Download - Chapter Thirty-Three
Chapter Thirty-Three
Law and Economics
Effects of Laws
Property right assignments affect
– asset, income and wealth distributions;e.g. nationalized vs. privately
owned industry.
Effects of Laws
Property right assignments affect
– asset, income and wealth distributions;e.g. nationalized vs. privately
owned industry.
– resource allocations; e.g. the tragedy of the commonse.g. patents encourage research.
Effects of Laws
Punishments affect
– incentives for illegal behavior;e.g. high speeding fines can
reduce the amount of speeding.
Effects of Laws
Punishments affect
– incentives for illegal behavior;e.g. high speeding fines can
reduce the amount of speeding.
– asset, income and wealth distributions;e.g. jail time results in lost
income.
Crime and Punishment
x is the quantity of an illegal activity produced by an individual.
C(x) is the production cost. B(x) is the benefit. Gain is B(x) - C(x). What is the rational choice of x?
Crime and Punishment
x0max B x C x( ) ( ).
First-order condition is
B x C x( ) ( ).
Notice that marginal costs matter more thando total costs.
Crime and Punishment
B x C x( ) ( )
B(x)
C(x), low MC
xx*
Crime and Punishment
B x C x( ) ( )
B(x)
C(x), low MC
xx*
C(x), higher, butsame MC
No change to illegal activity level.
Crime and Punishment
B x C x( ) ( )
B(x)
C(x), low MC
xx*
Crime and Punishment
B x C x( ) ( )
B(x)
C(x), low MC
C(x), high MC
xx*Higher marginal costs deter crime.
Crime and Punishment
Detection of a criminal is uncertain. e is police effort. (e) is detection probability;
(e) = 0 if e = 0(e) as e .
Crime and Punishment
Given e, the criminal’s problem is
x0max B x e C x( ) ( ) ( ).
Crime and Punishment
Given e, the criminal’s problem is
First-order condition is
x0max B x e C x( ) ( ) ( ).
B x e C x( ) ( ) ( ).
Crime and Punishment
Given e, the criminal’s problem is
First-order condition is
Low e low (e) low marg. cost. High e high (e) high marg. cost.
x0max B x e C x( ) ( ) ( ).
B x e C x( ) ( ) ( ).
Crime and Punishment
B x e C x( ) ( ) ( )
B(x)
xx*Higher police effort deters crime.
MC ( ) ( )e C xh
MC ( ) ( )e C xl
e el h
Crime and Punishment
Higher fines and larger police effort both raise marginal production costs of illegal activity.
Which is better for society -- higher fines, or more police effort?
Crime and Punishment
Higher fines and larger police effort both raise marginal production costs of illegal activity.
Which is better for society -- higher fines, or more police effort?
Police effort consumes resources; higher fines do not.
Better to fine heavily.
Liability Law
An injurer, IN, and a victim, V. x is effort by IN to avoid injuring V. cIN(x) is IN’s cost of effort x;
cIN(x) as x . L(x) is V’s loss when IN’s effort is x;
L(x) as x .
Liability Law
Society wishes to minimize total cost; i.e.
xmin c x L xIN( ) ( ).
Liability Law
Society wishes to minimize total cost; i.e.
Social optimality requires
I.e. IN’s private marginal cost of effort equals marginal benefit of her extra effort.
xmin c x L xIN( ) ( ).
c x L xIN ( *) ( *).
Liability Law
Liability rules:
– no liability rule
– strict liability rule
– negligence rule. Which is best?
Liability Law
No Liability Rule: IN faces only private cost, cIN(x). Hence chooses effort level No liability results in suboptimal low
care level and excessive injury.
x 0.
Liability Law
Full Liability Rule: IN faces private cost and V’s costs,
cIN(x) + L(x). Hence chooses the socially optimal
effort level where c x L xIN ( *) ( *).x*
Liability Law
Negligence Rule: IN is liable for V’s loss if and only if care effort level , a legally determined effort level.x x ~
Liability Law
Negligence Rule: IN is liable for V’s loss if and only if care effort level , a legally determined effort level.
What if the court sets , the socially optimal effort level?
x x ~
~ *x x
Liability Law
So full liability for IN; hence she chooses
x x *x x *.
Liability Law
So full liability for IN; hence she chooses
And no liability for IN; hence she chooses
x x *x x *.
x x *x x *.
Liability Law
So full liability for IN; hence she chooses
And no liability for IN; hence she chooses
I.e. the negligence rule is socially optimal when
x x *
x x *
~ *.x x
x x *.
x x *.
