Econ 522
Economics of Law
Dan Quint
Fall 2012
Lecture 16
Reminder
 HW3 due tomorrow night
 MT2 November 19
1
Today
 A few last odds and ends from contract law
 The basic economic model we’ll be using for tort law
2
Contract Law
3
Repeated games
4
Repeated games
Player 1 (you)
Don’t
Trust me
Player 2 (me)
(100, 0)
Share profits
(150, 50)
Keep all the money
(0, 200)
 Suppose we’ll play the game over and over

After each game, 10% chance relationship ends, 90% chance we
play at least once more…
5
Repeated games
 Suppose you’ve chosen to trust me
 Keep all the money: I get $200 today, nothing ever again
 Share profits: I get $50 today, $50 tomorrow, $50 day after…
 Value of relationship =
50
 500
50  50 .9  50 .9  50 .9  ... 
1  .9
2
3
 Since this is more than $200, we can get cooperation
6
Repeated games
 Suppose you’ve chosen to trust me
 Keep all the money: I get $200 today, nothing ever again
 Share profits: I get $50 today, $50 tomorrow, $50 day after…
 Value of relationship =
50
 500
50  50 .9  50 .9  50 .9  ... 
1  .9
2
3
 Since this is more than $200, we can get cooperation
7
Repeated games and reputation
 Diamond dealers in New York (Friedman)
“…people routinely exchange large sums of money for
envelopes containing lots of little stones without first
inspecting, weighing, and testing each one”
“Parties to a contract agree in advance to arbitration;
if… one of them refuses to accept the arbitrator’s verdict,
he is no longer a diamond merchant – because everyone
in the industry now knows he cannot be trusted.”
8
Repeated games and reputation
 The first purpose of contract law is to enable cooperation,
by converting games with noncooperative solutions into
games with cooperative solutions
 The sixth purpose of contract law is to foster enduring
relationships, which solve the problem of cooperation with
less reliance on courts to enforce contracts
 Law assigns legal duties to certain long-term relationships


Bank has fiduciary duty to depositors
McDonalds franchisee has certain duties to franchisor
9
Repeated games and the endgame problem
 Suppose we’ll play agency game 60 times


$50 x 60 = $3,000 > $200, so cooperation seems like no problem
But…
 In game #60, reputation has no value to me



Last time we’re going to interact
So I have no reason not to keep all the money
So you have no reason to trust me
 But if we weren’t going to cooperate in game #60, then in
game #59…
10
Repeated games and the endgame problem
 Endgame problem: once there’s a definite end to our
relationship, no reason to trust each other
 Example: collapse of communism in late 1980s





Communism believed to be much less efficient than capitalism
But fall of communism led to decrease in growth
Under communism, lots of production relied on gray market
Transactions weren’t protected by law, so they relied on long-term
relationships
Fall of communism upset these relationships
11
One other bit
I like from Friedman
12
Friedman on premarital sex
13
Friedman on premarital sex
14
That’s it for contract law
 Purposes for contract law:






Encourage cooperation
Encourage efficient disclosure of information
Secure optimal commitment to performance
Secure efficient reliance
Provide efficient default rules and regulations
Foster enduring relationships
End of material on second midterm
15
Tort Law
16
Monday
 Two liability rules we’ll be looking at
 Strict Liability


If I cause an accident, I owe victim damages
(Harm + Causation  Liable)
 Negligence


If I cause an accident, I only owe victim damages if I was negligent
(Harm + Causation + Breach of Duty/Negligence  Liable)
17
“Classic” legal theory of torts
 Harm
 Causation
 Breach of Duty
18
Element 3: Breach of Duty
(Sometimes required, sometimes not)
Strict Liability
• Harm
• Causation
Negligence
• Harm
• Causation
• Breach of duty (fault)
 When someone breaches a duty he owes to the
defendant, and this leads to the harm, the injurer is
at fault, or negligent


Injurers owe victims the duty of due care
Negligence rule: I’m only liable if I failed to take the required
standard of care – not if I was careful and the accident happened
anyway
19
Hence the language in the trolly example
“A tree fell on a moving trolly, injuring passengers. One of them
sued.
He succeeded in demonstrating that in order for the trolly to be
where it was when the tree fell on it the driver had to have driven
faster than the speed limit at some point during the trip.
Breaking the law is per se negligence, so the driver was
legally negligent whether or not his driving was actually unsafe.
If he had not driven over the speed limit, the trolly would not
have been under the tree when it fell, so, the plaintiff argued,
the driver’s negligence caused the injury.”
20
So under a negligence rule…
 If I breach my duty of due care and injure you, I am liable
 If I exercise the appropriate level of care but still injure
you, I’m not liable
 How is the standard of care determined?


