Econ 522
Economics of Law
Dan Quint
Fall 2013
Lecture 4
Reminder
 HW1 due 11:59 p.m. Thursday via Learn@UW
1
Last week, we…
 Defined efficiency


Maximizing total surplus achieved by everyone in society…
…with value measured by willingness-to-pay
 Asked whether efficiency is a good normative goal for a
legal system


Posner: yes, because ex ante (before we knew which part we would
play), we’d all agree to efficient rules
Cooter and Ulen: yes, because even if society has other goals in
mind, such as redistribution, it’s better to make the law efficient and
achieve redistribution through taxes
 Open discussion question


What are other plausible normative goals for a legal system?
When would you expect them to conflict with efficiency?
2
Some basic
game theory
3
A brief introduction to game theory
 Today, we focus on static games

Also known as simultaneous-move games
 A static game is completely described by three things:



Who the players are
What actions are available to each player
What payoff each player will get, as a function of


his own action, and
the actions of the other players
 Any complete description of these three things fully
characterizes a static game
4
A classic example: the Prisoner’s Dilemma
 (Story)
 Players: player 1 and player 2
 Two actions available to each player: rat on the other, or
keep mum
 Payoffs:





u1(mum, mum) = -1
u1(rat, mum) = 0
u1(mum, rat) = -10
u1(rat,rat) = -5
Same for player 2
5
In two-player games with finite actions, one
way to present game is payoff matrix
Player 2’s Action
Always Player 1
Mum
Rat
Mum
-1, -1
-10, 0
Rat
0, -10
-5, -5
Player 1’s Action
Player 1’s Payoff
Player 2’s Payoff
6
Nash Equilibrium
 We solve a game by looking for a Nash equilibrium
 Nash equilibrium is a strategy profile (an action for each
player) such that:


No player can improve his payoff by switching to a different action…
…given what his opponent/opponents are doing
7
A strategy profile is a Nash Equilibrium if no
player can gain by deviating
 Is (Mum, Mum) an
equilibrium?

Player 2’s Action
Player 1’s Action
 If any player can improve
his payoff by changing his
action, given his opponents’
actions, then it is not a Nash
equilibrium
Mum
Rat
Mum
-1, -1
-10, 0
Rat
0, -10
-5, -5
No, if player 2 is playing Mum
player 1 gains by deviating
8
In two-player games, we find Nash equilibria
by highlighting best responses
 My best response to a particular play by the other player
is whichever action(s) give me the highest payoff
 To find Nash Equilibria…




Circle payoff from player 1’s
Mum
best response to each action
by his opponent
-1, -1
Mum
Circle payoff from player 2’s
best response to each action
0, -10
Rat
Any box with both payoffs
circled is an equilibrium
Because each player is playing
a best-response to his opponent’s action…
…so neither one can improve by changing his strategy
Player 1’s Action

Player 2’s Action
Rat
-10, 0
-5, -5
9
Some games will have more than one
equilibrium
 Another classic: Battle of the Sexes
 (Story)
 Circle player 2’s
best responses
 We find two equilibria:
(ballgame, ballgame)
and (opera, opera)

Player 1’s Action
 Circle player 1’s
best responses
Player 2’s Action
Baseball Game
Opera
Baseball
Game
6, 3
0, 0
Opera
0, 0
3, 6
Game theory usually doesn’t have that much to say about which
equilibrium will get played when there are more than one
10
Sometimes, there will be a “good” and a
“bad” equilibrium
 Growth model
 (Story)
 Circle player 2’s
best responses
 Two equilibria:
(invest, invest)
and (consume, consume)

Player 1’s Action
 Circle player 1’s
best responses
Player 2’s Action
Invest
Consume
Invest
2, 2
0, 1
Consume
1, 0
1, 1
Some papers explain differences in growth across countries by
saying some are in “good” equilibrium and some are in “bad” one
11
Some games don’t have any equilibrium
where players only play one action