Liability Law Both full liability and negligence
rules are socially optimal, but full liability fully insures V always,
and the negligence rule fully insures V
only if IN’s care effort level .x x *
Liability Law Both full liability and negligence
rules are socially optimal, but full liability fully insures V always,
and the negligence rule fully insures V
only if IN’s care effort level . Victims prefer full liability; injurers
prefer the negligence rule.
x x *
Bilateral Accidents
V and IN can each exert effort to avoid a loss.
cV(xV) and cIN(xIN).
Loss is L(xV,xIN). Society wishes to
x xV IN
min,c x c x L x xV V IN IN V IN( ) ( ) ( , ).
Bilateral Accidents
Society wishes to
Social optimality requiresV’s MC of effort = MB of his effortIN’s MC of effort = MB of her effort.
I.e. c x L x x xV V
*V*
IN V( ) ( , ) /* c x L x x xIN IN
*V*
IN IN( ) ( , ) /*
x xV IN
min,c x c x L x xV V IN IN V IN( ) ( ) ( , ).
Bilateral Accidents
No Liability: Both V and IN face only their private effort costs, not the full social costs of their actions.
Bilateral Accidents
No Liability: Both V and IN face only their private effort costs, not the full social costs of their actions.
Hence V and IN both provide too little effort.
No liability is socially suboptimal.
Bilateral Accidents
Full Liability: V is fully compensated for all injury costs.
Bilateral Accidents
Full Liability: V is fully compensated for all injury costs.
Hence V chooses Full liability is socially suboptimal in
bilateral accidents.
xV 0.
Bilateral Accidents
Strict Division of Losses: IN must pay a fixed fraction, f, of loss caused.
IN minimizes IN chooses effort satisfying
c x f L x xIN IN V IN( ) ( , ).
c x f L x x xIN IN V IN IN( ) ( , ) / .
xIN
Bilateral Accidents
IN chooses effort satisfying
Optimality requires
Since f < 1, IN chooses less than the optimal effort level;
c x f L x x xIN IN V IN IN( ) ( , ) / .
x xIN IN* .
xIN
c x L x x xIN IN*
V*
IN IN( ) ( , ) /*
Bilateral Accidents
IN chooses effort satisfying
Optimality requires
Since f < 1, IN chooses less than the optimal effort level;
Strict division of losses is a socially suboptimal liability rule.
c x f L x x xIN IN V IN IN( ) ( , ) / .
x xIN IN* .
xIN
c x L x x xIN IN*
V*
IN IN( ) ( , ) /*
Bilateral Accidents
Negligence Rule: IN is fully liable for loss only if her effort level , a legally determined effort level.
Social optimality requires V and IN to choose effort levels
x x ~
c x L x x xV V*
V*
IN V( ) ( , ) /* c x L x x xIN IN
*V*
IN IN( ) ( , ) / .*
x xV V* x xIN IN
*and , where
and
Bilateral Accidents
Suppose V chooses Then IN is fully liable and wishes to
I.e. IN chooses
x xV V* .
xIN
min c x L x xIN IN V IN( ) ( , ).*
x xIN IN* .
Bilateral Accidents
Now suppose IN chooses Then V wishes to
I.e. V chooses
x xIN IN* .
xV
min c x L x xV V V IN( ) ( , ).*
x xV V* .
Bilateral Accidents
Now suppose IN chooses Then V wishes to
I.e. V chooses The Nash equilibrium of the
negligence rule game is the socially optimal outcome.
x xIN IN* .
xV
min c x L x xV V V IN( ) ( , ).*
x xV V* .
Bilateral Accidents
Strict Liability with Defense of Contributory Negligence Rule: IN is fully liable unless V’s care level is less than a specified level ~.x
Bilateral Accidents
IN is fully liable unless V’s care level is less than a specified level
If society chooses and V chooses , then IN is fully liable, so her best reply is
~.x~x x V
*
x xIN IN* .
x xV V*
Bilateral Accidents
IN is fully liable unless V’s care level is less than a specified level
If society chooses and V chooses , then IN is fully liable, so her best reply is
If IN chooses , then V’s best reply is
~.x
x xIN IN*
x xV V* .
~x x V*
x xIN IN* .
x xV V*
Bilateral Accidents
IN is fully liable unless V’s care level is less than a specified level
If society chooses and V chooses , then IN is fully liable, so her best reply is
If IN chooses , then V’s best reply is
I.e. the rule causes a socially optimal Nash equilibrium.
~.x
x xIN IN*
x xV V* .
