1. Econ 522 Economics of Law
Dan Quint
Fall 2016
Lecture 17

2. Reminders Third homework due tomorrow night
Second midterm is next Wednesday (11/16)
Exam is cumulative – includes property law and contract law, but not tort law 1 1

3. Monday, we began tort law
How to create incentives to avoid accidental harms?
Strict liability and negligence rules
Harm, causation, breach of duty
Simple economic model
unilateral harm
reduce behavior to a one-dimensional choice for each player, how careful to be (“precaution”)
think about effect of liability rule on precaution and on activity levels of both players

4. Model of unilateral harm
x level of precaution w marginal cost of precaution p(x) probability of an accident A cost of an accident
Model of unilateral harm
efficient precaution: minx { wx + p(x) A } $
wx + p(x) A (Total Social Cost)
Let’s graph some important quantities – with x (the level of precaution taken) on the x axis, and money on the y
We said the probability of an accident, p(x), is decreasing in the level of precaution
Since A is a constant, this means p(x) A – the expected cost of accidents – is downward-sloping
The cost of precaution is just a line, w times x
And we can add these together to calculate the total expected social cost related to accidents, wx + p(x) A
And now our goal in tort law becomes clear: to achieve the efficient level of precaution, which is the level of x that minimizes the total social cost
So we’ll put this in gold, and call it x*
(Of course, this assumes precaution is continuous – that you can take any amount you choose
Some precaution is discrete – you either turn on your headlights while you’re driving, or you don’t
But the conceptual goal is the same: to get headlight use when the reduction in accidents is greater than the cost
And to not get headlight use when the cost would be greater than the reduction in accidents)
wx (Cost of Precaution)
p(x) A (Cost of Accidents)
x* (Efficient Level of Precaution)
Precaution (x)

5. Benchmark: what happens if injurer faces no liability at all?
Injurer doesn’t perceive accidents as part of private cost
No incentive to take any costly precaution
No incentive to reduce activity, which will be above efficient level
Victim bears cost of accidents as part of private cost
Victim’s private cost = social cost
Faces incentive to take efficient amount of precaution
Faces incentive to reduce activity to efficient level
A rule of no liability leads to…
no injurer precaution and overly high injurer activity
but efficient victim precaution and victim activity level

6. Benchmark: No Liability
Injurer Precaution
Victim Precaution
Injurer Activity
Victim Activity
No Liability
Zero
Efficient
Too High
Efficient

7. Another way to think about this – with no liability…
Injurer precaution
Social cost: cost of precaution
Social benefit: reduction in accidents
Private cost to injurer: cost of precaution
Private benefit: nothing!
PC = SC, but PB < SB, so injurer takes less than efficient precaution
Victim precaution
Social cost: cost of precaution
Social benefit: reduction in accidents
Private cost to victim: cost of precaution
Private benefit: reduction in accidents
PC = SC and PB = SB, so victim takes efficient precaution

8. Another way to think about this – with no liability…
Injurer activity
Social cost: cost of activity, plus increase in accidents
Social benefit: benefit of activity
Private cost to injurer: cost of activity only
Private benefit: benefit of activity
PB = SB, but PC < SC, so injurer takes higher than efficient activity level
Victim activity
Social cost: cost of activity, plus increase in accidents
Social benefit: benefit of activity
Private cost to victim: cost of activity, plus increase in accidents
Private benefit: benefit of activity
PC = SC and PB = SB, so victim takes efficient activity level

9. Next: what happens under a strict liability rule?8 8

10. Strict Liability Perfect compensation: damages D = A
Under strict liability…
Injurer pays damages for any accidents he causes
So injurer bears cost of accidents, plus his own precaution
Injurer internalizes externality his actions cause  chooses efficiently
Victim is fully insured, no incentive for precaution
Next, 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
And suppose that compensation is perfect – D = A, so damages exactly compensate for the harm.
Go back to the example of reflective clothing
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
So the cyclist minimizes this by setting x = 0
Under strict liability, the victim doesn’t bear the cost of accidents, so he has no reason to take any precaution
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
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.
But on the other hand, if it’s the injurer who affects the probability of accidents, strict liability ends up working pretty well
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
So he’s facing the same problem as minimizing the total social cost of accidents – so he chooses x efficiently!
(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. 9 9