Look for Nash
Equilibria by
circling best
responses
No square with
both payoffs
circled
No equilibrium
where each
player plays a
single action
Player 1’s Action
 Scissors, Paper, Rock for $1
Player 2’s Action
Scissors
Paper
Rock
Scissors
0, 0
1, -1
-1, 1
Paper
-1, 1
0, 0
1, -1
Rock
1, -1
-1, 1
0, 0
 In this class, we’ll focus on games with a pure-strategy
Nash equilibrium
12
That’s a very quick introduction to static
games
 Now on to…
13
Property Law
14
Why do we need property law in the first
place?
 We already saw one reason
 Tragedy of Commons – overuse of land is held in common
 For another example, imagine two neighboring farmers
 Each has two choices: farm his own land, or steal crops
from his neighbor

Stealing is less efficient than planting my own crops




Have to carry the crops from your land to mine
Might drop some along the way
Have to steal at night  move slower
If I steal your crops, I avoid the effort of planting and watering
15
Why do we need property law in the first
place?
 Suppose that planting and watering costs 5, the crops either
farmer could grow are worth 15, and stealing costs 3
 With no legal system,
the game has the
following payoffs:
 We look for equilibrium
Player 1
Player 2
Farm
Steal
Farm
10, 10
-5, 12
Steal
12, -5
0, 0
 Like Prisoner’s Dilemma


both farmers stealing is the only equilibrium
but that outcome is Pareto-dominated by both farmers farming
16
So how do we fix the problem?
 Suppose there were lots of farmers facing this same
problem
 They come up with an idea:


Institute some property rights
And some type of government that would punish people who steal
 Setting up the system would cost something

Suppose it imposes a cost c on everyone who plays by the rules
17
ORIGINAL GAME
MODIFIED GAME
Player 2
Player 2
Farm
Steal
Farm
10, 10
-5, 12
Steal
12, -5
0, 0
Farm
Player 1
Player 1
So how do we fix the problem?
Steal
Farm 10 – c, 10 – c -5 – c, 12 – P
Steal 12 – P, -5 – c
-P, -P
 If P is big, and c is not too big, then 12 – P < 10 – c
 In that case, (Farm, Farm) is an equilibrium

Payoffs are (10 – c, 10 – c), instead of (0, 0) from before
18
So the idea here…
 Anarchy is inefficient



I spend time and effort stealing from you
You spend time and effort defending your property from thieves
Instead of doing productive work
 Establishing property rights, and a legal process for when
they’re violated, is one way around the problem
19
But once we have property rights, yours will
sometimes conflict with mine
20
Overview of Property Law
 Cooter and Ulen: property is
“A bundle of legal rights over resources that the owner is free to
exercise and whose exercise is protected from interference by others”
 Property rights are not absolute

Appendix to ch. 4 discusses different conceptions of property rights
 Any system has to answer four fundamental questions:




What things can be privately owned?
What can (and can’t) an owner do with his property?
How are property rights established?
What remedies are given when property rights are violated?
21
Answers to many of these seem obvious
 BUT…
source:
http://www.msnbc.msn.com/id/21088150/
22
How do we design property law to achieve
efficient outcomes?
23
Coase
24
How should property rights be allocated to
achieve efficiency?
 Coase’s surprising answer: it doesn’t matter
 (Under certain conditions)
25
The Coase Theorem
 Ronald Coase (1960), “The Problem of Social Cost”
 In the absence of transaction costs,
if property rights are well-defined
and tradable, voluntary negotiations
will lead to efficiency.



