim (see for example,
Rose-Ackerman, 1989).

14. Comparing Strict Liability and Negligence

Let us now summarise some of the main results of the previous sections. In the
case of unilateral accidents, both the rule of strict liability and the rule of
negligence achieve a socially optimal outcome, provided that courts set the
level of due care equal to the socially optimal level of care, that the legal
sanction equals the harm, and that the level of activity is constant. Relaxing
these assumptions provides further insights favouring the rule of strict liability.
Under strict liability, all the courts need to do is to determine the size of the
damage, whereas, under the negligence rule, the courts also need to determine
the level of due care as a legal standard for the socially optimal level, and they
have to determine the level of care actually taken in order to see whether the
injurer was negligent or not. These information requirements are difficult and
costly to acquire. Moreover, the average costs of resolving claims tend to be
higher under negligence.

A major drawback of the rule of strict liability in unilateral accidents,
though, emerges when we relax the second assumption. Whenever damages are
not perfectly compensatory, that is, compensation is below the level that would
make the victim indifferent between the case of no accident and that of an
accident with compensation, the potential injurer does not have an efficient
incentive to exercise the socially optimal level of care.

Another important advantage of the rule of strict liability emerges when
allowing for variable levels of activity. Under negligence, the injurer has no
reason to consider the effect that her activity has on others because she can
escape liability by taking due care. Thus, the injurer will choose too high a level
of activity. Under strict liability, the injurer internalises the total amount of
social costs and reduces the level of activity to the socially optimal level.

So far the results suggest that the rule of strict liability achieves socially
optimal results provided that damages are set at the perfectly compensatory
level. What happens, though, when an accident is bilateral requiring both
parties to take precaution against accidents? Now the efficiency of the rule of
strict liability becomes problematic because, even though strict liability may at
first create the right incentives for potential injurers, it will create an incentive
problem for potential victims and will in return lead injurers to exercise
suboptimal care. This can be seen by noting that strict liability is the mirror
image of no liability. One rule fails to create incentives for precaution by the
victim, the other rule fails to create incentives for precaution by the injurer.

Therefore, our analysis suggests that in the case of bilateral accidents we
should apply either one of the negligence rules or the rules of strict liability
with the defence of contributory or relative negligence. All of them lead to
socially optimal outcomes, provided that the courts set the legal standard of
precaution at the efficient level, because self-interested agents have an incentive
to choose the legal standard of care.

This conclusion is reinforced when allowing for inequality between the legal
sanction and the damage actually caused. Under any of the negligence rules and
under the rules of strict liability with the defence of contributory or relative
negligence, equality between legal sanction and harm does not matter as long
as the sanction is sufficiently large so that the private costs of the parties are
minimised by conforming to the legal standard.

When allowing for various levels of activity, finally, we concluded that no
liability rule at all leads to socially optimal levels of activity. This conclusion
again confirms that in the case of bilateral accidents the negligence rules or the
rules of strict liability with the defence of contributory or relative negligence are
equivalent.

15. Liability and Contracts

In the previous sections of this article, we concentrated on situations where
parties do not enter into contractual relationships because of high transaction
costs such as the costs of bargaining. The notion of transaction costs, however,
is crucial for the analysis of liability and deterrence. Recall the basic insight of
the Coase Theorem which says that when parties can bargain with each other
in order to settle their disagreements, their behaviour will be efficient
regardless of the underlying rule of law. This implies that, whenever
transaction costs are low, people enter into contractual relationships and the
rules of contract law apply. Conversely, whenever transaction costs are high,
people do not enter into contractual relationships and the rules of tort apply.
There are a few areas, however, where tort law and contract law seem to merge,
such as ‘products liability’ and ‘implicit contracts’.

We now examine the allocative effects of various forms of liability rules in
those cases where parties have entered into contractual relationships. We
assume profit-maximising behaviour of firms and perfect competition. That is,
the price of a product equals total unit costs including liability costs. It is also
assumed that rational consumers buy a product only if the utility of the product
exceeds its perceived price, that is, the price actually charged plus expected
accident costs not covered by liability payments.

