Upload
godfrey-hall
View
219
Download
1
Embed Size (px)
Citation preview
Econ 522Economics of Law
Dan Quint
Fall 2010
Lecture 3
HW1 is online (due 5 p.m. Sept 24)Also lecture notes – try View Notes Page
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
Monday, we talked about efficiency
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?
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?
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)
I completely mangled the example about fishing (externalities causing inefficiency)
6 1290 3
Hours fishing, per day, per fisherman
Total fish
caught “Maximum sustainable
yield”
Efficientlevel offishing
“Equilibrium”fishinglevel
H (260 – H)
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)
Next, we asked: Should efficiency be the normative goal of the law?
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
But there are problems with efficiency as a normative goal
“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
Friedman has his own take on why we should study efficiency
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
Cooter and Ulen give a more pragmatic defense of efficiency as a goal for the law
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
Four reasons the tax system is a better way to redistribute wealth than the legal system
13
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?
To make this last point, an example(The question I distributed Monday)
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”
So, summing up… is efficiency a good goal for the law?
15
I don’t have many “absolute beliefs” about economics Some people do
I hope that doesn’t make things too confusing
Before we move on, a quick digression…
16
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
Before we move on, a quick digression…
17
introduce some basic game theory
begin property law
Rest of today:
18
Some basicgame theory
19
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
A brief introduction to game theory
20
(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
A classic example: the Prisoner’s Dilemma
21
In two-player games with finite actions, one way to present game is payoff matrix
-1, -1 -10, 0
0, -10 -5, -5
Mum Rat
Mum
Rat
Player 2’s Action
Player 1’s Action
Player 1’s Payoff Player 2’s Payoff
Always Player 1
22
In the Prisoner’s Dilemma, one player’s best action is the same, regardless of what his opponent does
This is called a dominant strategy Regardless of what he thinks 2 will do, 1 would rather play Rat
Dominant Strategies (skipped this in lecture)
-1, -1 -10, 0
0, -10 -5, -5
Mum Rat
Mum
Rat
Player 2’s ActionP
laye
r 1’
s A
ctio
n
23
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
Nash Equilibrium
24
If any player can improvehis payoff by changing hisaction, given his opponents’actions, then it is not a Nashequilibrium
Is (Mum, Mum) an equilibrium? No, if player 2 is playing Mum
player 1 gains by deviating
A strategy profile is a Nash Equilibrium if no player can gain by deviating
-1, -1 -10, 0
0, -10 -5, -5
Mum Rat
Mum
Rat
Player 2’s Action
Pla
yer
1’s
Act
ion
25
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
best response to each action by his opponent
Circle payoff from player 2’sbest response to each action
Any box with both payoffscircled is an equilibrium
Because each player is playinga best-response to his opponent’s action…
…so neither one can improve by changing his strategy
In two-player games, we find Nash equilibria by highlighting best responses
-1, -1 -10, 0
0, -10 -5, -5
Mum Rat
Mum
Rat
Player 2’s Action
Pla
yer
1’s
Act
ion
26
Another classic: Battle of the Sexes
(Story)
Circle player 1’sbest responses
Circle player 2’sbest responses
We find two equilibria: (ballgame, ballgame) and (opera, opera) Game theory usually doesn’t have that much to say about which
equilibrium will get played when there are more than one
Some games will have more than one equilibrium
6, 3 0, 0
0, 0 3, 6
Baseball Game Opera
BaseballGame
Opera
Player 2’s Action
Pla
yer
1’s
Act
ion
27
Growth model
(Story)
Circle player 1’sbest responses
Circle player 2’sbest responses
Two equilibria: (invest, invest)and (consume, consume) Some papers explain differences in growth across countries by
saying some are in “good” equilibrium and some are in “bad” one
Sometimes, there will be a “good” and a “bad” equilibrium
2, 2 0, 1
1, 0 1, 1
Invest Consume
Invest
Consume
Player 2’s Action
Pla
yer
1’s
Act
ion
28
Scissors, Paper, Rock for $1 Look for Nash
Equilibria by circling best responses
No square with both payoffs circled
No equilibrium where each player plays a single action
In this class, we’ll focus on games with a pure-strategyNash equilibrium
Some games don’t have any equilibrium where players only play one action
0, 0 1, -1
-1, 1 0, 0
Scissors Paper
Scissors
Paper
Player 2’s Action
Pla
yer
1’s
Act
ion -1, 1
1, -1
Rock
1, -1 -1, 1Rock 0, 0
29
Now on to…
That’s a very quick introduction to static games
30
Property Law
31
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
Why do we need property law at all?
32
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
Like Prisoner’s Dilemma both farmers stealing is the only equilibrium but that outcome is Pareto-dominated by both farmers farming
Why do we need property law?
10, 10 -5, 12
12, -5 0, 0
Farm Steal
Farm
Steal
Player 2
Pla
yer
1
33
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
So how do we fix the problem?
34
So how do we fix the problem?
10 – c, 10 – c -5 – c, 12 – P
12 – P, -5 – c -P, -P
Farm Steal
Farm
Steal
Player 2
Pla
yer
110, 10 -5, 12
12, -5 0, 0
Farm Steal
Farm
Steal
Player 2
Pla
yer
1
MODIFIED GAMEORIGINAL GAME
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
35
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
So the idea here…
36
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?
Overview of Property Law
37
BUT…
http://www.msnbc.msn.com/id/21088150/
Answers to many of these seem obvious
38
Please see me if you’re not yet registered
Take a look at Coase, “The Problem of Social Cost”
Have a good weekend
Monday: Coase
39
(I doubt we’ll get to…)
40
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?
One early, “classic” property law case
41
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
Pierson v. Post
42
Pierson gets the fox
simpler rule (finders keepers)
easier to implement
fewer disputes
Same tradeoff we saw earlier:
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