It doesn’t matter how rights are allocated
initially…
…because if they’re allocated inefficiently
at first, they can always be sold/traded…
so the allocation will end up efficient anyway
Ronald Coase
1910-2013
 Initial allocation does matter for distribution, though

And if there are transaction costs, may matter for efficiency too 26
Example of Coase: you have a car worth
$3,000 to you, $4,000 to me
 Obviously, efficient for me to own it…
 …but we don’t need the law to give me the car



If I start out owning the car:
no reason for you to buy it, I end up with it  efficient
If you start out owning the car:
clear incentive for me to buy it, I end up with it  efficient
Regardless of who owns the car at first, we get to the efficient
outcome




I’d rather start out with the car – so I don’t have to pay you for it
You’d rather start out with it – so you end up with more money
Efficiency doesn’t care about distribution – how much money we each
end up with – just who ends up with the car at the end.
And that doesn’t depend on who starts with it.
 The key: lack of transaction costs
27
Another example: you want to have a party
in the house next door to mine
 If it’s efficient for you to have the party…



Your benefit from having the party is greater than my benefit from a
good night’s sleep
If you start out with the right to have the party, no problem
If I start out with the right to quiet, you can pay me for the right to
have the party
 If it’s efficient for you not to have the party…



Good night sleep is worth more to me
If I have right to silence, no problem
If you have right to party, I can pay you not to have it
 The point: either way, we achieve efficiency



If it’s efficient to have the party, you have the party
If it’s efficient not to, you don’t
Regardless of who started off with the right
28
The conditions for this to hold
 Property rights have to be well-defined…

We need to be clear on who has what rights, so we know the
starting point for negotiations
 …and tradable…

We need to be allowed to sell/transfer/reallocate rights if we want
 …and there can’t be transaction costs

It can’t be difficult or costly for us to buy/sell the right
29
Coase’s example: a rancher and a farmer
30
Rancher’s versus farmer’s rights
 English common law: “closed range” or “fencing-in”
(or “farmer’s rights”)


Ranchers have responsibility to control their cattle
Rancher must pay for any damage done by his herd
 Much of the U.S. at various times: “open range” or
“fencing-out” (or “rancher’s rights”)


Rancher can let his cattle roam free
Not liable for damage they do to farmer’s crops
(unless farmer had a good fence and they broke through anyway)
 Which rule is more efficient?
31
Open range versus closed range
32
Coase: either law will lead to efficiency
 If it’s cheaper for the farmer to protect his crops than for the
rancher to control his herd…


Under open range law, that’s what he’ll do
Under closed range law, rancher can pay farmer to build fence
 If smaller herd is more efficient, farmer can pay rancher to
keep fewer cattle
 Coase:



Whatever is the efficient combination of cattle, crops, fences, etc.…
…the rancher and farmer will negotiate to that efficient outcome,
regardless of which law is in place…
…as long as the rights are well-defined and tradable and there are
no transaction costs
33
Note that there’s no sense of “blame” here
 Pigovian tax (Arthur Pigou)


Penalize firms for causing negative externalities
Requires us to “blame” one party
 Coase: doesn’t matter who is “causing” the harm

“It is true that there would be no crop damage without the cattle.
It is equally true that there would be no crop damage without the
crops.”
 Coase isn’t worried about “justice”, just efficiency



Doesn’t matter if a polluter is actually charged for polluting…
…or is allowed to pollute, but could be bribed to not pollute
Either way, without transaction costs, we’ll end up getting the
efficient amount of pollution!
34
Rancher and farmer: numerical example
 Three possibilities:



Rancher builds fence around herd… costs $400
Farmer builds fence around crops… costs $200
Do nothing, live with damage… costs nothing
 If expected crop damage = $100


Open range: farmer lives with damage rather than building fence
Closed range: rancher pays for damage rather than fence
 If expected crop damage = $500



Open range: farmer builds fence – efficient
Coase: closed range: rancher pays farmer to build fence
So efficient outcome under either rule
35
Other examples from Coase
 Lots of examples from case law