If the customers’ knowledge of risk is perfect, firms will take optimal care
under any liability rule, even under the rule of no liability. This is because
customers would immediately notice whether firms took less than optimal care
or not. Thus, the perceived price of the product including expected losses would
be higher than the product price of firms exercising optimal care. The potential
loss of customers forces firms to exercise optimal care regardless of the
underlying rule of liability. Also, the level of consumption is optimal because
the price of the product as compared by customers with their utility includes
expected accident losses.

These results change, however, once we assume that customers have
imperfect knowledge of the risk associated with a product. If customers cannot
determine product risks, they will not reward firms for making products safer.
Therefore, firms do not have any incentive to take optimal care unless there is
some rule of liability. Moreover, under the rule of no liability and under the
negligence rule, the level of consumption will not be optimal. Only under strict
liability does the misperception of risks not matter, because customers are fully
compensated for their losses anyway, and market prices reflect the true risk of
accident losses. In all other cases, market prices, and thus consumption, are
either too high or too low.

16. Multiple Tortfeasors

We now turn to the case of multiple tortfeasors. Landes and Posner (1980) were
the first authors to study the incentives to take care in the case of multiple
tortfeasors, yet restricting their attention to negligence. For a more general
discussion see Kornhauser (1989).

We will consider situations where there is more than one injurer affecting
the probability of accident losses. Furthermore, we need to distinguish between
cases where injurers act independently with the victim’s harm being indivisible,
and cases where injurers act together (in concert) to cause the victim’s harm.

Under strict liability, injurers who act independently will not always act
optimally in equilibrium. Assuming that each injurer is liable for a fixed
fraction of losses only, any increase in the injurer’s exercise of care diminishes
her liability by only a fraction of the reduction in expected losses which induces
the injurer to take a level of care clearly below the optimal level of care. When
injurers act together, however, their minimisation problem obviously turns into
a situation exactly equivalent to the one where there is only a single injurer.
Thus, under strict liability and if injurers act in concert, injurers take optimal
care. Note that this result is not obtained if injurers pay a fraction identical to
their probability of causation.

Under the rule of negligence, we obtain different results. Injurers will now
act optimally (they will take due care) in equilibrium both in cases where they
act independently and in cases where they act together, provided that the due
level of care is optimally determined, of course. Again, the analysis is
straightforward and is precisely analogous to the previous analysis of situations
of bilateral accidents. If one injurer alone fails to take due care, she will be held
liable for the total amount of accident losses. A rationally self-interested injurer
will now assume that another equally self-interested injurer has decided to
exercise efficient precaution and, that being so, it is reasonable for that injurer
also to exercise efficient precaution. Note that this outcome is unique and
stable, and that it also holds true if injurers act in concert.

17. Risk Aversion, Liability Law and Insurance

So far we have constrained our analysis to the case of risk-neutral parties. We
will now extend the analysis by allowing for risk-averse individuals, and we
will discuss the interaction between risk aversion, liability law and insurance.

Risk aversion depends on the concavity of the utility function of wealth, that
is the rate at which utility losses grow with losses of wealth. The concavity of
the utility function implies that a $1,000 loss will cause greater harm to a
person with assets of $10,000 than to a person with assets of $100,000. The
shifting of risks from the more to the less risk-averse will raise social welfare
given that social welfare is the sum of the individuals’ expected utilities. Social
welfare will also increase if risks are shared among risk-averse parties thereby
reducing the potential extent of the losses that each party might suffer.

One way of shifting and sharing risks is by insurance. Insurance can be
described as a private system of liability law in which contracts determine the
allocation of risks. In the theory of insurance, a distinction has to be made
between the cases in which the insured persons can influence risks and the
cases in which they cannot. In the situations where the probability of damage
cannot be affected by the actions taken by the insured persons, an insurance
policy that offers complete coverage is socially optimal. If the insured, however,
can influence risks, complete reimbursement creates the problem of moral
hazard: the individual has no incentive to take care at all.

