The left-hand side of Eq. 9 represents the marginal cost of an increase in L. It captures the increase in the present value of expected litigation costs when L is increased by one period,
where p1 2 H x
s
1 qH x
s
is the probability of an accident, and [1 2 Fc
v
] gL is the number of new cases filed in the event of an accident. The right-hand side captures the
marginal benefit of an increase in L in terms of increased deterrence. The term x
s
L represents the increase in the threshold for care when L is raised, which is weighted by h x
s
, the fraction of injurers with cost of care equal to x
s
. The bracketed term represents the net savings in social costs when one more injurer takes care, where this term is positive due to
the general underdeterrence under strict liability. According to Eq. 9, the optimal statute length balances the increased litigation costs from a longer statute against the increased
deterrence benefits.
4. Negligence
Negligence differs from strict liability in that a victim will not recover against the injurer, even if she files in a timely manner, if the injurer took due care. Following Hylton 1990, we define
due care by the Hand Rule,
6
which, in the current context, says that an injurer is negligent if he failed to take care and x , p 2 q ED [ x
H
; that is, if his cost of care is less than the social benefit of care x
H
in a world of zero litigation costs.
7
The court can apply this rule because we assumed that it can observe the injurer’s care choice and cost of care after the fact.
Victims, however, cannot observe injurers’ costs of care, nor can they observe whether a given injurer has taken care at the time that they make their filing decision. Thus, they can
at best calculate the probability that an injurer will be found negligent, given that an accident has occurred. Let this probability be w, which we will define below. Thus, victims for whom
wD c
v
and t L will file suit under negligence. The probability of a suit, given that an accident occurs, is therefore gt[1 2 Fc
v
w] for any t L, and zero thereafter. Given the above, note that an injurer with x . x
H
will never take care because he will never be judged negligent by the court. Thus, only injurers with x x
H
are “potentially negligent” in the sense that they will be judged negligent if they failed to take care and the
victim files suit following an accident. A potentially negligent injurer who takes care incurs expected costs of
x 1 q 1 2 F~c
v
w
E
L
c
i
e
2rt
g~tdt .
10 Thus, he incurs only the cost of care plus his expected litigation costs, given that he will be
found non-negligent at trial. In contrast, when a potentially negligent injurer does not take care, his expected costs are
6
See U.S. v. Carroll Towing, 159 F.2d 169 2d Cir. 1947.
7
The results would be qualitatively the same if the due standard were based on the optimal standard in the presence of litigation costs. See note 9 infra.
387 T.J. Miceli International Review of Law and Economics 20 2000 383–394
pG~L
E
c
v
w `
DdF~D 1 1 2 F~c
v
w
E
L
c
i
e
2rt
g~tdt ,
11 which includes expected liability plus litigation costs. Combining Eq. 10 and Eq. 11 gives
the condition for the injurer to take care:
x pG~L
E
c
v
w `
DdF~D 1 ~ p 2 q 1 2 F~c
v
w
E
L
c
i
e
2rt
g~tdt ; x
N
~L, 12
where the right-hand side is the highest cost injurer who chooses to take care under negligence.
We can now calculate the equilibrium value of w, which, recall, is the probability that a given injurer will be found negligent, given that an accident has occurred. Since victims
correctly anticipate the likelihood of a negligent verdict, we can use Bayes’ Rule to calculate
w~L 5 pH~ x
H
2 H~ x
N
~L p
1 2 H~ x
N
~L 1 qH~ x
N
~L .
13 The numerator is the probability of an accident when the injurer does not take care times the
probability that the injurer is both potentially negligent and fails to take care, while the denominator is the overall probability of an accident. Note that w is positive if and only if
x
H
. x
N
L, implying that there are some injurers who are potentially negligent and fail to take care. Although this need not be true in general, it must be true in a negligence
equilibrium.
8
Assuming that an equilibrium exists, we can totally differentiate Eq. 12 and Eq. 13 and solve simultaneously to find the impact of varying L on the equilibrium [Eq. 14]:
x
N
L
. 0,
w
L
, 0.