11. Strict Liability (Damages = A) Injurer’s private cost is p(x) A + wx
Minimized at efficient precaution level x = x*
Victim’s private cost is just wx
Minimized at x = 0
So rule of strict liability leads to efficient precaution by injurers, no precaution by victims $
Private cost to injurer
Private cost to victim
wx + p(x) A wx
Next, we consider Rule 2: Strict Liability
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
And suppose that compensation is perfect – D = A, so the damages exactly compensate the victim for the harm.
Go back to the example of reflective clothing
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
So the cyclist minimizes this by setting x = 0
Under strict liability, the victim doesn’t bear the cost of accidents, so he has no reason to take any precaution
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
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.
But on the other hand, if it’s the injurer who affects the probability of accidents, strict liability ends up working pretty well
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
So he’s facing the same problem as minimizing the total social cost of accidents – so he chooses x efficiently!
(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.
p(x) A x* x 10 10

12. Strict Liability Injurer Precaution Victim Precaution Injurer Activity
Victim Activity
No Liability
Zero
Efficient
Too High
Efficient
Strict Liability
Efficient
Zero 11 11

13. What about activity level?
Under strict liability, injurer internalizes cost of accidents
Weighs benefit from driving against cost of accidents
Takes efficient activity level
Under strict liability, victim does not bear cost of accidents
Ignores cost of accidents when deciding how much to bike
Sets inefficiently high activity level
A rule of strict liability leads to the efficiently level of injurer activity, but an inefficiently high level of victim activity
The exact opposite will happen under strict liability
Under strict liability, you know you will be compensated for any accidents, so you don’t worry about their costs
Therefore, you take insufficient precautions, and you set too high an activity level
On the other hand, I know I’m paying for any accidents that happen, so I consider their costs when I make my decisions
I take efficient precautions
and I set an efficient activity level. 12 12

14. Strict Liability Injurer Precaution Victim Precaution Injurer Activity
Victim Activity
No Liability
Zero
Efficient
Too High
Efficient
Strict Liability
Efficient
Zero
Efficient
Too High 13 13

15. So… For both precaution and activity level…
“No liability” leads to inefficient behavior by injurer, efficient behavior by victim
“Strict liability” leads to efficient behavior by injurer, inefficient behavior by victim
Reminiscent of paradox of compensation
One rule sets multiple incentives…
…can’t get them all right
But in tort law, we have a trick…
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
And when only the injurer is able to take precautions, a rule of strict liability is preferable.
(This is exactly analogous to the problem we saw in contract law, of allocating a risk to the lowest-cost avoider
When one party – in this case, victim or injurer – can take precautions and the other cannot, that first party is the low-cost avoider
Making them bear the cost of the accident leads to efficient unilateral precaution.) 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
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
So in settings with bilateral precaution – situations where both parties have the possibility of precaution – neither of these rules will lead to efficiency
(With bilateral precaution, things get a little more complicated – you’ll see an example of this on the homework.)
However, in tort law, there is a trick
We already defined a negligence rule, under which the injurer is liable for harm only if he did not take certain precautions
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
This may allow us to get both incentives right. 14 14

16. Negligence

17. Negligence Rule
Negligence rule: injurer is only liable if he breached the duty of due care
Within our model:
Legal standard of care xn
Injurer owes damages if precaution level was below that level
x < xn  D = A
x ³ xn  D = 0
So on our graph from before, private cost to injurer is…
wx + p(x) A for x < xn
wx for x ³ xn
Best shot at achieving efficiency is to set xn = x*
Rule 3: Negligence Rule
Let’s think first about just injurer precaution
A negligence rule says that the injurer is liable for damages if his precaution level was below the legal standard of care, xn
So for x < xn, damages would be D = A
For x >= xn, damages would be D = 0
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 < xn, and just wx for x >= xn, since when x >= xn, the injurer is not liable for damages.
How this actually looks will depend on how xn, the legal standard for precaution, relates to x*, the efficient level of precaution
For now, let’s assume they’re equal, that is, xn = x*
(Our goal is to design an efficient legal system; so for now, let’s assume the court can set the efficient legal standard for negligence. We’ll see later what happens when it can’t.)

