Part D-II
The Economics of Tort Law
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Objectives
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Bilateral precaution
No liability/strict liability rules under
bilateral precaution
The problem of efficient tort rules under
bilateral precaution
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Recall that we considered
two classes of risk
A risk situation is one of unilateral precaution if only
the potential victim or only the potential injurer
can take precaution but not both.
A risk situation is one of bilateral precaution if both
the potential victim and the potential injurer can
take precaution.
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Unilateral Precaution
Recall
The efficient tort rule for risks characterized by
unilateral precaution is:
- if only the potential victim can take precaution, then no
liability
- if only the potential injurer can take precaution, then strict
liability with perfect damages
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Bilateral Precaution
There are many risk situations which are not unilateral risk
situations
For many types of risk both the potential victim and the
potential injurer can take precautions
- driving safely/seatbelts
- driving safely/bicycle helmets
- walking (not running) over an icy
sidewalk
- taking medication as directed
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Bilateral Precaution
In such situations, neither the rule of no liability nor the rule
of strict liability will lead to the ‘efficient’ level of precaution
being taken.
Both the potential injurer and the potential victim should be
taking precaution – they share control over the risk.
But the rules of no liability and strict liability/ perfect damages
lead to only the potential victim or only the potential injurer
taking precaution.
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Bilateral Precaution
NOTE: The potential victim’s precaution is different from
the potential injurer’s precaution. They are essentially
different activities.
Important point Getting the potential injurer (victim) to
take more precaution when the potential victim (injurer)
takes too little precaution will not be efficient.
One agent cannot generally compensate for the shortfall of
the other agent (not in an efficient manner)
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REMINDER: When we say ‘take
precaution’ we mean do something (or
not do something) that results in a
decrease in the probability of an
accident occurring (lower the risk of an
accident).
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Recall the social costs of accidents can be expressed as:
SC = wv xv + wi xi + p(xv, xi)A
Under unilateral precaution:
If only the potential victim can control risk, then
Δp(xv, xi)/Δxi = 0 we wrote p(xv, xi=0) = p(xv)
If only the potential injurer can control risk, then
Δp(xv, xi)/Δxv = 0
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we wrote p(xv=0, xi) = p(xi)
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The change in the probability of an
accident as the amount of precaution
changes Δp(xv, xi)/Δxv
p(xv, xi)
p1(xv, xi)
Δp(xv, xi)
p2(xv, xi)
Δxv
0
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xv1
p(xv , xi)
xv2
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x= xv
Precaution
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But under bilateral precaution:
Δp(xv, xi)/Δxi < 0
and
Δp(xv, xi)/Δxv < 0
Note: the potential victim and potential injurer control
different aspects of the risk (xv and xi are generally
different types of expenditures, actions, etc.)
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Will a rule of no liability be efficient if the risk requires
bilateral precaution?
No, because no liability causes the potential injurer to
completely externalize the cost of harm and therefore take
no precaution.
Will a rule of strict liability/perfect damages be efficient if the
risk requires bilateral precaution?
No, because strict liability/perfect damages causes the
potential victim to completely externalize the cost of harm
and therefore take no precaution.
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If both the potential injurer and the potential victim control
the risk, efficiency will require that both of them take
precaution.
How much precaution should each take?
That depends on the nature of the risk and the types
and costs of precaution available.
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The answer to the previously question will differ in each risk
situation (for each type of potential accident)
We want a general rule that will ensure that the potential
victim and the potential injurer will each take the efficient
amount of precaution for any given type of potential
accident
Does such a legal rule exist?
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What is the efficient amount of precaution for each agent?
SC = wv xv + wi xi + p(xv, xi)A
If we want to minimize the social costs of accidents with respect to
both xv and xi our friends in mathematics would say:
- take the derivative of SC with respect to xv and set it equal to zero:
wv + Δp(xv, xi)/Δxv A = 0
or
And
wv = - Δp(xv, xi)/Δxv A
1)
- take the derivative of SC with respect to xi and set it equal to zero:
wi + Δp(xv, xi)/Δxi A = 0
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or
wi = - Δp(xv, xi)/Δxi A
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2)
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What is the efficient amount of precaution for each agent?