That is, how careful do I have to be to avoid liability, and who
decides?
Is it negligent to drive 40 MPH on a particular road at a particular
time of day? What about 41 MPH? 42?
21
How is the standard of care determined?
 Some settings: government imposes safety regulations
that are also used as standard for negligence



Speed limits for highway driving
Requirement that bicycles have brakes
Workplace regulations
 Some standards are left vague




“Reckless driving” may depend on road, time of day, weather…
Common law focuses on duty of reasonable care
Level of care a reasonable person would have taken
(Civil law relies less on “reasonableness” tests, tries to spell out
what level of care is required)
22
Strict liability versus negligence
 Strict liability rule: plaintiff must prove harm and
causation
 Negligence rule: must prove harm, causation, and
negligence
 A little history



Early Europe: strict liability was usual rule
By early 1900s, negligence became usual rule
Second half of 1900s, strict liability became more common again,
especially for manufacturer liability in American consumer products

U.S. manufacturers now held liable for harms caused by defective
products, whether or not they were at fault
23
Next question
 Like with contract law, our main concern is with the
incentives created by liability rules
 So… what incentives are we interested in?
24
Precaution
25
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
 Similarly…


Construction company can reduce accidents with better safety
equipment, better training, working shorter days, all of which cost
money
Manufacturer can reduce accidents by designing/inspecting
products more carefully – again, more expensive
26
Actions by both injurer and victim impact
number of accidents
• speed like hell
• drive slowly
• drive drunk while texting
• drive carefully
• cheap, hasty manufacturing
• careful quality control
• save money
• install smoke detectors, other
safety equipment
• wear helmet and use light
• bicycle at night wearing black
LESS EFFORT TO
PREVENT ACCIDENTS
“LESS PRECAUTION”
GREATER EFFORT TO
PREVENT ACCIDENTS
“MORE PRECAUTION”
27
We will call all these things precaution
 Precaution: anything either injurer or victim could do to
reduce likelihood of an accident (or damage done)
 The next two questions should be obvious…
 How much precaution do we want?

What is efficient level of precaution?
 How do we design the law to get it?
28
To answer these questions, we’ll introduce a
very simple model of accidents
 Car hits a bicycle



In real life: driver probably has insurance
In real life: some damage to bicycle, some damage to driver’s car
In real life: driver and bicyclist may not even know what the law is
 We’ll simplify things a lot, by assuming…



Only one party is harmed
Parties know the law, don’t have insurance (for now)
We’ll focus on one party’s precaution at a time
29
Simple economic model
for thinking about tort law
30
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 consider both, but 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
31
Model of unilateral harm
x
w
p(x)
A
level of precaution
marginal cost of precaution
probability of an accident
cost of an accident
efficient precaution: minx { wx + p(x) A }
$
w + p’(x) A
marginal
social cost
of precaution
w
marginal social
benefit of
precaution
=
0
=
– p’(x) A
wx + p(x) A
(Total Social Cost)
wx (Cost of Precaution)
p(x) A (Cost of Accidents)
x* (Efficient Level
of Precaution)
x < x*
x > x*
Precaution (x)
32
Effect of liability rules on precaution
 We know what’s efficient

Level of precaution that minimizes total social cost = wx + p(x) A
 We’ll consider what happens if there is…



no liability rule in place
a strict liability rule
a negligence rule
33
Benchmark: what happens
without any liability rule?
34
Benchmark: No Liability
 In a world with no liability…






Injurer does not have to pay for accidents
So, bears cost of any precautions he takes, but does not receive
any benefit
Injurer has no incentive to take precaution
Victim bears cost of any accidents, plus cost of precaution he takes
(Victim precaution imposes no externality on injurer)
Victim precaution will be efficient
35
Benchmark: No Liability
$
 Injurer’s private cost
is just wx

Private cost to injurer
Private cost to victim
Minimized at x = 0
 Victim’s private cost
is p(x) A + wx

wx + p(x) A
wx
Minimized at efficient
precaution level x = x*
p(x) A
x*
x
 So rule of no liability leads to efficient precaution by
victims, no precaution by injurers
36
Benchmark: No Liability
No Liability
Injurer
Precaution
Victim
Precaution
Zero
Efficient
37
Precaution isn’t the only thing that
determines number of accidents
 Precaution – actions which make an activity less dangerous


