Econ 522
Economics of Law
Dan Quint
Fall 2010
Lecture 3
HW1 is online (due 5 p.m. Sept 24)
Also lecture notes – try View  Notes Page
Monday, we talked about efficiency
 Efficiency: “no available Kaldor-Hicks improvements”


roughly, maximizing total value, or total surplus, or total payoffs, to
everyone in society
but translating everything into dollars, so we can add/compare
across people
 Means that…



each scarce resource is owned by whoever values it most
goods are produced whenever their value is greater than their cost
and so on
I completely mangled the example about
fishing (externalities causing inefficiency)




20 fishermen
Catch 260 – H fish per hour of fishing
Get disutility of 8 fish per hour
What would be the efficient amount to fish?
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
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Each fisherman gets utility h(260 – H) – 8h
Total fish caught = H(260 – H), total disutility cost = 8H
Efficiency: maximize H(260 – H) – 8H = 252H – H2
Derivative = 252 – 2H = 0, so H = 126
So efficiency requires 126 total man-hours of fishing per week
If everyone fishes same amount, that’s 126/20 = 6.3 hours/day
H = 126, so people catch 260 – 126 = 134 fish/hour
Each person’s utility is 6.3 (134) – 6.3 (8) = 844.2 – 50.4 =
793.8 fish/day
I completely mangled the example about
fishing (externalities causing inefficiency)




20 fishermen
Catch 260 – H fish per hour of fishing
Get disutility of 8 fish per hour
What will people choose to do on their own?
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
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Each fisherman gets utility h(260 – H) – 8h
Maximize private gain = h(260 – H) – 8h = h(260 – H – h) – 8h
= 252h – Hh – h2
Derivative = 252 – H – 2h = 0, so h = 252 – H – h = 252 – H
So everyone fishes the same amount, so H = 20h,
and h = 252 – 20h or 21h = 252 or h = 12
So everyone fishes 12 hours/day
H = 240, so people catch 260 – 240 = 20 fish/hour
Each person’s utility is 12 (20) – 12 (8) = 240 – 96 = 144 fish/day
I completely mangled the example about
fishing (externalities causing inefficiency)




20 fishermen
Catch 260 – H fish per hour of fishing
Get disutility of 8 fish per hour
So…


Efficient level of fishing is 6.3 hours/day for each person,
giving everyone utility of 793.8 fish/day
But acting in their own interest, everyone fishes 12 hours/day,
giving everyone utility of 144 fish/day
 The point: since fishing imposes a negative externality,
people naturally do it “too much” (more than the efficient
amount)
I completely mangled the example about
fishing (externalities causing inefficiency)
H (260 – H)
Total
fish
caught
Efficient
level of
fishing
0
3
6
“Maximum
sustainable
yield”
“Equilibrium”
fishing
level
9
Hours fishing, per day, per fisherman
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Next, we asked: Should efficiency be the
normative goal of the law?
 Posner: yes – ex-ante, we would all have agreed to
efficient laws
 Analogy to lottery ticket with highest expected value
 We saw an example for asymmetric situations (landlords
and tenants)
But there are problems with efficiency as a
normative goal
 Ignores distribution of wealth
 Doesn’t consider procedural fairness

Auctioning off last seats for this class
 Value is equated with willingness to pay

I need a heart transplant, someone else is willing to pay more to
use heart as decoration
Friedman has his own take on why we
should study efficiency
“The central question [in this book]… is a simple one: what set of
rules and institutions maximize the size of the pie? What legal
rules are economically efficient?
There are at least three reasons why that is the question we ask.
The first is that while economic efficiency… is not the only thing
that matters to human beings, it is something that matters quite a
lot to most human beings.
The second reason is that there is evidence that considerable parts
of the legal system we live in can be explained as tools to generate
efficient outcomes… It is a lot easier to make sense out of a tool if
you know what it is designed to do.
A final reason is that figuring out what rules lead to… efficient
outcomes is one of the things economists know how to do –
and when you have a hammer, everything looks like a nail.”
- Friedman, Law’s Order, p. 312
Cooter and Ulen give a more pragmatic
defense of efficiency as a goal for the law
 Cooter and Ulen (textbook ch. 1)
 Efficiency should not necessarily be the goal of society
 But efficiency should be the goal of the legal system
 If redistribution is desirable, it’s better to make the legal
system efficient, and address distribution through taxes

