Econ 522 – Lecture 16 (March 26 2009)
Tuesday, we began tort law with an experiment (DISCUSS)
After that, we…
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Defined the three elements of a tort under the traditional theory
o harm
o causation
o breach of duty (not always required)
Defined a strict liability rule as one which assigns liability based only on harm
and causation
And a negligence rule as one which requires all three elements
o That is, under strict liability, you’re responsible for any damage you do
o Under negligence, you’re responsible for any damage you do if you were
being careless (if you breached the duty of due care)
Today, we move on to an economic model of torts.
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Obviously, the more carefully I drive, the less likely I am to hit you
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If transaction costs are low, we can negotiate ahead of time, not for my right to hit
you, but for how carefully I’ll drive
o If it’s efficient for me to drive a little more carefully, and therefore be a
little less likely to hit you, we can negotiate that
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Obviously, this doesn’t work in practice; too many drivers, and too hard to
“commit” to the correct level of care
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Instead, what I expect will happen to me in the event I hit you, will affect how
carefully I drive
o that is, tort law creates incentives, and I will decide on my behavior as a
response
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As we said earlier, the essence of tort law is to use liability to get injurers to
internalize the externalities their behaviors cause.
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Ssuppose there is some type of accident that may or may not happen
 I may run into you in my car
 A manufacturer may accidentally use lead paint in its toys, etc
For simplicity, we will focus on the case of unilateral harm
 that is, there is only one victim
 (not the case with car accidents where both parties get hurt)
There is also some amount of precaution that can be taken that makes the accident less
likely.
Let
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x denote the level of precaution
w the cost of each incremental unit of precaution (could be money, time,
inconvenience)
p(x) the probability an accident occurs, given that level of precaution
o so p(x) is decreasing in x – more precaution = fewer accidents
A be the cost of an accident
o borne by victim
Then the cost of precaution is wx, and the expected cost of accidents is p(x) A
We can graph these against x, the level of precaution:
wx
p(x) A
precaution
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The total social cost due to this type of accident is the expected cost of accidents,
plus the resources spent in prevention:
Social Cost = wx + p(x) A
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So the efficient level of precaution will be the level of precaution that minimizes
this.
o (Add social cost to the graph)
wx + p(x)A
wx
p(x) A
precaution
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Graphically: we’re interested in the lowest point on the curve wx + p(x) A
o where total social costs are minimized
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Calculus: to minimize wx + p(x) A, we take the derivative, and find
w + p’(x)A = 0
or at the efficient level of precaution, x*,
w = – p’(x*) A
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LHS is marginal social cost of precaution
RHS is marginal social benefit
optimal level sets marginal cost = marginal benefit
Under reasonable assumptions…
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When x < x*, -p’(x) A > w; the marginal social benefit of more precaution is
bigger than its cost, and so more precaution is better.
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When x > x*, -p’(x) A < w; the marginal social benefit of more precaution is less
than its cost, and so less precaution would be optimal.