18. “Simple Negligence”: Injurer precaution$
Private cost to injurer
wx + p(x) A wx
What will injurer do?
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.
But now, what about the victim’s incentives?
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
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.
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.
(We’ll come back to what happens when standard for care is set incorrectly later.)
p(x) A
xn = x* x
Private cost is wx + p(x) A if x < xn, only wx otherwise
If standard of care is set efficiently (xn = x*), injurer minimizes private cost by taking efficient precaution

19. “Simple Negligence”: Victim precaution
What about victim?
We just said, injurer will take efficient precaution
Which means injurer will not be liable
So victim bears costs of any accidents
(Victim bears residual risk)
So victim’s private cost is wx + p(x) A
Victim minimizes private cost by taking efficient level of precaution too! $
Private cost to victim
(assuming injurer takes efficient level of precaution and is therefore not liable for damages)
wx + p(x) A wx
p(x) A x*

20. Simple Negligence Injurer Precaution Victim Precaution
Injurer Activity
Victim Activity
No Liability
Zero
Efficient
Too High
Efficient
Strict Liability
Efficient
Zero
Efficient
Too High
Simple Negligence, xn = x*
Efficient
Efficient

21. Other negligence rules
Rule we just saw is called “simple negligence”
Only consider injurer’s actions in determining liability
But we could also consider whether victim was negligence in deciding whether injurer is liable
“Negligence with a defense of contributory negligence” – injurer owes nothing if victim was also negligent
“Comparative negligence” – if both were negligent, share cost
“Strict liability with defense of contributory negligence” – injurer is liable (even if he wasn’t negligence), unless victim was negligent
Any of these rules (with efficient standard of care) will lead to efficient precaution by both parties!
(We could show this for each the way we already did for simple negligence, but that would get boring and repetitive,
so instead, let’s consider a different example, with discrete precaution)

22. Discrete example of bilateral precaution
A $1,000 w $20 for either party p 10% / 6% / 2%
No “levels” of precaution – each party can either take precaution or not
Each accident causes $1,000 of harm
Precaution costs $20 for each party
Chance of an accident is
10% if nobody takes precaution
6% if one party takes precaution
2% if both parties take precaution
Note that precaution is efficient for both parties
Costs $20; reduces expected accidents by 4% X $1,000 = $40

23. Negligence with a Defense of Contributory Negligence
A $1,000 w $20 for either party p 10% / 6% / 2%
Injurer is liable if he failed to take precaution…
Unless victim did too
Precaution is always best-response for victim
If injurer is not taking precaution, victim wants to avoid liability
If injurer is taking precaution, victim bears residual risk, wants to minimize accidents
For injurer, precaution is the best-response to precaution
“Both take precaution” is the only Nash equilibrium
And, is the efficient outcome
victim pays for precaution, and any accidents that happen
injurer pays for precaution, not liable for accidents
Victim
Precaution
None
-20, -40
-20, -60
Precaution
Injurer
-60, -20
0, -100
None 22 22

24. Comparative Negligence
A $1,000 w $20 for either party p 10% / 6% / 2%
If both parties were negligent…
…divide cost proportionally
Precaution is again always a best response for victim
Now it’s a best response for injurer too
Again, “both take precaution” is the only equilibrium
(And the efficient outcome)
Victim
Precaution
None
-20, -40
-20, -60
Precaution
Injurer
-60, -20
-50, -50
None 23 23

25. Strict Liability with a Defense of Contributory Negligence
A $1,000 w $20 for either party p 10% / 6% / 2%
Now, injurer is liable, regardless of whether he took precaution…
…unless victim was negligent
Once again, “both take precaution” is the only equilibrium
Victim
Precaution
None
-40, -20
-20, -60
Precaution
Injurer
-60, -20
0, -100
None 24 24