We now turn to the discussion of the interaction between risk aversion,
liability law and insurance. Under the assumption that injurers are subject to
liability, but that there is no insurance, the comparison of liability rules shows
that the rule of negligence is preferable when victims are less risk-averse than
injurers, and the rule of strict liability is preferable when the reverse holds true.
The rationale behind these results is that under the negligence rule injurers will
not bear risk when taking due care, whereas victims will bear their losses.
Thus, social welfare will be lower if victims are more risk-averse than injurers.
The outcome is quite different under the rule of strict liability. Injurers will bear
risk regardless of the level of care they take. If injurers are more risk-averse
than victims social welfare will decrease.

Under the assumption that insurance is available, both the rule of
negligence and the rule of strict liability yield socially optimal outcomes
because individuals, if risk-averse, can obtain liability insurance. The more
efficient rule is the one that costs less. Assuming, for instance, that consumers
can insure more cheaply than manufacturers strict product liability should be
limited.

18. Liability and Uncertain Legal Standards

In the real world, legal standards are frequently uncertain. Factors leading to
uncertainty are, amongst others, courts’ errors in determining due levels of
care, courts’ errors in assessing a party’s true level of care, and parties’
inability to control their momentary level of care. Craswell and Calfee (1984)
focus on this issue. These sources of uncertainty change the deterrent impact
of legal rules by creating two opposing effects. The first effect can give even
risk-neutral parties an incentive to overcomply, that is injurers take more
precaution than is prescribed by the legal standard of care. Overcompliance
enables potential injurers to increase the chance that they will not be held
responsible for the social costs of their behaviour, thus giving themselves a
margin of error to be sure that they avoid liability. However, uncertainty also
reduces incentives to comply by creating a positive chance that someone who
violates the legal standard will not be held liable.

In order to determine whether the net incentives are to undercomply or to
overcomply we need to know the relative strength of these two effects. It is
difficult, however, to identify the exact relationship between a defendant’s
behaviour and the actual probability of her being held liable. In general,
uncertainty will tend to lead parties to take more than due care as long as there
is a positive probability of underassessment of their levels of care and
uncertainty is relatively small. If there is, on the other hand, a high enough
chance of overassessment of care and if the uncertainty generated by the legal
system is relatively broad, parties are likely to take less than due care. More
specifically, under the two seemingly plausible assumptions that uncertainty is
distributed normally around the optimal level of compliance and that the
distribution of errors is not too dispersed, the result under any liability standard
will be too much precaution. Note, however, that overprecaution is less under
comparative negligence than it is under any other form of the negligence rule
because under comparative negligence losses are shared between the two parties
rather than being concentrated on one party.

This possible effect of an uncertain precautionary standard cannot, of
course, arise under a system of strict liability.

The picture changes drastically, however, if an uncertain legal standard is
combined with a total damage compensation which is higher than the total loss
of society. This possibility arises especially in the case of economic losses.
Wrongful behaviour can lead to economic losses for some parties and, at the
same time, to economic gains for other parties that are such that the total social
losses are only a small fraction of the economic losses. Thus, a system of strict
liability results in overcompensation and overdeterrence. Under a negligence
rule, overcompensation does not distort the incentives if the standard of due
care is precisely defined as the tortfeasor can avoid excessive cost by complying
with the legal standard. If, however, the standard is not precise, negligence will
almost certainly lead to overcompliance because there is an extra pay-off
decreasing the probability of being held liable. In some legal orders, this
problem is solved by negligence rules which restrict compensation to cases of
obvious negligence or to wilful behaviour such as in § 826 of the German Civil
Code. This makes the negligence standard more precise and thus avoids
overdeterrence.


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