~x x V*
x xIN IN* .
x xV V*
Bilateral Accidents
Notes:
– socially optimal liability rules do not generally fully compensate the victim.
– socially optimal accident deterrence is distinct from optimal accident compensation.
Treble Damages & Antitrust Law
The Sherman and Clayton Acts allow an agent damaged by price-fixing to sue and recover treble damages.
How does such a penalty affect the behavior of a price-fixing cartel?
Treble Damages & Antitrust Law
Assume firms collude to form a cartel with a constant marginal production cost,
Market demand is
c.
x p( ).
Treble Damages & Antitrust Law
Assume firms collude to form a cartel with a constant marginal production cost,
Market demand is Cartel’s goal is
c.
x p( ).
pmax ( ) ( ) ( ).p p c x p
Treble Damages & Antitrust Law
Assume firms collude to form a cartel with a constant marginal production cost,
Market demand is Cartel’s goal is
Solution is
c.
x p( ).
pmax ( ) ( ).p c x p
p p x x pm m m ( ).
Treble Damages & Antitrust Law
Suppose fixing price at results in damages to a victim V.
V’s probability of winning suit against the cartel is
If V wins, the cartel must pay
D p( )p
.
D p( ).
Treble Damages & Antitrust Law
Suppose fixing price at results in damages to a victim V.
V’s probability of winning suit against the cartel is
If V wins, the cartel must pay Cartel’s problem is now
D p( )p
.
D p( ).
pmax ( ) ( ) ( ).p c x p D p
Treble Damages & Antitrust Law
Cartel’s problem is now
Solution is not generally the same as for the original problem
So generally cartel behavior is affected by the penalty.
pmax ( ) ( ) ( ).p c x p D p
pmax ( ) ( ).p c x p
Treble Damages & Antitrust Law
Special case -- suppose is the cartel’s profit. The cartel’s goal is
D p( )
pmax ( ) ( ) ( ) ( )( ) ( ).p c x p D p p c x p 1
Treble Damages & Antitrust Law
Special case -- suppose is the cartel’s profit. The cartel’s goal is
Maximizing after-penalty profit requires maximizing before-penalty profit.
D p( )
pmax ( ) ( ) ( ) ( )( ) ( ).p c x p D p p c x p 1
Treble Damages & Antitrust Law
Special case -- suppose is the cartel’s profit. The cartel’s goal is
Maximizing after-penalty profit requires maximizing before-penalty profit.
The cartel’s behavior is unaffected by the penalty.
D p( )
pmax ( ) ( ) ( ) ( )( ) ( ).p c x p D p p c x p 1
Treble Damages & Antitrust Law
What if consumers can seek to be damaged?
Treble Damages & Antitrust Law
What if consumers can seek to be damaged?
Suppose consumer utility is quasi-linear;
Consumer can win damages
So consumer’s goal is
u x m px( ) .
D p c x ( ) .
u x m px p c x( ) ( ) . maxx
Treble Damages & Antitrust Law
Consumer’s goal is
I.e.
u x m px p c x( ) ( ) . maxx
u x m p p c x( ) [ ( ) ] . maxx
Treble Damages & Antitrust Law
Consumer’s goal is
I.e.u x m p p c x
p
( ) [ ( ) ] .
effective price, max
x
u x m px p c x( ) ( ) . maxx
Treble Damages & Antitrust Law
Consumer’s goal is
Since consumer’s action depends upon the effective price, rewrite the cartel’s problem as
u x m p p c x
p
( ) [ ( ) ] .
effective price, max
x
maxp
( ) ( ).p c x p
Treble Damages & Antitrust Law
Consumer’s goal is
Since consumer’s action depends upon the effective price, rewrite the cartel’s problem as
Solution is the sameas the original problem;
u x m p p c x
p
( ) [ ( ) ] .
effective price, max
x
maxp
( ) ( ).p c x p
.p pm
Treble Damages & Antitrust Law
Solution is the same as the original problem;
is the price paid by buyers. Then
.p pmp*
p pm *p p p cm * ( * ).
Treble Damages & Antitrust Law
Solution is the same as the original problem;
is the price paid by buyers. Then
So
.p pmp*
p p p cm * ( * ).
pp c
pp c
pm
mm
m*( )
.
1 1
Treble Damages & Antitrust Law
The cartel’s price , the price set in the absence of damage penalties.
But the effective price to both consumers and the cartel is the same as in the no damages case.
p pm*
pp c
pp c
pm
mm
m*( )
.
1 1