Econ 522 Economics of Law

1. Econ 522Economics of Law Dan Quint Spring 2010 Lecture 16

2. The law as a setof incentives

3. The law as incentives – HW2 Q3(from old midterm) A physician comes upon an auto accident, stops, and treats an unconscious and badly bleeding victim. A week later the victim receives a bill for services rendered. Must he pay it? Under current U.S. law the answer is yes. Consider the following alternatives: i. The victim need not pay anything ii. The victim must pay only the value of whatever materials were used up in treating him (bandages, etc.) iii. The victim must pay the going market rate for comparable medical services iv. The victim must pay whatever the doctor demands Which of these do you expect to lead to the most efficient outcomes? Why?

4. If we think about payoffs after the fact(after accident, after treatment)… • Suppose value of treatment is $100,000, cost of materials $50, value of doctor’s time $450, market rate $1,000 • After the fact, all remedies are equally efficient • So this can’t be the right way to think about the problem! PayNothing Cost of Materials MarketRate Whatever Doc Asks Patient’s Payoff $100,000 $99,950 $99,000 -$900,000 Doctor’s Payoff -500 -450 500 999,500 Combined Payoffs 99,500 99,500 99,500 99,500

5. So what is the right way to think about the problem? • Need to think about incentive each rule creates, therefore the behavior it will lead to • Patient pays nothing • Patient pays for materials • Patient pays market rate • Patient pays whatever doctor asks

6. Something to remember distributionbut notefficiency efficiency

7. Back totort law

8. Monday… • Elements of a tort • Harm; causation; breach of duty (negligence) • Strict liability: no need to prove negligence, just harm and causation • Negligence: need to prove all three elements • Precaution: any actions taken to reduce likelihood of an accident • Today: economic model of torts

9. Precaution • The more carefully I drive, the less likely I am to hit you • But, driving more carefully is also more costly to me • Must be some efficient level of care

10. Precaution • The more carefully I drive, the less likely I am to hit you • But, driving more carefully is also more costly to me • Must be some efficient level of care • What determines how carefully I drive is what I think will happen if I hit you • Tort law creates incentives • We ended Monday with two questions: • What is the efficient level of precaution? • How do we design the law to achieve it? • Like with nuisance and contract law… easiest way is to design the law so that I internalize the externality I cause when I hit you

11. x level of precautionw marginal cost of precautionp(x) probability of an accidentA cost of an accident Model of unilateral harm • Unilateral harm – just one victim • Precaution – costly actions that make accident less likely • Could be taken by either victim or injurer • We’ll focus on one at a time • Notation • x – the amount of precaution that is taken • w – the cost of each “unit” of precaution • so total cost of precaution is wx • p(x) – probability of an accident, given precaution x • p is decreasing in x • A – cost of accident (to victim) • so expected cost of accidents is p(x) A

12. x level of precautionw marginal cost of precautionp(x) probability of an accidentA cost of an accident Model of unilateral harm $ wx + p(x) A(Total Social Cost) wx (Cost of Precaution) p(x) A (Cost of Accidents) Precaution (x) x* (Efficient Level of Precaution)

13. x level of precautionw marginal cost of precautionp(x) probability of an accidentA cost of an accident Model of unilateral harm efficient precaution: minx { wx + p(x) A } w + p’(x) A = 0 w = – p’(x) A • Under reasonable assumptions (p(x) convex)… • x < x*  w < – p’(x) A MSC < MSB  more precaution efficient • x > x*  w > – p’(x) A MSC > MSB  less precaution efficient • x = x*  MSC = MSB marginal social cost of precaution marginal social benefit of precaution

14. x level of precautionw marginal cost of precautionp(x) probability of an accidentA cost of an accident Model of unilateral harm $ wx + p(x) A wx p(x) A x x < x* x* x > x*

15. Model of unilateral harm • We haven’t yet said who is taking precaution • Some situations, only injurer can reduce accidents • Some situations, victim can too • Bilateral precaution is a little bit tricky, but if we look at the two parties one at a time, everything works fine • Next: consider effect of different liability rules on precaution

16. Effect of Liability Ruleson Precaution

17. Effect of liability rules on precaution • Three rules we’ll consider: • No liability • Strict liability • Negligence

18. Rule 1: No Liability • In a world with no liability… • Victim bears the cost of any accidents, plus the cost of any precaution he takes • Injurer bears cost of any precaution he takes, does not have to pay for accidents

19. Rule 1: No LiabilityInjurer precaution $ Private cost to injurer wx + p(x) A wx p(x) A x x* • Injurer’s private cost is just wx • Injurer minimizes private cost by setting x = 0

20. Rule 1: No LiabilityVictim precaution $ Private cost to victim wx + p(x) A wx p(x) A x x* • Victim’s private cost is wx + p(x) A • To minimize this, victim takes efficient level of precaution

21. Rule 1: No Liability • So in a world with no liability… • Injurer takes inefficiently low level of precaution • (zero, or minimal amount) • Victim takes efficient amount of precaution

22. Rule 2: Strict Liability • Perfect compensation: damages D = A • Under strict liability… • Injurer pays damages for any accidents he causes • So injurer bears cost of accidents, plus his own precaution • Victim pays only for his precaution

23. Rule 2: Strict LiabilityInjurer precaution $ Private cost to injurer wx + p(x) A wx p(x) A x x* • Injurer’s private cost is wx + p(x) A • Injurer minimizes this by taking efficient level of precaution

24. Rule 2: Strict LiabilityVictim precaution $ Private cost to victim wx + p(x) A wx p(x) A x x* • Victim’s private cost is wx • No incentive to take any precaution, victim sets x = 0

25. Effect of liability rules on precaution Victimprecaution Injurerprecaution No Liability Efficient Zero Strict Liability Zero Efficient

