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 commons
e.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
max B ( x )  C ( x ).
x0
First-order condition is
B  ( x )  C  ( x ).
Notice that marginal costs matter more than
do total costs.
Crime and Punishment
B(x)
C(x), low MC
B ( x )  C  ( x )
x*
x
Crime and Punishment
B(x)
C(x), higher, but
same MC
C(x), low MC
B ( x )  C  ( x )
x*
x
No change to illegal activity level.
Crime and Punishment
B(x)
C(x), low MC
B ( x )  C  ( x )
x*
x
Crime and Punishment
B(x)
C(x), high MC
C(x), low MC
B ( x )  C  ( x )
x*
x
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
max B ( x )   ( e )C ( x ).
x0
Crime and Punishment
 Given
e, the criminal’s problem is
max B ( x )   ( e )C ( x ).
x0
 First-order
condition is
B  ( x )   ( e )C  ( x ).
Crime and Punishment
 Given
e, the criminal’s problem is
max B ( x )   ( e )C ( x ).
x0
 First-order
condition is
B  ( x )   ( e )C  ( x ).
e  low (e)  low marg. cost.
 High e  high (e)  high marg. cost.
 Low
Crime and Punishment
B(x)
el  eh
MC   ( eh )C  ( x )
MC   ( el )C  ( x )
B  ( x )   ( e )C  ( x )
x*
x
Higher police effort deters crime.
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. min c ( x )  L( x ).
x
IN
Liability Law
 Society
wishes to minimize total
cost; i.e. min c ( x )  L( x ).
x
 Social
IN
optimality requires
cIN
 ( x*)   L  ( x*).
 I.e. IN’s private marginal cost of effort
equals marginal benefit of her extra
effort.
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 x   0.
 No liability results in suboptimal low
care level and excessive injury.
Liability Law
 Full
Liability Rule:
 IN faces private cost and V’s costs,
cIN(x) + L(x).
 Hence chooses the socially optimal
effort level x * where
cIN
 ( x*)   L  ( x*).
Liability Law
Rule: IN is liable for V’s
loss if and only if care effort level
x  x~, a legally determined effort
level.
 Negligence
Liability Law
Rule: IN is liable for V’s
loss if and only if care effort level
x  x~, a legally determined effort
level.
~  x *, the
 What if the court sets x
socially optimal effort level?
 Negligence
Liability Law
x  x *  full liability for IN;
hence she chooses x  x*.
 So
Liability Law
x  x *  full liability for IN;
hence she chooses x  x*.
 And x  x *  no liability for IN;
hence she chooses x  x*.
 So
Liability Law
x  x *  full liability for IN;
hence she chooses x  x*.
 And x  x *  no liability for IN;
hence she chooses x  x*.
 I.e. the negligence rule is socially
optimal when x~  x*.
 So
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 x  x *.
 Victims prefer full liability; injurers
prefer the negligence rule.
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
min cV ( xV )  cIN ( xIN )  L( xV , xIN ).
xV , xIN
Bilateral Accidents
 Society
wishes to
min cV ( xV )  cIN ( xIN )  L( xV , xIN ).
xV , xIN
 Social
optimality requires
V’s MC of effort = MB of his effort
IN’s MC of effort = MB of her effort.
 I.e.
*
* *
cV
 ( xV )    L( xV , xIN ) /  xV
*
* *
cIN
 ( xIN )    L( xV , xIN ) /  xIN
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 xV  0.
 Full liability is socially suboptimal in
bilateral accidents.
Bilateral Accidents
 Strict
Division of Losses: IN must
pay a fixed fraction, f, of loss caused.
 IN minimizes cIN ( xIN )  f L ( xV , xIN ).
 IN chooses effort xIN
 satisfying
cIN ( xIN
 )   f  L( xV , xIN ) /  xIN .
Bilateral Accidents
 IN
 satisfying
chooses effort xIN
cIN ( xIN
 )   f  L( xV , xIN ) /  xIN .
 Optimality
requires
cIN
 ( x*IN )    L( x*V , x*IN ) /  xIN
 Since f < 1, IN chooses less than the
*
optimal effort level; xIN
  xIN .
Bilateral Accidents
 IN
 satisfying
chooses effort xIN
cIN ( xIN
 )   f  L( xV , xIN ) /  xIN .
 Optimality
requires
cIN
 ( x*IN )    L( x*V , x*IN ) /  xIN
 Since f < 1, IN chooses less than the
*
optimal effort level; xIN
  xIN .
 Strict division of losses is a socially
suboptimal liability rule.
Bilateral Accidents
 Negligence
Rule: IN is fully liable for
loss only if her effort level x  x~ , a
legally determined effort level.
 Social optimality requires V and IN to
choose effort levels
xV  x*V and xIN  x*IN , where
*
* *
cV
 ( xV )    L( xV , xIN ) /  xV
*
* *
and cIN
 ( xIN )    L( xV , xIN ) /  xIN .
Bilateral Accidents
*
 Suppose V chooses xV  xV .
 Then
IN is fully liable and wishes to
*
min cIN ( xIN )  L( xV , xIN ).
xIN
 I.e.
IN chooses xIN  x*IN .
Bilateral Accidents
*
 Now suppose IN chooses xIN  xIN .
 Then
V wishes to
