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?


x0max B x C x( ) ( ).

First-order condition is

B x C x( ) ( ).

Notice that marginal costs matter more thando total costs.


B x C x( ) ( )

B(x)

C(x), low MC

xx*


B x C x( ) ( )

B(x)

C(x), low MC

xx*

C(x), higher, butsame MC

No change to illegal activity level.


B x C x( ) ( )

B(x)

C(x), low MC

xx*


B x C x( ) ( )

B(x)

C(x), low MC

C(x), high MC

xx*Higher marginal costs deter crime.


Detection of a criminal is uncertain. e is police effort. (e) is detection probability;

(e) = 0 if e = 0(e) as e .


Given e, the criminal’s problem is

x0max B x e C x( ) ( ) ( ).




x0max B x e C x( ) ( ) ( ).

B x e C x( ) ( ) ( ).




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( ) ( ) ( ).


B x e C x( ) ( ) ( )

B(x)

xx*Higher police effort deters crime.

MC ( ) ( )e C xh

MC ( ) ( )e C xl

e el h


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?


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


And no liability for IN; hence she chooses

x x *x x *.

x x *x x *.

Liability Law


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;


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.


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



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



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?


Assume firms collude to form a cartel with a constant marginal production cost,

Market demand is

c.

x p( ).



Market demand is Cartel’s goal is

c.

x p( ).

pmax ( ) ( ) ( ).p p c x p



Market demand is Cartel’s goal is

Solution is

c.

x p( ).

pmax ( ) ( ).p c x p

p p x x pm m m ( ).


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( ).


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


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


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



Maximizing after-penalty profit requires maximizing before-penalty profit.

D p( )

pmax ( ) ( ) ( ) ( )( ) ( ).p c x p D p p c x p 1



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


What if consumers can seek to be damaged?


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


Consumer’s goal is

I.e.


u x m p p c x( ) [ ( ) ] . maxx



I.e.u x m p p c x

p

( ) [ ( ) ] .

effective price, max

x




Since consumer’s action depends upon the effective price, rewrite the cartel’s problem as

u x m p p c x

p

( ) [ ( ) ] .


x

maxp

( ) ( ).p c x p



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

( ) [ ( ) ] .


x

maxp

( ) ( ).p c x p

.p pm


Solution is the same as the original problem;

is the price paid by buyers. Then

.p pmp*

p pm *p p p cm * ( * ).


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


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

chapter thirty-three

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