26. Negligence
Injurer Precaution
Victim Precaution
Injurer Activity
Victim Activity
No Liability
Zero
Efficient
Too High
Efficient
Strict Liability
Efficient
Zero
Efficient
Too High
Simple Negligence
Efficient
Efficient
assuming all relevant standards of care are set to the efficient levels
Negligence with a Defense of Contributory Negligence
Efficient
Efficient
(We can also think about this via externalities.
Under strict liability, you are fully compensated for any accidents I cause
So my choice of how much to drive doesn’t affect your well-being
So there is no externality, and I drive the efficient amount.
On the other hand, under strict liability, if you bicycle more, it increases the likelihood that I hit you and have to pay,
so it imposes a negative externality on me,
so you do it too much.)
Comparative Negligence
Efficient
Efficient
Strict Liability with Defense of Contributory Negligence
Efficient
Efficient

27. What about activity levels under a negligence rule?
Simple negligence: injurer is only liable if he was negligent
Leads injurer to take efficient precaution, so injurer expects to not be liable for any accidents that do occur
So injurer ignores cost of accidents when deciding on activity level (how much to drive)
Injurer drives carefully, but still drives too much
Victim bears “residual risk”
Victim bikes carefully, and bikes efficient amount

28. Adding activity levels to our results on precaution…
Injurer Precaution
Victim Precaution
Injurer Activity
Victim Activity
No Liability
Zero
Efficient
Too High
Efficient
Strict Liability
Efficient
Zero
Efficient
Too High
Simple Negligence
Efficient
Efficient
Too High
Efficient
Negligence with a Defense of Contributory Negligence
Efficient
Efficient
Comparative Negligence
Efficient
Efficient
Strict Liability with Defense of Contributory Negligence
Efficient
Efficient

29. Negligence with Defense of Contributory Negligence, and Comparative Negligence
Either rule: efficient precaution by both parties
Either rule: if neither party was negligent, injurer does not owe damages
So victim is residual risk bearer (pays for accidents)
So victim weighs cost of accidents against benefits of activity, takes efficient activity level
Injurer ignores cost of accidents, takes inefficiently high activity level

30. Negligence Injurer Precaution Victim Precaution Injurer Activity
Victim Activity
No Liability
Zero
Efficient
Too High
Efficient
Strict Liability
Efficient
Zero
Efficient
Too High
Simple Negligence
Efficient
Efficient
Too High
Efficient
Negligence with a Defense of Contributory Negligence
Efficient
Efficient
Too High
Efficient
Comparative Negligence
Efficient
Efficient
Too High
Efficient
Strict Liability with Defense of Contributory Negligence
Efficient
Efficient

31. Strict Liability with Defense of Contributory Negligence
If victim is not negligent, injurer is liable
Leads to efficient precaution by both, so injurer is liable
Injurer is residual risk bearer
Injurer weighs cost of accidents against benefits of activity, takes efficient activity level
Victim ignores cost of accidents, takes inefficient high activity level

32. Negligence Injurer Precaution Victim Precaution Injurer Activity
Victim Activity
No Liability
Zero
Efficient
Too High
Efficient
Strict Liability
Efficient
Zero
Efficient
Too High
Simple Negligence
Efficient
Efficient
Too High
Efficient
Negligence with a Defense of Contributory Negligence
Efficient
Efficient
Too High
Efficient
Comparative Negligence
Efficient
Efficient
Too High
Efficient
Strict Liability with Defense of Contributory Negligence
Efficient
Efficient
Efficient
Too High

33. An easier (perhaps) way to understand all of this
take precaution only to AVOID liability
precaution is efficient, but activity level is too high
Injurer Precaution
Victim Precaution
Injurer Activity
Victim Activity
No Liability
Zero
Efficient
Too High
Efficient
Strict Liability
Efficient
Zero
Efficient
Too High
Simple Negligence
Efficient
Efficient
Too High
Efficient
Negligence with a Defense of Contributory Negligence
Efficient
Efficient
Too High
Efficient
Comparative Negligence
Efficient
Efficient
Too High
Efficient
Strict Liability with Defense of Contributory Negligence
Efficient
Efficient
Efficient
Too High