26. So for accidents with unilateral precaution… • When it’s the injurer who can take precautions, a rule of strict liability is more efficient • When it’s the victim who can take precautions, a rule of no liability is more efficient • Each rule works well for one incentive, poorly for other • Similar to paradox of compensation we saw in contract law • Negligence rule may allow us to get both incentives right

27. Rule 3: Simple Negligence • “Simple Negligence” rule • Legal standard of care xn • Injurer is liable for damages if precaution level was below the legal standard of care • x < xn D = A • x ³ xn  D = 0 • So on our graph from before, private cost to injurer is… • wx + p(x) A for x < xn • wx for x ³ xn

28. Rule 3: Simple NegligenceInjurer precaution $ Private cost to injurer wx + p(x) A wx p(x) A x xn = x* • Private cost is wx + p(x) A if x < xn, only wx otherwise • If standard of care is set efficiently (xn = x*), injurer minimizes private cost by taking efficient precaution

29. Rule 3: Simple NegligenceVictim precaution • What about victim? • We just said, injurer will take efficient precaution • Which means injurer will not be liable • So victim bears costs of any accidents • (Victim bears residual risk) • So victim’s private cost is wx + p(x) A • Victim minimizes private cost by taking efficient level of precaution too! $ Private cost to victim (assuming injurer takes efficient level of precaution and is therefore not liable for damages) wx + p(x) A wx p(x) A x*

30. Effect of liability rules on precaution Victimprecaution Injurerprecaution No Liability Efficient Zero Strict Liability Zero Efficient Simple Negligence,with xn = x* Efficient Efficient

31. For bilateral precaution, there are several ways to implement a negligence rule • Rule we just saw: injurer is liable if he was negligent, not liable if he was not • “Simple Negligence” • But we can consider both whether injurer was negligent… • …and whether victim was negligent… • …when determining whether injurer owes damages(and how much)

32. Different negligence rules Does injurer owe victim damages when… Neither party negligent? Only victim negligent? Only injurer negligent? Both parties negligent? Simple Negligence No No Yes Yes Negligence with Defense of Contributory Negligence No No Yes No

33. Different negligence rules Does injurer owe victim damages when… Neither party negligent? Only victim negligent? Only injurer negligent? Both parties negligent? Simple Negligence No No Yes Yes Negligence with Defense of Contributory Negligence No No Yes No Comparative Negligence No No Yes Partial Strict Liability with Defense of Contributory Negligence Yes No Yes No

34. Here’s the cool part… • When standards of care for both injurer and victim are set to the efficient level… • …anyof these negligence rules lead to efficient level of precaution by both parties! • Already saw this works for simple negligence • Could show the others the same way • Instead, we’ll do a discrete example

35. Discrete example ofbilateral precaution A $1,000w $20 for either partyp 10% / 6% / 2% • No “levels” of precaution – each party can either take precaution or not • Each accident causes $1,000 of harm • Precaution costs $20 for each party • Chance of an accident is • 10% if nobody takes precaution • 6% if one party takes precaution • 2% if both parties take precaution • Note that precaution is efficient for both parties • Costs $20; reduces expected accidents by 4% X $1,000 = $40

36. Negligence with a Defenseof Contributory Negligence A $1,000w $20 for either partyp 10% / 6% / 2% • Injurer is liable if he was negligent… • Unless victim was negligent too • Precaution is a dominantstrategy for victim • If injurer is not takingprecaution, victim wantsto avoid liability • If injurer is takingprecaution, victim bearsresidual risk, wants tominimize accidents • For injurer, precaution is the best-response to precaution • “Both take precaution” is the only Nash equilibrium Victim Precaution None -20, -40 -20, -60 Precaution Injurer -60, -20 0, -100 None 35

37. Comparative Negligence A $1,000w $20 for either partyp 10% / 6% / 2% • If both parties were negligent… • …divide cost proportionally • Precaution is again adominant strategy forvictim • Now it’s a dominant strategyfor injurer too • Again, “both take precaution” is the only equilibrium Victim Precaution None -20, -40 -20, -60 Precaution Injurer -60, -20 -50, -50 None 36

38. Strict Liability with a Defenseof Contributory Negligence A $1,000w $20 for either partyp 10% / 6% / 2% • Now, injurer is liable,regardless of whetherhe was negligent… • …unless victimwas negligent • Once again, “bothtake precaution” isthe only equilibrium Victim Precaution None -40, -20 -20, -60 Precaution Injurer -60, -20 0, -100 None 37

39. So even with bilateral precaution… Victimprecaution Injurerprecaution No Liability Efficient Zero Strict Liability Zero Efficient Simple negligence Efficient Efficient Negligence with Defense of Contributory Negligence Efficient Efficient assuming standards of care are set equal to efficient levels Comparative negligence Efficient Efficient Strict Liability with Defense of Contributory Negligence Efficient Efficient

40. (I mentioned, with bilateral precaution, things occasionally get more complicated…) • Redundant precaution – either party could take precaution, efficiency only requires one of them • If precaution is continuous, any negligence rule still leads to efficient precaution level by both • When precaution is discontinuous, not always • Driver can fasten seatbelt, or car company can design seatbelt that buckles itself (more costly) • Simple negligence: car company might be liable if designed manual seatbelt and driver didn’t use it, so car company might design automatic belt • Negligence with defense of contributory negligence: car company escapes liability, so designs manual belt, rational driver uses it • But as long as precaution is continuous, no problem

41. So far, our results seem to favor negligence rules… but… Victimprecaution Injurerprecaution No Liability Efficient Zero Strict Liability Zero Efficient Efficient Efficient Any negligence rule with efficient legal standards of care • Next week: activity levels • Steven Shavell, “Strict Liability Versus Negligence”