*
min cV ( xV )  L( xV , xIN ).
xV
 I.e.
V chooses xV  x*V .
Bilateral Accidents
*
 Now suppose IN chooses xIN  xIN .
 Then
V wishes to
*
min cV ( xV )  L( xV , xIN ).
xV
V chooses xV  x*V .
 The Nash equilibrium of the
negligence rule game is the socially
optimal outcome.
 I.e.
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 x~ .
*
~
 If society chooses x  xV and V
*
chooses xV  xV , then IN is fully
liable, so her best reply is xIN  x*IN .
Bilateral Accidents
 IN
is fully liable unless V’s care level
is less than a specified level x~ .
*
~
 If society chooses x  xV and V
*
chooses xV  xV , then IN is fully
liable, so her best reply is xIN  x*IN .
*
 If IN chooses xIN  xIN , then V’s best
reply is xV  x*V .
Bilateral Accidents
 IN
is fully liable unless V’s care level
is less than a specified level x~ .
*
~
 If society chooses x  xV and V
*
chooses xV  xV , then IN is fully
liable, so her best reply is xIN  x*IN .
*
 If IN chooses xIN  xIN , then V’s best
reply is xV  x*V .
 I.e. the rule causes a socially optimal
Nash equilibrium.
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, c.
 Market demand is x ( p ).
Treble Damages & Antitrust Law
 Assume
firms collude to form a
cartel with a constant marginal
production cost, c.
 Market demand is x ( p ).
 Cartel’s goal is max  ( p )  ( p  c ) x ( p ).
p
Treble Damages & Antitrust Law
 Assume
firms collude to form a
cartel with a constant marginal
production cost, c.
 Market demand is x ( p ).
 Cartel’s goal is max ( p  c ) x ( p ).
 Solution
is p  p
p
m
 x m  x ( p m ).
Treble Damages & Antitrust Law
fixing price at p results in
damages D( p ) to a victim V.
 V’s probability of winning suit
against the cartel is  .
 If V wins, the cartel must pay  D( p ).
 Suppose
Treble Damages & Antitrust Law
fixing price at p results in
damages D( p ) to a victim V.
 V’s probability of winning suit
against the cartel is  .
 If V wins, the cartel must pay  D( p ).
 Cartel’s problem is now
max ( p  c ) x ( p )   D( p ).
 Suppose
p
Treble Damages & Antitrust Law
 Cartel’s
problem is now
max ( p  c ) x ( p )   D( p ).
p
 Solution
is not generally the same as
for the original problem max ( p  c ) x ( p ).
p
 So
generally cartel behavior is
affected by the penalty.
Treble Damages & Antitrust Law
case -- suppose D( p ) is the
cartel’s profit. The cartel’s goal is
 Special
max ( p  c ) x ( p )   D( p )  (1   )( p  c ) x ( p ).
p
Treble Damages & Antitrust Law
case -- suppose D( p ) is the
cartel’s profit. The cartel’s goal is
 Special
max ( p  c ) x ( p )   D( p )  (1   )( p  c ) x ( p ).
p
 Maximizing
after-penalty profit
requires maximizing before-penalty
profit.
Treble Damages & Antitrust Law
case -- suppose D( p ) is the
cartel’s profit. The cartel’s goal is
 Special
max ( p  c ) x ( p )   D( p )  (1   )( p  c ) x ( p ).
p
 Maximizing
after-penalty profit
requires maximizing before-penalty
profit.
 The cartel’s behavior is unaffected by
the penalty.
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 quasilinear; u( x )  m  px .
 Consumer can win damages
D   ( p  c ) x .
 So
consumer’s goal is
max u( x )  m  px   ( p  c ) x .
x
Treble Damages & Antitrust Law
 Consumer’s
goal is
max u( x )  m  px   ( p  c ) x .
 I.e.
x
max u( x )  m  [ p   ( p  c ) ]x .
x
Treble Damages & Antitrust Law
 Consumer’s
goal is
max u( x )  m  px   ( p  c ) x .
 I.e.
x
p   ( p  c ) ]x .
max u( x )  m  [ 


x
effective price, p
Treble Damages & Antitrust Law
 Consumer’s
goal is
max u( x )  m  [ p   ( p  c ) ]x .


x
effective price, p
 Since
consumer’s action depends
upon the effective price, rewrite the
cartel’s problem as max ( p  c ) x ( p ).
p
Treble Damages & Antitrust Law
 Consumer’s
goal is
max u( x )  m  [ p   ( p  c ) ]x .


x
effective price, p
 Since
consumer’s action depends
upon the effective price, rewrite the
cartel’s problem as max ( p  c ) x ( p ).
p
 Solution is the same
m
as the original problem; p  p .
Treble Damages & Antitrust Law
 Solution
is the same as the original
m
problem; p  p .
 p* is the price paid by buyers. Then
m pm  p * 
p  p *  ( p *  c ).
Treble Damages & Antitrust Law
 Solution
is the same as the original
m
problem; p  p .
 p* is the price paid by buyers. Then
m
p  p *  ( p *  c ).
 So
m
m
p   c
m  ( p  c )
m
p* 
 p 
p .
1  
1  
Treble Damages & Antitrust Law
m

m
p   c
m  ( p  c )
m
p* 
 p 
p .
1  
1  
m
cartel’s price p*  p , 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.
 The