34. An easier (perhaps) way to understand all of this
to reduce accidents, since he bears their cost
precaution and activity level are both efficient
Injurer Precaution
Victim Precaution
Injurer Activity
Victim Activity
No Liability
Zero
Efficient
Too High
Efficient
Strict Liability
Efficient
Zero
Efficient
Too High
Simple Negligence
Efficient
Efficient
Too High
Efficient
Negligence with a Defense of Contributory Negligence
Efficient
Efficient
Too High
Efficient
Comparative Negligence
Efficient
Efficient
Too High
Efficient
Strict Liability with Defense of Contributory Negligence
Efficient
Efficient
Efficient
Too High

35. With each negligence rule…
One party can avoid liability by taking efficient precaution
Leads to efficient precaution
But inefficient activity level
Other party is the residual risk bearer – even when he takes precaution, he is still liable
And also efficient activity level
Who should bear residual risk?
One way to answer is to ask whose activity level has greater impact on efficiency

36. So which rule is best? “Put the incentive where it does the most good”
Efficient rule depends on which choices have greatest impact
If only injurer’s choices (precaution + activity) matter  strict liability is better rule
If bilateral precaution  negligence
Which negligence rule – depends whose activity level is more important
Friedman (citing Posner): this is why very dangerous activities often covered by strict liability
Blasting with dynamite, keeping a lion as a pet
Even with proper precaution, still very dangerous, so injurer activity level is important
Which rule is the most efficient, then, depends on the situation
That is, it depends on whose choices have the bigger impact.
In situations with unilateral precaution – situations where only one party needs to take steps to avoid accidents – no liability or strict liability work perfectly well
In situation with bilateral precaution, negligence rules give appropriate incentives for precaution on both sides
However, under any negligence rule, one of the two parties still bears whatever losses do occur – one party is the residual bearer of the harm of accidents, and the other party is not
Any negligence rule yields an efficient activity level by the residual risk bearer, but an inefficient activity level by the other party
Thus, the optimal rule depends on whose activity level is most important.
Friedman mentions that Posner uses this to explain why highly dangerous activities – blasting with dynamite, or keeping a lion as a pet – are often governed by strict liability
Wikipedia offers the example of a tiger rehabilitation center – if a tiger escapes and causes injuries, the owner is responsible, no matter how careful he was
if an activity is dangerous enough, the only meaningful type of precaution may be to not do them at all
Strict liability leads to efficient levels of both care (if you choose to do them) and a choice of whether or not to do them in the first place.

37. Friedman: activity is just unobservable precaution
Activity is just another type of precaution, but type where court can’t determine efficient level
Court can tell inefficient for me to drive at night with headlights off
Can’t tell how many miles it’s efficient for me to drive
Determination of negligence can only be based on observable precaution, not unobservable
Negligence rule leads to efficient levels of observable precaution by both parties
Simple negligence leads only to efficient observable precaution by injurer, but efficient precaution by victim as well
Strict liability leads to efficient observable and unobservable precaution by injurer, but no precaution by victim
Friedman has a different take on activity levels
He argues that reducing your activity level is just another type of precaution
But it’s a type of precaution where it’s impossible for the court to determine the efficient level
(A court might be able to figure out that it’s efficient for me to drive with my headlights on at night, but unable to figure out how many miles it’s optimal for me to drive in a given day
Therefore, a court might find me negligent if I was driving without headlights
But it’s hard for a court to decide whether a particular trip was socially efficient, and therefore whether I was negligent by being in my car!)
Instead of distinguishing precaution from activity levels, Friedman distinguishes observable precaution from unobservable precaution
He points out that any negligence rule only causes an efficient level of observable precaution, since that’s all that can be used to determine whether someone exercised due care or was negligent
So a negligence rule does not lead to an efficient level of unobservable precaution
Strict liability, on the other hand, leads the injurer to internalize the cost of accidents, so it leads to efficient levels of both observable and unobservable precaution – the same result as we already saw, just in different words

38. This is for accidents between strangers
What we’ve done so far assumes there’s no preexisting relationship between injurer and victim
Another interesting case: accidents that occur between a business and its customers, or between a business and people who aren’t its customers
Forces are very similar, but details are different
Article by Shavell, “Strict Liability Versus Negligence”, covers this well – we’ll talk about it next week
Up next: determining the legal standard to use for negligence