Econ 522
Economics of Law
Dan Quint
Spring 2010
Lecture 16
The law as a set
of incentives
1
The law as incentives – HW2 Q3
(from old midterm)
A physician comes upon an auto accident, stops, and treats an
unconscious and badly bleeding victim. A week later the victim
receives a bill for services rendered. Must he pay it?
Under current U.S. law the answer is yes.
Consider the following alternatives:
i. The victim need not pay anything
ii. The victim must pay only the value of whatever materials were used
up in treating him (bandages, etc.)
iii. The victim must pay the going market rate for comparable medical
services
iv. The victim must pay whatever the doctor demands
Which of these do you expect to lead to the most efficient
outcomes? Why?
2
If we think about payoffs after the fact
(after accident, after treatment)…
 Suppose value of treatment is $100,000, cost of materials $50,
value of doctor’s time $450, market rate $1,000
Pay
Nothing
Cost of
Materials
Market
Rate
Whatever
Doc Asks
Patient’s
Payoff
$100,000
$99,950
$99,000
-$900,000
Doctor’s
Payoff
-500
-450
500
999,500
99,500
99,500
99,500
99,500
Combined
Payoffs
 After the fact, all remedies are equally efficient
 So this can’t be the right way to think about the problem!
3
So what is the right way to think about the
problem?
 Need to think about incentive each rule creates, therefore
the behavior it will lead to

Patient pays nothing

Patient pays for materials

Patient pays market rate

Patient pays whatever doctor asks
4
Something to remember
distribution
but not
efficiency
efficiency
5
Back to
tort law
6
Monday…
 Elements of a tort

Harm; causation; breach of duty (negligence)
 Strict liability: no need to prove negligence, just harm and
causation
 Negligence: need to prove all three elements
 Precaution: any actions taken to reduce likelihood of an
accident
 Today: economic model of torts
7
Precaution
 The more carefully I drive, the less likely I am to hit you


But, driving more carefully is also more costly to me
Must be some efficient level of care
8
Precaution
 The more carefully I drive, the less likely I am to hit you


But, driving more carefully is also more costly to me
Must be some efficient level of care
 What determines how carefully I drive is what I think will
happen if I hit you

Tort law creates incentives
 We ended Monday with two questions:



What is the efficient level of precaution?
How do we design the law to achieve it?
Like with nuisance and contract law… easiest way is to design the
law so that I internalize the externality I cause when I hit you
9
Model of unilateral harm
x
w
p(x)
A
level of precaution
marginal cost of precaution
probability of an accident
cost of an accident
 Unilateral harm – just one victim
 Precaution – costly actions that make accident less likely


Could be taken by either victim or injurer
We’ll focus on one at a time
 Notation


x – the amount of precaution that is taken
w – the cost of each “unit” of precaution


p(x) – probability of an accident, given precaution x


so total cost of precaution is wx
p is decreasing in x
A – cost of accident (to victim)

so expected cost of accidents is p(x) A
10
Model of unilateral harm
x
w
p(x)
A
level of precaution
marginal cost of precaution
probability of an accident
cost of an accident
$
wx + p(x) A
(Total Social Cost)
wx (Cost of Precaution)
p(x) A (Cost of Accidents)
x* (Efficient Level
of Precaution)
Precaution (x)
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x
w
p(x)
A
Model of unilateral harm
efficient precaution:
minx { wx + p(x) A }
w + p’(x) A
marginal social cost
of precaution
w
level of precaution
marginal cost of precaution
probability of an accident
cost of an accident
=
=
0
– p’(x) A
marginal social
benefit of precaution
 Under reasonable assumptions (p(x) convex)…



x < x*

w < – p’(x) A
MSC < MSB  more precaution efficient
x > x*

w > – p’(x) A
MSC > MSB  less precaution efficient
x = x*

MSC = MSB
12
Model of unilateral harm
x
w
p(x)
A
level of precaution
marginal cost of precaution
probability of an accident
cost of an accident
$
wx + p(x) A
wx
p(x) A
x < x*
x* x > x*
x
13
Model of unilateral harm
 We haven’t yet said who is taking precaution

Some situations, only injurer can reduce accidents

Some situations, victim can too

Bilateral precaution is a little bit tricky, but if we look at the two
parties one at a time, everything works fine
 Next: consider effect of different liability rules on precaution
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Effect of Liability Rules
on Precaution
15
Effect of liability rules on precaution
 Three rules we’ll consider:

No liability

Strict liability

Negligence
16
Rule 1: No Liability
 In a world with no liability…


Victim bears the cost of any accidents, plus the cost of any
precaution he takes
Injurer bears cost of any precaution he takes, does not have to pay
for accidents
17
Rule 1: No Liability
Injurer precaution
$
Private cost to injurer
wx + p(x) A
wx
p(x) A
x*
x
 Injurer’s private cost is just wx
 Injurer minimizes private cost by setting x = 0
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Rule 1: No Liability
Victim precaution
$
Private cost to victim
wx + p(x) A
wx
p(x) A
x*
x
 Victim’s private cost is wx + p(x) A
 To minimize this, victim takes efficient level of precaution 19
Rule 1: No Liability
 So in a world with no liability…
 Injurer takes inefficiently low level of precaution

