Econ 522
Economics of Law
Dan Quint
Spring 2010
Lecture 3
Lecture notes are online
View  Notes Page to see slide and my notes
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
 Should efficiency be the normative goal of the law?



Posner: yes, we would all have agreed to efficient laws ex-ante
analogy to lottery ticket with highest expected value
for asymmetric situations…
Example: why everyone might want efficient
laws even with asymmetries
 Two possible laws: landlords pay heat, tenants pay heat




If tenants pay heat, it costs $50 a month
If landlords pay heat, tenants will run heater all day – costs $100 a
month, makes tenants $10 happier
Suppose currently, tenants pay heat, tenants get value $650 from
apartment (with heat), landlord faces costs of $400, rent is $500
Switch to landlords paying heat: tenants costs go down $50,
landlord costs go up $100, suppose rent goes up $75
Tenants payoff
Landlords payoff

Tenants pay heat
Landlords pay heat
650 – 500 – 50 = 100
660 – 575 = 85
500 – 400 = 100
575 – 100 – 400 = 75
Both sides are worse off with switch to inefficient law!
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
Cooter and Ulen gave a more pragmatic
defense of efficiency as goal of law
 If we’re worried about distribution of wealth…


it’s better to have legal system achieve efficiency,
and handle distribution through tax system
 Multiple reasons why tax system is a better way to
redistribute wealth


Redistribution through laws would be like “narrowly-targeted taxes”
on particular activities…
…but narrow taxes are worse than broad 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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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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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:



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:





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
 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:


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…




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



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




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:


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



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:




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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One early, “classic” property law case
 Pierson v. Post (NY Supreme Court, 1805)




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
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Monday: Coase
 Please see me if you’re not yet registered
 Take a look at Coase and Demsetz papers
 Have a good weekend
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