a building that blocked air currents from turning a windmill
a building which cast a shadow over the swimming pool and
sunbathing area of a hotel next door
a doctor next door to a confectioner
a chemical manufacturer
a house whose chimney no longer worked well after the neighbors
rebuilt their house to be taller
 In each case, regardless of who is initially held liable, the
parties can negotiate with each other and take whichever
remedy is cheapest to fix (or endure) the situation
36
Quoting from Coase (p. 13):
Judges have to decide on legal liability but this should not
confuse economists about the nature of the economic
problem involved.
In the case of the cattle and the crops, it is true that there
would be no crop damage without the cattle. It is equally
true that there would be no crop damage without the crops.
The doctor’s work would not have been disturbed if the
confectioner had not worked his machinery; but the
machinery would have disturbed no one if the doctor had
not set up his consulting room in that particular place…
37
Quoting from Coase (p. 13):
If we are to discuss the problem in terms of causation, both
parties cause the damage.
If we are to attain an optimum allocation of resources, it is
therefore desirable that both parties should take the
harmful effects into account when deciding on their course
of action.
It is one of the beauties of a smoothly operating pricing
system that… the fall in the value of production due to the
harmful effect would be a cost for both parties.
38
What does Coase mean by “a cost for both
parties”?
 If the cheapest alternative is for the farmer to build a fence
for $200…


The cost to build a fence is $200
But the cost to not build a fence is more than $200 – since under a
closed-range law, the farmer could ask the rancher for more than
$200 to build the fence
 “Opportunity cost”
39
So, summing up…
 Coase Theorem: In the absence of transaction costs,
if property rights are well-defined and tradeable,
voluntary negotiations will lead to efficiency.

The initial allocation of property rights therefore does not matter
for achieving efficiency…

…provided there are no transaction costs

(But if there are transaction costs, then the initial allocation can
matter for efficiency…

…and it will always matter for distribution)
40
Foxes
41
One early, “classic” property law case
 Pierson v. Post (NY Supreme Court, 1805)




Lodowick Post organized a fox hunt, was chasing
a fox
Jesse Pierson appeared “out of nowhere,” killed
the fox and took it
Post sued to get the fox back
Lower court sided with Post; Pierson appealed
to NY Supreme Court
 Question: when do you own an animal?
42
One early, “classic” property law case
 Court ruled for Pierson (the one who killed the fox)


“If the first seeing, starting, or pursuing such animals… should
afford the basis of actions against others for intercepting and killing
them, it would prove a fertile source of quarrels and litigation”
(Also: just because an action is “uncourteous or unkind” does not
make it illegal)
 Dissenting opinion: a fox is a “wild and noxious beast,” and
killing foxes is “meritorious and of public benefit”

Post should own the fox, in order to encourage fox hunting
43
Same tradeoff we saw earlier:
Pierson gets the fox

simpler rule (finders
keepers)

easier to implement

fewer disputes
Post gets the fox

more efficient incentives

(stronger incentive to pursue
animals that may be hard to
catch)
 Just like Fast Fish/Loose Fish vs Iron Holds The Whale


Fast Fish/Loose Fish is the simpler rule, leads to fewer disputes
Iron Holds the Whale is more complicated, but is necessary with
whales where hunting them the old-fashioned way is too dangerous
44
Doesn’t Coase make Pierson v Post
irrelevant?
 Coase seems to say: for efficiency, it doesn’t matter who
starts off with the right to the fox


If Post values it more, he can buy it from Pierson, or vice versa
Seems to imply: one rule is just as good as the other, as long as we
all know what the rule is
 So why does Pierson v Post matter?



Transaction costs!
Majority: if Post gets the fox back, “it would prove a fertile course of
quarrels and litigation” – the ensuing lawsuits would be costly
Dissent: killing foxes is a good thing (externality), so lots of people
benefit – so hard to get efficient amount of fox hunting through
bargaining
45
Transaction costs
 Coase: “in the absence of transaction costs,
if property rights are well-defined and tradable,
voluntary negotiations will lead to efficiency.”
 This suggests that if there are transaction costs,
voluntary negotiations may not lead to efficiency
 Car example (yet again)