(zero, or minimal amount)
 Victim takes efficient amount of precaution
20
Rule 2: 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
Victim pays only for his precaution
21
Rule 2: Strict Liability
Injurer precaution
$
Private cost to injurer
wx + p(x) A
wx
p(x) A
x*
x
 Injurer’s private cost is wx + p(x) A
 Injurer minimizes this by taking efficient level of precaution
22
Rule 2: Strict Liability
Victim precaution
$
Private cost to victim
wx + p(x) A
wx
p(x) A
x*
x
 Victim’s private cost is wx
 No incentive to take any precaution, victim sets x = 0
23
Effect of liability rules on precaution
No Liability
Strict Liability
Victim
precaution
Injurer
precaution
Efficient
Zero
Zero
Efficient
24
So for accidents with unilateral precaution…
 When it’s the injurer who can take precautions, a rule of
strict liability is more efficient
 When it’s the victim who can take precautions, a rule of
no liability is more efficient
 Each rule works well for one incentive, poorly for other


Similar to paradox of compensation we saw in contract law
Negligence rule may allow us to get both incentives right
25
Rule 3: Simple Negligence
 “Simple Negligence” rule
 Legal standard of care xn
 Injurer is liable for damages if precaution level was below
the legal standard of care


x < xn  D = A
x  xn  D = 0
 So on our graph from before, private cost to injurer is…


wx + p(x) A
wx
for x < xn
for x  xn
26
Rule 3: Simple Negligence
Injurer precaution
$
Private cost to injurer
wx + p(x) A
wx
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
27
Rule 3: 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*
28
Effect of liability rules on precaution
No Liability
Strict Liability
Simple Negligence,
with xn = x*
Victim
precaution
Injurer
precaution
Efficient
Zero
Zero
Efficient
Efficient
Efficient
29
For bilateral precaution, there are several
ways to implement a negligence rule
 Rule we just saw: injurer is liable if he was negligent, not
liable if he was not

“Simple Negligence”
 But we can consider both whether injurer was negligent…
 …and whether victim was negligent…
 …when determining whether injurer owes damages
(and how much)
30
Different negligence rules
Does injurer owe victim damages when…
Neither party
negligent?
Only victim
negligent?
Only injurer
negligent?
Both parties
negligent?
Simple Negligence
No
No
Yes
Yes
Negligence with Defense of
Contributory Negligence
No
No
Yes
No
31
Different negligence rules
Does injurer owe victim damages when…
Neither party
negligent?
Only victim
negligent?
Only injurer
negligent?
Both parties
negligent?
Simple Negligence
No
No
Yes
Yes
Negligence with Defense of
Contributory Negligence
No
No
Yes
No
Comparative Negligence
No
No
Yes
Partial
Strict Liability with Defense
of Contributory Negligence
Yes
No
Yes
No
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Here’s the cool part…
 When standards of care for both injurer and victim are set
to the efficient level…
 …any of these negligence rules lead to efficient level of
precaution by both parties!



Already saw this works for simple negligence
Could show the others the same way
Instead, we’ll do a discrete example
33
Discrete example of
bilateral precaution
A
w
p
$1,000
$20 for either party
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
34
Negligence with a Defense
of Contributory Negligence
 If injurer is not taking
precaution, victim wants
to avoid liability
 If injurer is taking
precaution, victim bears
residual risk, wants to
minimize accidents
Injurer
 Injurer is liable if he was negligent…
 Unless victim was negligent too
 Precaution is a dominant
strategy for victim
A
w
p
$1,000
$20 for either party
10% / 6% / 2%
Victim
Precaution
None
Precaution
-20, -40
-20, -60
None
-60, -20
0, -100
 For injurer, precaution is the best-response to precaution
 “Both take precaution” is the only Nash equilibrium
35
A
w
p
Comparative Negligence
$1,000
$20 for either party
10% / 6% / 2%
 If both parties were negligent…
Victim
 Precaution is again a
dominant strategy for
victim
Injurer
 …divide cost proportionally
Precaution
None
Precaution
-20, -40
-20, -60
None
-60, -20
-50, -50
 Now it’s a dominant strategy
for injurer too
 Again, “both take precaution” is the only equilibrium 36
Strict Liability with a Defense
of Contributory Negligence
 Now, injurer is liable,
regardless of whether
he was negligent…
$1,000
$20 for either party
10% / 6% / 2%
Victim
Injurer
 …unless victim
was negligent
A
w
p
Precaution
None
Precaution
-40, -20
-20, -60
None
-60, -20
0, -100
 Once again, “both
take precaution” is
the only equilibrium
37
Victim
precaution
Injurer
precaution
Efficient
Zero
Zero
Efficient
Simple negligence
Efficient
Efficient
Negligence with Defense of
Contributory Negligence
Efficient
Efficient
Comparative negligence
Efficient
Efficient
Strict Liability with Defense
of Contributory Negligence
Efficient
Efficient
No Liability
Strict Liability
assuming standards of
care are set equal to
efficient levels
So even with bilateral precaution…
38
(I mentioned, with bilateral precaution,
things occasionally get more complicated…)
 Redundant precaution – either party could take
precaution, efficiency only requires one of them
 If precaution is continuous, any negligence rule still leads
to efficient precaution level by both
 When precaution is discontinuous, not always

Driver can fasten seatbelt, or car company can design seatbelt that buckles
itself (more costly)
 Simple negligence: car company might be liable if designed manual seatbelt
and driver didn’t use it, so car company might design automatic belt
 Negligence with defense of contributory negligence: car company escapes
liability, so designs manual belt, rational driver uses it
 But as long as precaution is continuous, no problem
39
So far, our results seem to favor negligence
rules… but…
No Liability
Strict Liability
Any negligence rule
with efficient legal
standards of care
Victim
precaution
Injurer
precaution
Efficient
Zero
Zero
Efficient
Efficient
Efficient
 Next week: activity levels
 Steven Shavell, “Strict Liability Versus Negligence”
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