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 criminal’s problem is

14. Crime and Punishment Given e, the criminal’s problem is
First-order condition is

15. 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.

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 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 .

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. IN’s 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 V’s costs, cIN(x) + L(x).
Hence chooses the socially optimal effort level where

25. Liability Law
Negligence Rule: IN is liable for V’s loss if and only if care effort level , a legally determined effort level.

26. 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?

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 IN’s 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 IN’s 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 V’s MC of effort = MB of his effort IN’s 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 < 1, IN chooses less than the optimal effort level;

40. 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.

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 V’s care level is less than a specified level

46. 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

47. 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

48. 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.

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
Cartel’s goal is

53. 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

54. 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

55. 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

56. 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.

57. Treble Damages & Antitrust Law
Special case -- suppose is the cartel’s profit. The cartel’s goal is

58. 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.

59. 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.

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 consumer’s goal is

62. Treble Damages & Antitrust Law
Consumer’s goal is
I.e.

63. Treble Damages & Antitrust Law
Consumer’s goal is
I.e.

64. Treble Damages & Antitrust Law
Consumer’s goal is
Since consumer’s action depends upon the effective price, rewrite the cartel’s problem as

65. 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 same as 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 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.