Chapter Thirty-Three

1
Chapter Thirty-Three

• Law and Economics

2
Effects of Laws

• Property right assignments affect
• asset, income and wealth distributions
• e.g. nationalized vs. privately owned industry.

3
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.

4
Effects of Laws

• Punishments affect
• incentives for illegal behavior
• e.g. high speeding fines can reduce the amount of
  speeding.

5
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.

6
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?

7
Crime and Punishment
First-order condition is
Notice that marginal costs matter more than do
total costs.
8
Crime and Punishment
B(x)
C(x), low MC
9
Crime and Punishment
B(x)
C(x), higher, but same MC
C(x), low MC
No change to illegal activity level.
10
Crime and Punishment
B(x)
C(x), low MC
11
Crime and Punishment
B(x)
C(x), high MC
C(x), low MC
Higher marginal costs deter crime.
12
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 ?.

13
Crime and Punishment

• Given e, the criminals problem is

14
Crime and Punishment

• Given e, the criminals problem is
• First-order condition is

15
Crime and Punishment

• Given e, the criminals problem is
• First-order condition is
• Low e ? low ?(e) ? low marg. cost.
• High e ? high ?(e) ? high marg. cost.

16
Crime and Punishment
B(x)
Higher police effort deters crime.
17
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?

18
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.

19
Liability Law

• An injurer, IN, and a victim, V.
• x is effort by IN to avoid injuring V.
• cIN(x) is INs cost of effort x cIN(x) ? as x
  ?.
• L(x) is Vs loss when INs effort is x L(x) ?
  as x ?.

20
Liability Law

• Society wishes to minimize total cost i.e.

21
Liability Law

• Society wishes to minimize total cost i.e.
• Social optimality requires
• I.e. INs private marginal cost of effort equals
  marginal benefit of her extra effort.

22
Liability Law

• Liability rules
• no liability rule
• strict liability rule
• negligence rule.
• Which is best?

23
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.

24
Liability Law

• Full Liability Rule
• IN faces private cost and Vs costs, cIN(x)
  L(x).
• Hence chooses the socially optimal effort level
  where

25
Liability Law

• Negligence Rule IN is liable for Vs loss if
  and only if care effort level , a legally
  determined effort level.

26
Liability Law

• Negligence Rule IN is liable for Vs loss if
  and only if care effort level , a legally
  determined effort level.
• What if the court sets , the socially
  optimal effort level?

27
Liability Law

• So ? full liability for IN hence
  she chooses

28
Liability Law

• So ? full liability for IN hence
  she chooses
• And ? no liability for IN hence she
  chooses

29
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

30
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 INs
  care effort level .

31
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 INs
  care effort level .
• Victims prefer full liability injurers prefer
  the negligence rule.

32
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

33
Bilateral Accidents

• Society wishes to
• Social optimality requires Vs MC of effort
  MB of his effort INs MC of effort MB of her
  effort.
• I.e.

34
Bilateral Accidents

• No Liability Both V and IN face only their
  private effort costs, not the full social costs
  of their actions.

35
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.

36
Bilateral Accidents

• Full Liability V is fully compensated for all
  injury costs.

37
Bilateral Accidents

• Full Liability V is fully compensated for all
  injury costs.
• Hence V chooses
• Full liability is socially suboptimal in
  bilateral accidents.

38
Bilateral Accidents

• Strict Division of Losses IN must pay a fixed
  fraction, f, of loss caused.
• IN minimizes
• IN chooses effort satisfying

39
Bilateral Accidents

• IN chooses effort satisfying
• Optimality requires
• Since f lt 1, IN chooses less than the optimal
  effort level

40
Bilateral Accidents

• IN chooses effort satisfying
• Optimality requires
• Since f lt 1, IN chooses less than the optimal
  effort level
• Strict division of losses is a socially
  suboptimal liability rule.

41
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

and
, where
and
42
Bilateral Accidents

• Suppose V chooses
• Then IN is fully liable and wishes to
• I.e. IN chooses

43
Bilateral Accidents

• Now suppose IN chooses
• Then V wishes to
• I.e. V chooses

44
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.

45
Bilateral Accidents

• Strict Liability with Defense of Contributory
  Negligence Rule IN is fully liable unless Vs
  care level is less than a specified level

46
Bilateral Accidents

• IN is fully liable unless Vs care level is less
  than a specified level
• If society chooses and V chooses
  , then IN is fully liable, so her best
  reply is

47
Bilateral Accidents

• IN is fully liable unless Vs 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 Vs best
  reply is

48
Bilateral Accidents

• IN is fully liable unless Vs 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 Vs best
  reply is
• I.e. the rule causes a socially optimal Nash
  equilibrium.

49
Bilateral Accidents

• Notes
• socially optimal liability rules do not generally
  fully compensate the victim.
• socially optimal accident deterrence is distinct
  from optimal accident compensation.

50
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?

51
Treble Damages Antitrust Law

• Assume firms collude to form a cartel with a
  constant marginal production cost,
• Market demand is

52
Treble Damages Antitrust Law

• Assume firms collude to form a cartel with a
  constant marginal production cost,
• Market demand is
• Cartels goal is

53
Treble Damages Antitrust Law

• Assume firms collude to form a cartel with a
  constant marginal production cost,
• Market demand is
• Cartels goal is
• Solution is

54
Treble Damages Antitrust Law

• Suppose fixing price at results in damages
  to a victim V.
• Vs probability of winning suit against the
  cartel is
• If V wins, the cartel must pay

55
Treble Damages Antitrust Law

• Suppose fixing price at results in damages
  to a victim V.
• Vs probability of winning suit against the
  cartel is
• If V wins, the cartel must pay
• Cartels problem is now

56
Treble Damages Antitrust Law

• Cartels problem is now
• Solution is not generally the same as for the
  original problem
• So generally cartel behavior is affected by the
  penalty.

57
Treble Damages Antitrust Law

• Special case -- suppose is the cartels
  profit. The cartels goal is

58
Treble Damages Antitrust Law

• Special case -- suppose is the cartels
  profit. The cartels goal is
• Maximizing after-penalty profit requires
  maximizing before-penalty profit.

59
Treble Damages Antitrust Law

• Special case -- suppose is the cartels
  profit. The cartels goal is
• Maximizing after-penalty profit requires
  maximizing before-penalty profit.
• The cartels behavior is unaffected by the
  penalty.

60
Treble Damages Antitrust Law

• What if consumers can seek to be damaged?

61
Treble Damages Antitrust Law

• What if consumers can seek to be damaged?
• Suppose consumer utility is quasi-linear
• Consumer can win damages
• So consumers goal is

62
Treble Damages Antitrust Law

• Consumers goal is
• I.e.

63
Treble Damages Antitrust Law

• Consumers goal is
• I.e.

64
Treble Damages Antitrust Law

• Consumers goal is
• Since consumers action depends upon the
  effective price, rewrite the cartels problem as

65
Treble Damages Antitrust Law

• Consumers goal is
• Since consumers action depends upon the
  effective price, rewrite the cartels problem as
• Solution is the sameas the original problem

66
Treble Damages Antitrust Law

• Solution is the same as the original problem
• is the price paid by buyers. Then

67
Treble Damages Antitrust Law

• Solution is the same as the original problem
• is the price paid by buyers. Then
• So

68
Treble Damages Antitrust Law

• The cartels 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.