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Note that we haven’t yet specified who is taking this precaution
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In many cases, it is mainly the injurer who can take precautions to reduce the
likelihood of accidents
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In some cases, the victim can also take precautions
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The book gives a bunch of examples where both the injurer and the victim has
some influence on the likelihood of an accident:
Accident
Faulty electrical wiring
causes house fire
Moving car hits parked car
Car hits pedestrian
Software fails
Exploding coke bottles
Medicine causes side
effects
Injurer’s precaution
Manufacture wiring more
carefully
Drive more safely
Drive more safety
Better design of software
Improve quality control
Improve warning label
Victim’s precaution
Fireproof the house
Park car in safer location
Walk more safely
Back up data at risk*
Handle bottles carefully
Study warning
level/interactions carefully
(* This one doesn’t really fit their setup, since it really lowers the cost of each accident,
not the probability of an accident occurring)
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For now, we will focus on the case of unilateral precaution
o that is, just one party is in a position to reduce the likelihood of an
accident
o (but it could be either party)
o Under certain assumptions, what we say will generalize to bilateral
precaution – when both parties affect the likelihood of accidents
o But the bilateral case is harder, so for now, we’ll stick to unilateral
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Rule 1: No Liability
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First, we consider a world without lawsuits, where nobody is liable for any harms
that they cause accidentally
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Suppose first that it’s the victim who can take actions to prevent the accident
o say, a bicyclist who could wear reflective clothing and use a light when
riding at night, so he’s more visible to drivers
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x is the level of precaution taken by the victim, and p(x) the probability of an
accident
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If there is no liability, the victim incurs the full cost of the accidents, A
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So the victim chooses a precaution level to minimize
w x + p(x) A
which leads him to a level of precaution xv* which solves
w = - p’(x) A
(again, LHS is his marginal cost of more precaution, the RHS is his marginal
private benefit)
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But this is exactly the efficient level of precaution from before
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So when it is only the victim who can prevent accidents, a rule of no liability
leads to efficiency
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This makes sense: since the victim bears the cost of accidents, he gets the full
benefit from taking precaution; he also pays the full cost of it; so there is no
externality caused by the level of precaution, and he sets it efficiently
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But on the other hand, suppose it is the injurer whose actions determine how
likely accidents are
o for example, x can be a measure of how carefully you drive
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Under a system of no liability, the injurer doesn’t face any costs from accidents he
causes
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So he simply tries to minimize wx
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Which means when there is no liability, the injurer has no incentive to take costly
precautions, so he sets x = 0, which is lower than the social optimum.
So a rule of no liability leads the injurer to select an inefficiently low level of
precaution.
We can put these two results into a table:
Legal Rule
No liability
Strict liability
Victim’s Precaution
Efficient
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Injurer’s Precaution
Zero
Next, we consider Rule 2: Strict Liability
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Suppose we are in a world with strict liability, where in the event of an accident,
the injurer will have to pay damages D to the victim
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And suppose that compensation is perfect – D = A, so the damages exactly
compensate the victim for the harm.
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Go back to the example of reflective clothing
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Now the bicyclist knows that if he’s in an accident, he’ll incur harm of A and
receive damages of D, so now the costs he faces are
w x + p(x) (A – D) = wx
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So the cyclist minimizes this by setting x = 0
o Under strict liability, the victim doesn’t bear the cost of accidents, so he
has no reason to take any precaution
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Is this efficient? No. The total social cost of accidents is
wx + p(x) A
the transfer of money from injurer to victim is just a transfer
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So it would be efficient to set a higher level of precaution.
So a strict liability rule leads the victim to select an inefficiently low level of
precaution.
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But on the other hand, if it’s the injurer who affects the probability of accidents,
strict liability ends up working pretty well
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The injurer knows if there’s an accident, he’ll have to pay damages of D, so he
minimizes
wx + p(x) D
and with D = A, this is
wx + p(x) A
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So he’s facing the same problem as minimizing the total social cost of accidents –
so he chooses x efficiently!
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(This is because, under strict liability, the victim is actually indifferent between
accident and no accident – so the injurer’s actions cause no externality, so he
chooses efficiently.)
So a strict liability rule leads the injurer to take efficient precaution.
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And we can update our table:
Legal Rule
No liability
Strict liability
Victim’s Precaution
Efficient
Zero
Injurer’s Precaution
Zero
Efficient
That’s what happens when there’s only one party that can take precautions to prevent an
accident; which is referred to as unilateral precaution
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Our results so far suggest that when only the victim is able to take precautions to
prevent the accident, a rule of no liability is preferable
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And when only the injurer is able to take precautions, a rule of strict liability is
preferable.
o (This is exactly analogous to the problem we saw in contract law, of
allocating a risk to the lowest-cost avoider
o When one party – in this case, victim or injurer – can take precautions and
the other cannot, that first party is the low-cost avoider
o Making them bear the cost of the accident leads to efficient unilateral
precaution.)
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However, there are lots of cases of bilateral precaution – situations where both
parties have the possibility of precaution
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In that case, the probability of an accident is a function of both parties’ precaution
levels, and the social cost of accidents is
SC = wv xv + wi xi + p(xv, xi) A
And in that case, things get more complicated.
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(You’ll see an example of this on the homework.)