If transactions are costly, we may not trade
And if we do trade, we incur that cost
46
Quoting Coase…
“If market transactions were costless, all that matters (questions
of equity apart) is that the rights of the various parties should be
well-defined and the results of legal actions easy to forecast.
But… the situation is quite different when market
transactions are so costly as to make it difficult to change
the arrangement of rights established by the law.
In such cases, the courts directly influence economic activity.
…Even when it is possible to change the legal delimitation of
rights through market transactions, it is obviously desirable to
reduce the need for such transactions and thus reduce the
employment of resources in carrying them out.
47
We can see the Coase Theorem as either a
positive or negative result
 “In the absence of transaction costs, if property rights are
well-defined and tradable, voluntary negotiations will lead
to efficiency.”
 We can read this as…


“As long as transaction costs aren’t a big deal, we’ll get efficiency”
Or as, “we’ll only get efficiency automatically if there are no
transaction costs”
 Coase also gives two examples of institutions that may
emerge in response to high transaction costs:


Firms
Government regulation
48
Many externalities can be thought of as
missing property rights
 Overfishing in communal lake?

It’s because property rights over those fish aren’t well-defined
 Firm polluting too much?

It’s because property rights over clean air aren’t well-defined
 So one solution…



Make property rights complete enough to cover “everything,” and
tradable, and use the law to minimize transaction costs…
…Then Coase kicks in and we get efficiency! (Booya!)
So why not do this? COSTS!
49
That’s it for today
 HW1 due (online submission) midnight Thursday
 For Wednesday


Demsetz, “Toward a Theory of Property Rights”
Calabresi and Melamed, “Property Rules, Liability Rules, and
Inalienability: One View of the Cathedral”
50
Bargaining
(we won’t get to this
on Monday)
51
Some vocabulary about bargaining
 Example from before:


Your car is worth $3,000 to you, and $4,000 to me
Suppose I have $10,000
 $10,000 is my threat point


the payoff I can get on my own, by refusing to cooperate with you
also called reservation utility, or outside option
 $3,000 is your threat point
 Any outcome we both agree to must make us both at least
as well-off as our threat point
52
Some vocabulary about bargaining
 If I don’t buy the car from you…



my payoff is 10,000 (my threat point)
your payoff is 3,000
combined payoffs are 13,000
 If I buy the car for some price P



my payoff is 4,000 + 10,000 – P = 14,000 – P
your payoff is P
combined payoffs are 14,000 – P + P = 14,000
 $1,000 are the gains from trade (or gains from cooperation)



no trade  combined payoffs of $13,000
I buy car  combined payoffs of $14,000
if we cooperate, our combined payoffs increase by $1,000
53
Some vocabulary about bargaining
 Threat points: 10,000 and 3,000
 Gains from cooperation: 1,000
 Suppose the gains from cooperation were split equally



we’d each get 500 more than threat point
my payoff would be 10,500, yours 3,500
which means P = $3,500
 (Coase doesn’t specify gains will be divided equally, just
that they’ll be divided in some way)
54
Let’s go back to the rancher and farmer
 Cows do $500 damage; fence around herd costs $400;
fence around crops costs $200
Rancher’s Rights
Rancher’s Threat Point
Farmer’s Rights
0
-400
-200
0
Gains From Cooperation
0
200
Rancher’s Payoff (IF…)
0
-300
Farmer’s Threat Point
Farmer’s Payoff
-200
Combined Payoffs
-200

100
=
-200
55
Relating Coase to general equilibrium/
first welfare theorem
 General equilibrium



given prices, consumers maximize utility
given prices, firms maximize profits
prices are such that all markets clear
 First Welfare Theorem: general equilibrium is efficient
 But not when there are externalities, or “missing markets”
 Allowing the consumer to negotiate with the firm is like
introducing a “missing market” in air rights
56
Relating Coase to general equilibrium/
first welfare theorem
 General equilibrium



given prices, consumers maximize utility
given prices, firms maximize profits
prices are such that all markets clear
 First Welfare Theorem: general equilibrium is efficient
 But not when there are externalities, or “missing markets”
 Allowing the consumer to negotiate with the firm is like
introducing a “missing market” in air rights
57