Driving carefully
Wearing bright-colored clothing while bicycling
 The amount we do each activity also affects the number of
accidents


I decide how much to drive
You decide how much to bicycle
 Liability rules create incentives for activity levels as well as
precaution
38
With no liability rule…
 With no liability, I’m not responsible if I hit you





I don’t consider cost of accidents when deciding how fast to
drive…
…and I also don’t consider cost of accidents when deciding
deciding how much to drive
So I drive too recklessly, and I drive too much
(or: if there is no liability, social cost of driving includes cost of
accidents, but private cost to me does not;
driving imposes negative externality, so I do it too much)
 So with no liability, injurer’s activity level is inefficiently high
39
What about victims?
 With no liability, victim bears full cost of accidents




Greater activity by victim (more bike-riding) leads to more accidents
Victim weighs cost of accidents when deciding how carefully to ride,
and when deciding how much to ride
(Private cost = social cost)
Victim takes efficient level of precaution, and efficient level of
activity
 A rule of no liability leads to an inefficiently high level of
injurer activity, but the efficient level of victim activity
40
Benchmark: No Liability
No Liability
Injurer
Precaution
Victim
Precaution
Injurer
Activity
Victim
Activity
Zero
Efficient
Too High
Efficient
41
Next: what happens under a
strict liability rule?
42
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
43
Strict Liability
$
 (Damages = A)
 Injurer’s private cost
is p(x) A + wx

Private cost to injurer
Private cost to victim
Minimized at efficient
precaution level x = x*
wx + p(x) A
 Victim’s private cost
is just wx

wx
p(x) A
Minimized at x = 0
x*
x
 So rule of strict liability leads to efficient precaution by
injurers, no precaution by victims
44
Strict Liability
No Liability
Strict Liability
Injurer
Precaution
Victim
Precaution
Injurer
Activity
Victim
Activity
Zero
Efficient
Too High
Efficient
Efficient
Zero
45
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
46
Strict Liability
No Liability
Strict Liability
Injurer
Precaution
Victim
Precaution
Injurer
Activity
Victim
Activity
Zero
Efficient
Too High
Efficient
Efficient
Zero
Efficient
Too High
47
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…
48
Negligence
(won’t get to)
49
Negligence Rule
 Negligence rule: injurer is 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  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
 Best shot at achieving efficiency is to set xn = x*
50
“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
51
“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*
52
Simple Negligence
Injurer
Precaution
Victim
Precaution
Injurer
Activity
Victim
Activity
Zero
Efficient
Too High
Efficient
Strict Liability
Efficient
Zero
Efficient
Too High
Simple Negligence, xn = x*
Efficient
Efficient
No Liability
53
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!
54
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
55
Different negligence rules
A
w
p
$1,000
$20 for either party
10% / 6% / 2%
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
56
Negligence with a Defense
of Contributory Negligence
A
w
p
$1,000
$20 for either party
10% / 6% / 2%
 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
victim pays for
 Injurer is liable if he failed to take precaution… precaution,
and any
accidents that happen
 Unless victim did too
injurer pays for
Victim
precaution, not liable
 Precaution is always
for accidents
Precaution
None
best-response for victim
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
 And, is the efficient outcome
57
Different negligence rules
A
w
p
$1,000
$20 for either party
10% / 6% / 2%
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
58
A
w
p
Comparative Negligence
$1,000
$20 for either party
10% / 6% / 2%
 If both parties were negligent…
 Precaution is again a
dominant strategy for
victim
Injurer
 …divide cost proportionally
 Now it’s a dominant strategy
for injurer too
Victim
Precaution
None
Precaution
-20, -40
-20, -60
None
-60, -20
-50, -50
 Again, “both take precaution” is the only equilibrium
 (And the efficient outcome)
59
Different negligence rules
A
w
p
$1,000
$20 for either party
10% / 6% / 2%
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
60
Strict Liability with a Defense
of Contributory Negligence
 Now, injurer is liable,
regardless of whether
he took precaution…
$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
61
Negligence
Injurer
Precaution
Victim
Precaution
Injurer
Activity
Victim
Activity
Zero
Efficient
Too High
Efficient
Strict Liability
Efficient
Zero
Efficient
Too High
Simple Negligence
Efficient
Efficient
No Liability
Negligence with a Defense
of Contributory Negligence
Efficient
Efficient
Comparative Negligence
Efficient
Efficient
Strict Liability with Defense
of Contributory Negligence
Efficient
Efficient
assuming all
relevant
standards of
care are set to
the efficient
levels
62