Conclusion #1
In order to minimize the expected social costs of accidents
both the potential victim and the potential injurer must
‘purchase’ an amount of precaution such that the marginal
cost of precaution (w) is just equal to the decrease in the
expected cost of harm from the expenditure (- Δp(xv,
xi)/Δx A) for each of them.
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What is the efficient amount of precaution for each agent?
We can divide expression 1) by expression 2) and get:
wv / wi = [Δp(xv, xi)/Δxv] / [Δp(xv, xi)/Δxi]
or
[Δp(xv, xi)/Δxv] / wv = [Δp(xv, xi)/Δxi] / wi
Conclusion #2
The ratio of the prices of a unit of precaution taken by the
potential victim and that taken by the potential injurer
must equal the inverse of the ratio of marginal declines in
the probability of an accident occurring resulting from an
additional unit of xv and xi.
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What is the efficient amount of precaution for each agent?
Conclusion to this point:
The efficient level of precaution for the potential victim and
potential injurer will depend on the price of each type of
precaution and the nature of the impact of each type of
precaution on the probability of an accident
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A little bit of intuition
Efficiency requires that:
to the extent that the cost of precaution to the potential victim
is relatively inexpensive, or the precaution taken by the
potential victim is relatively effective, the potential victim
should take relatively more precaution.
to the extent that the cost of precaution to the potential
injurer is relatively inexpensive, or the precaution taken by
the potential injurer is relatively effective, the potential
injurer should take relatively more precaution.
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Such a general rule will need to account for
wv and wi
- how much each type of precaution cost
and
Δp(xv, xi)/Δxi and
Δp(xv, xi)/Δxv
- the marginal effect of the alternative types of
precaution on the probability of an accident
Does such a general rule exist?
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Again, will a rule of no liability be efficient if the risk requires
bilateral precaution?
No, because no liability causes the potential injurer to
completely externalize the cost of harm and therefore take
no precaution.
Will a rule of strict liability/perfect damages be efficient if the
risk requires bilateral precaution?
No, because strict liability/perfect damages causes the
potential victim to completely externalize the cost of harm
and therefore take no precaution.
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We need both the potential victim and potential injurer to
internalize the full cost of harm
p(xv, xi)A
When they determine how much precaution to take
xv and xi
So no liability and strict liability/perfect damages will not be
efficient tort rules – they will create the wrong incentives
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An intuitive rule that won’t work
Since both the potential injurer and the potential victim
can take precaution, why not just set damages at
50% of harm for each?
This means that the potential victim and the potential injurer
will each bear 50% of the cost of harm.
Under this rule of liability/damages
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D = 0.5 A
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What is the cost of accidents to the potential victim?
wv xv + p(xv, xi)(0.5A)
since D = 0.5 A
What is the optimal amount of precaution for the potential
victim to take? What will be in the potential victim’s own
self-interest? Keep ‘buying’ precaution until,
wv = - Δ p(xv, xi)/Δxv (0.5A)
Potential victim’s
marginal cost of
precaution
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= 0.5 of the potential victim’s
marginal benefit
from precaution
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What is the cost of accidents to the potential injurer?
wi xi + p(xv, xi)(0.5A) since D = 0.5 A
What is the optimal amount of precaution for the potential
injurer to take? What will be in the potential injurer’s own
self-interest. Keep ‘buying’ precaution until,
wi = - Δ p(xv, xi)/Δxi (0.5A)
Potential injurer’s = 0.5 of the potential injurer’s
marginal cost of
marginal benefit
precaution
from precaution
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What’s wrong with this outcome?
The potential victim and the potential injurer are each
minimizing their private costs of accidents (the portion of
the cost that they are responsible for) but they are
ignoring 50% of the cost of harm – the 50% for which they
are not liable.
Each of them is only internalizing 50% of the expected cost of
harm – they will only make half an effort at precaution
A simple 50%/50% rule (or any other arbitrary split of the
liability) results in each agent only internalizing their
assigned share of the cost of harm.
There will be too little precaution taken by both the potential
victim and the potential injurer
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We have a real problem.
How can we encourage (provide the appropriate incentives to)
both the potential injurer and the potential victim to internalize
the total cost of harm (A) when they decide on the appropriate
level of precaution?
Simply dividing up the cost of harm will not work.
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