Econ 522
Economics of Law
Dan Quint
Spring 2012
Lecture 3
HW1 is online (due 11:59 p.m. Thurs Feb 9)
Also lecture notes – try View  Notes Page
Last week, we defined efficiency
 Efficiency: “all available Kaldor-Hicks improvements made”


roughly, maximizing total value, or total surplus, or total payoffs, to
everyone in society…
…where everything is translated into dollars, so we’re able to
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
And we discussed some forces that lead to
inefficiency
 Externalities




People make choices based on private cost and private benefit
Efficiency is based on social cost and social benefit
When social cost > private cost, negative externality
 people will do something more than efficient amount
When social benefit > private benefit, positive externality
 people will do something less than efficient amount
 Barriers to trade, taxes
 Monopoly/private information
And 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
Example for asymmetric situations (landlords and tenants)
 Cooter & Ulen: yes – if we want to adjust the distribution of
wealth, better to do it through tax system

Several reasons taxes better than legal system for redistributing
wealth
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
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?
6
Discussion question
 Aside from maximizing efficiency, what are other
plausible normative goals for a legal system?
 When would you expect these goals to be in
conflict with efficiency?
A nice blog post about why policy evaluation
should at least start with efficiency…
Let’s first dispense with the straw man. I’ve never heard of an
economist who believes that every efficient policy is good, and I’ve
heard of very few who believe that every inefficient policy is bad.
It’s true that most economists do seem to believe that any good policy
analysis should start by considering efficiency. That doesn’t mean it
should end there.
I think economists are right to emphasize efficiency, and I think so for
(at least) two reasons. First, emphasizing efficiency forces us to
concentrate on the most important problems. Second,
emphasizing efficiency forces us to be honest about our goals.
– Steven Landsburg
http://www.thebigquestions.com/2010/08/30/efficiency-experts
“Emphasizing efficiency forces us to be
honest about our goals”
Politician: Here’s my program to make the health care system work better by
subsidizing health care for the poor.
Economist: Your program costs a billion dollars and delivers half a billion
dollars worth of benefits. That’s inefficient.
Politician: So what?
Economist: Well, the “so what” is that maybe you could take that billion
dollars and deliver a full billion dollars worth of benefits instead if you spent it a
little differently. Why not just hand the cash out to poor people?
Politician: Because I don’t want to help all poor people. I only want to help
sick poor people – and this is the only way I can think of to do that.
Economist: Ah. So your goal here is not to make the health care system work
better at all. Instead it’s to transfer resources to sick poor people.
Politician: I guess so.
Economist: That’s fine. Now we can have a healthy debate about whether
that’s what we want to do.
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
11
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
12
Rest of today:
 introduce some basic game theory
 begin property law
13
Some basic
game theory
14
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
15
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
16
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
17
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
18
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
19
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
20
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
21
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
22
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
23
That’s a very quick introduction to static
games
 Now on to…
24
Property Law
25
To begin, a story
26
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
27
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
28
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
29
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
30
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
31
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?
32
Answers to many of these seem obvious
 BUT…
source:
http://www.msnbc.msn.com/id/21088150/
33
Wednesday: Coase
 Take a look at Coase, “The Problem of Social Cost”
 See you Wednesday
34