14 Intuitively, an increase in the statute of limitations increases the expected liability of injurers,
thereby causing more injurers to take care x
N
L increases, but because more injurers take care, the probability that a given injurer will be found negligent by the court wL
decreases. We now turn to social costs. When the injurer takes care, expected social costs are given by
x 1 qE~D 1 ~ 1 2 F~c
v
w
E
L
~c
i
1 c
v
e
2rt
g~tdt ,
15
8
The intuition is as follows. If all potentially negligent injurers take care, then w50 and no victims will file suit. But then injurers have no incentive to take care since they face no threat of a suit. For more details, see
Ordover 1978 and Hylton 1990. 388
T.J. Miceli International Review of Law and Economics 20 2000 383–394
which is equivalent to 5 except that c
v
w replaces c
v
as the lowest value of D that results in a suit. When the injurer does not take care, expected social costs are
pE~D 1 1 2 F~c
v
w
E
L
~c
i
1 c
v
e
2rt
g~tdt ,
16 which similarly differs from Eq. 6. Combining Eq. 15 and Eq. 16 yields the condition
for care to be socially desirable [Eq. 17]:
x ~ p 2 qE~D 1 1 2 F~c
v
w
E
L
~c
i
1 c
v
e
2rt
g~tdt ; x
N
~L, 17
where x
N
L is the highest cost injurer for whom care is socially desirable under negli- gence. Note that x
N
L . x
H
due to the absence of litigation costs from x
H
. Further, since x
H
. x
N
L for existence of a negligence equilibrium, it follows that x
N
L . x
N
L, or that negligence, like strict liability, underdeters in equilibrium Hylton, 1990.
9
As above, the optimal statute of limitations under negligence minimizes expected social costs, which is given by Eq. 15 multiplied by the fraction of injurers taking care, H x
N
L, plus Eq. 16 multiplied by the fraction not taking care, 1 2 H x
N
L. After rearranging, this becomes
SC
N
~L 5 pE~D 1 1 2 F~c
v
w
E
L
~c
i
1 c
v
e
2rt
g~tdt 2 H~ x
N
~L~ p 2 q
3 E~D 1 1 2 F~c
v
w
E
L
~c
i
1 c
v
e
2rt
g~tdt 1
E
x
N
~L
xdH~ x .
18 where, recall, w is a function of L. Minimization of Eq. 18 yields the first-order condition
1 2 F~c
v
we
2rL
~c
i
1 c
v
g~L p~1 2 H~ x
N
1 qH~ x
N
5
S
x
N
L
D
h~ x
N
3 x
N
~L 2 x
N
~L 2
S
w
L
D
f~c
v
w~c
v
w
2
E
L
~c
i
1 c
v
e
2rt
g~tdt 3
p~1 2 H~ x
N
1 qH~ x
N
. 19
9
The results of the analysis would therefore be unaffected if the due standard applied by the court is set at x
N
rather than at x
H
. However, use of x
H
greatly simplifies the model because x
H
is independent of L, whereas x
N
is not. Moreover, there is no reason to believe that courts use x
N
rather than x
H
as the due standard of care. 389
T.J. Miceli International Review of Law and Economics 20 2000 383–394
Note that the first two terms of this condition resemble the two terms in Eq. 9 and have the same interpretation. Specifically, the term on the left-hand side of Eq. 19 is the
marginal cost of a longer statute length in terms of increased litigation costs, while the first term on the right-hand side is the marginal deterrence benefits of an increased statute
length. As was true under strict liability, greater deterrence is socially desirable because in equilibrium, negligence underdeters as captured by the fact that x
N
L 2 x
N
L . 0. What is different here compared to strict liability is the second term on the right-hand side
of Eq. 19, which is positive given that wL , 0. This term captures an additional marginal benefit of increasing the statute length under negligence in the form of fewer
lawsuits being filed in each period up to t 5 L. Intuitively, an increase in L lowers the probability that any given injurer will be judged negligent given that wL , 0, thereby
making lawsuits less profitable for victims. Note that this effect was absent under strict liability because that rule did not require victims to prove negligence by injurers as a
condition for recovery.
The extra marginal benefit term in Eq. 19 suggests that the optimal statute length should be longer under negligence as compared to strict liability. This result cannot be established
definitively because a comparison of the corresponding terms in Eq. 9 and Eq. 19 for any L
is ambiguous. However, if these common effects are roughly offsetting, one would expect that the additional term in Eq. 19 would dominate, resulting in a longer statute length under
negligence.
5. Applications of the analysis