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With contracts, we saw that there was no breach remedy that set efficient
incentives for both the promisor and the promisee – the paradox of
compensation
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Here, we find the same thing: a rule that sets the correct incentive for injurer
precaution leads to too little victim precaution, and vice versa
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However, in tort law, there is a trick
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We already defined a negligence rule, under which the injurer is liable for harm
only if he did not take certain precautions
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That is, in tort law, we can make damages depend not only on whether an
accident occurred, but also on the level of precaution that the parties took ahead
of time
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This may allow us to get both incentives right.
Rule 3: Negligence Rule
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A negligence rule says that the injurer is liable for damages if his precaution level
was below the legal standard of care, x~
o So for x < x~, damages would be D = A
o For x >= x~, damages would be D = 0
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If we go back to the graphs we drew earlier, then, the total expected cost to the
injurer (from both precaution and expected damages) will be
wx + p(x) A
for x < x~, and just wx for x >= x~, since when x >= x~, the injurer is not liable
for damages.
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How this actually looks will depend on how x~, the legal standard for precaution,
relates to x*, the efficient level of precaution
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For now, let’s assume they’re equal, that is, x~ = x*
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The dark-shaded curve is the injurer’s expected private costs under a liability rule,
when x~ = x*:
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wx + p(x) A
wx
x~ = x*
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precaution
At x < x*, we know that wx + p(x)A is decreasing; and so the injurer’s expected
costs are decreasing
Similarly, we know that wx is increasing, so above x*, the injurer’s expected
costs, which are just wx, are increasing
So expected costs are minimized by setting x = x*, the efficient level.
So a negligence rule, with a legal standard of care x~ equal to the efficient level x*,
leads to an efficient level of injurer precaution.
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What about the victim’s incentives?
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The victim knows that under a negligence rule, the injurer will take precaution x*;
and therefore, if an accident occurs, the injurer will not be liable
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So now the victim is facing the full cost of any accident which occurs; which
means that the victim also takes the efficient level of precaution.
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So now we’ve found a solution to the paradox of compensation
A negligence rule, combined with an efficient legal standard for care, leads to
efficient precaution by both injurer and victim.
Which is pretty cool.
So we can add another row to our table of results from before:
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Legal Rule
No liability
Strict liability
Negligence, x~ = x*
Victim’s Precaution
Efficient
Zero
Efficient
Injurer’s Precaution
Zero
Efficient
Efficient
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This works great for cases of unilateral precaution – when in each situation, only
one party has a way to reduce the risk of accidents
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It also works pretty well in cases of bilateral precaution
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However, in cases of bilateral precaution, there are several different ways to
implement a negligence rule
The one that we have seen so far is called simple negligence
o Under a simple negligence rule, the injurer is liable if his level of
precaution, xi, was below the legal standard, xi~; if it was above xi~, he is
not liable
o And that’s the whole story
o (What the victim was doing doesn’t matter.)
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Under a different rule, however, a negligent injurer can escape liability if the
victim was also being negligent
For example, if I’m driving carelessly (talking on my phone, changing CDs) and
hit someone, I may be liable
But if I can show that the guy I hit was drunk, and stumbled into the street right in
front of me, his negligence cancels out mine and I don’t owe him damages
This type of rule is called negligence with a defense of contributory negligence
o Under this rule, if the injurer took insufficient precautions, xi < xi~, and
the victim took sufficient precautions, xv >= xv~, then the injurer is liable
for damages
o However, if the injurer took sufficient care, xi >= xi~; OR the injurer was
negligent, xi < xi~, but so was the victim, xv < xv~, then the injurer is not
liable for damages.
Like simple negligence, a rule of negligence with a defense of contributory
negligence (with standards of care equal to their efficient levels) leads to efficient
precaution by both parties
o The injurer expects the victim to take the efficient precautions, xv = xv~;
so he knows that if he takes insufficient care, xi < xi~, he’ll be liable, and
if he takes sufficient care, xi >= xi~, he will not be; so he minimizes
expected costs by setting xi = xi~ = xi*
o The victim, on the other hand, expects the injurer to take efficient
precautions, so he expects to receive no damages, whether or not he
himself is negligent; so he sets the efficient level of care, xv = xv*.