Cooter and Ulen offer four reasons why the tax system is a better
way to redistribute wealth than the legal system
Four reasons the tax system is a better way
to redistribute wealth than the legal system
1.
Taxes can target “rich” and “poor” more precisely than the
legal system can
2.
Distributional effects of legal changes are harder to
predict
3.
Lawyers are more expensive than accountants
4.
More narrowly-targeted taxes cause greater distortion
than broad-based taxes
To make this last point, an example
(The question I distributed Monday)
Two goods: beer (x), pizza (y)
One consumer, with $60 and utility u(x,y) = x0.5 y0.5
a. Given prices p for beer and q for pizza, calculate demand.
(x,y) = (30/p, 30/q)
Beer and pizza are produced at $1 per unit, and perfectly competitive markets
So without any taxes, p = q = $1
b. Calculate demand, and utility, with no tax.
(x,y) = (30, 30)
u(x,y) = 300.5 300.5 = 30
c. Calculate demand and utility with $0.50 tax on beer.
(x,y) = (20, 30)
u(x,y) = 200.5 300.5 = 6000.5  24.49
d. How much revenue does $0.50 tax on beer raise?
20 X $0.50 = $10
e. Calculate demand and utility with $0.20 tax on both goods.
(x,y) = (25, 25)
u(x,y) = 250.5 250.5 = 25
f. How much revenue does $0.20 tax on both goods raise?
25 X $0.20 + 25 X $0.20 = $10
g. Which is the better way to raise revenue?
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So, summing up… is efficiency a good goal
for the law?
 We’ve seen two arguments in favor


Posner: it’s what we all would have agreed on ex-ante
C&U: if you want to redistribute, it’s better to do it through taxes
 But there are definitely some problems with efficiency

Distribution matters; not everything is monetizable; people might
care about procedural fairness
 My take


In this class, we’ll mostly focus on the positive questions
But in the background, I think of efficiency as a “pretty good”, but
definitely imperfect, measure of “goodness”
Before we move on, a quick digression…
 I don’t have many “absolute beliefs” about economics

Some people do
 I hope that doesn’t make things too confusing
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Before we move on, a quick digression…
 I don’t have many “absolute beliefs” about economics

Some people do
 I hope that doesn’t make things too confusing
 Relatedly, if I don’t see economics as a set of rules to
memorize, how do I know what I know?

I need to see a model, or an example, that demonstrates it
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Rest of today:
 introduce some basic game theory
 begin property law
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Some basic
game theory
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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:
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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
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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:
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u1(mum, mum) = -1
u1(rat, mum) = 0
u1(mum, rat) = -10
u1(rat,rat) = -5
Same for player 2
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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
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Dominant Strategies (skipped this in lecture)
 In the Prisoner’s Dilemma, one player’s best action is the
same, regardless of what his opponent does
Player 1’s Action
Player 2’s Action
Mum
Rat
Mum
-1, -1
-10, 0
Rat
0, -10
-5, -5
 This is called a dominant strategy

Regardless of what he thinks 2 will do, 1 would rather play Rat
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Nash Equilibrium
 In most games, players won’t have a single move that’s
always best
 We solve a game by looking for a Nash equilibrium
 Nash equilibrium is a strategy profile (an action for each
player) such that:
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No player can improve his payoff by switching to a different action…
…given what his opponent/opponents are doing
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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
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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…
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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
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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
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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
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Some games don’t have any equilibrium
where players only play one action
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

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
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That’s a very quick introduction to static
games
 Now on to…
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Property Law
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Why do we need property law at all?
 In a sense, same question as,
why do we prefer organized society of any sort to anarchy?
 Suppose there are two neighboring farmers
 Each can either farm his own land, or steal crops from his
neighbor

Stealing is less efficient than planting my own crops
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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
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Why do we need property law?
 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
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So how do we fix the problem?
 Suppose there were lots of farmers facing this same
problem
 They come up with an idea:
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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
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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
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So the idea here…
 Anarchy is inefficient
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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
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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:
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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?
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Answers to many of these seem obvious
 BUT…
 http://www.msnbc.msn.com/id/21088150/
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Monday: Coase
 Please see me if you’re not yet registered
 Take a look at Coase, “The Problem of Social Cost”
 Have a good weekend
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(I doubt we’ll get to…)
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One early, “classic” property law case
 Pierson v. Post (NY Supreme Court, 1805)

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Post organized a fox hunt, was chasing a fox
Pierson appeared “out of nowhere,” killed the fox, took it
Post sued to get the fox back
Lower court sided with Post; Pierson appealed to NY Sup Ct

Both were wealthy, pursued the case on principle or out of spite
 Question: when do you own an animal?
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Pierson v. Post
 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
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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
41