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A third type of negligence rule holds that if both parties are negligent and an
accident occurs, then since they share the blame, they should share the
responsibility
This is referred to as comparative negligence
o If the injurer is not negligent, xi >= xi~, he owes no damages
o If the injurer is negligent, xi < xi~, and the victim is not, xv >= xv~, then
the injurer bears the full cost of the accident
o But if both were negligent, xi < xi~ and xv < xv~, then they share the cost
of the accident; damages are paid, but they are less than the full cost of the
accident.
o (In theory, the damages are based on the relative contribution of each
side’s negligence to the accident, or the relative amounts that each one is
at fault.)
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Like the other two rules, comparative negligence (with efficient legal standards)
also leads to both parties taking the efficient level of precaution
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We’ve now considered three variations of a negligence rule:
o Simple negligence
o Negligence with a defense of contributory negligence
o Comparative negligence
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One other variation to consider is a rule of strict liability with a defense of
contributory negligence
That is, regardless of his level of care xi, the injurer is liable for damages, unless
the victim was negligent, in which case he is not
o Formally, if xv >= xv~, the injurer is liable; if xv < xv~, the injurer is not
o This rule is sometimes used with consumer products
o A manufacturer of a defective product is often liable for damages, except
when the consumer was negligent in how they used the product
o (If a coke bottle explodes in my hand, Coca-Cola is liable; but if I left it in
the sun and shook it, then not so much.)
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Once again, this type of rule (with appropriate standards) leads to efficient
precaution by both parties
The logic is the same
o The victim, knowing he will be liable if he is negligent, does best by
choosing the legally required level of care, xv = xv~
o So the injurer internalizes the full cost of any accidents, and therefore
takes the efficient level of care, xi = xi*.
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So we have now seen the following:
 No liability leads to efficient care by the victim, but no care by the injurer
 Strict liability leads to no care by the victim, efficient care by the injurer
 Any of the four variations on a negligence rule (with legal standards equal to
efficient levels of precaution) lead to efficient care by both parties
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(With basically any version of a negligence rule, one of the two parties can escape
liability by meeting the legal standard for care
As long as that legal standard coincides with the efficient level, that leads one
party to take efficient precaution
But this leaves the other party facing the entire social cost of the accident, and
therefore leads that party to take the efficient level of precaution as well, for the
purely selfish reason of minimizing expected private cost.)
Our original table was for unilateral precaution – just one party can take actions
that affect the likelihood of accidents
Negligence rules are better for cases of bilateral precaution – cases where some
degree of care from both parties is efficient.
(There are also some instances where either party could take precaution, but
efficiency only requires one of them to
o Picture two drivers on a dark road that both of them know well
o Really only one of them needs to have his headlights on – it could be
either one.
o This is referred to as redundant precaution
When precaution is continuous – you can take any amount – everything still
carries through
However, when precaution is discontinuous – such as your headlights being on or
off – different negligence rules will not all lead to efficient precaution
Cooter and Ulen give an example:
o A driver can fasten his seat belt a lot more easily than a car company
could design a seat belt that fastens automatically
o Under a simple negligence rule, a driver who didn’t buckle his seat belt
could sue the car company, so the car company might choose to incur the
higher costs of the auto-buckle
o Under a negligence rule with a defense of contributory negligence, the car
company would not have to do this to escape liability, and a rational driver
might choose to buckle up manually.
As long as things are continuous, though, redundant precaution isn’t a problem)
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So far, we’ve come up with the following conclusions:
Legal Rule
No liability
Strict liability
“Any” negligence rule with
efficient standards of care
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Victim’s Precaution
Efficient
Zero
Efficient
Injurer’s Precaution
Zero
Efficient
Efficient
However, there is another dimension in which peoples’ choices affect the
likelihood of an accident: activity level
o I can choose to drive carefully or recklessly, and I can also choose to drive
more or less often
o You can look both ways before crossing the street, or not; and you can
choose how many streets to cross
Next Tuesday, we’ll extend our model of torts to include both precaution and
activity levels
Also, the Shavell paper on the syllabus, “Strict Liability versus Negligence,” is all
about these incentives, including some other cases we didn’t talk about today –
we’ll discuss it Tuesday, take a look if you’re interested
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