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Part D-II Part D-II

The Economics of Tort Law The Economics of Tort Law

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ObjectivesObjectives

Negligence rulesNegligence rules

Liability rules under bilateral precautionLiability rules under bilateral precaution

Efficient tort law under bilateral precautionEfficient tort law under bilateral precaution

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Risks characterized by Risks characterized by bilateral precautionbilateral precaution present us with a present us with a real problem: real problem:

How do we encourage (provide the appropriate incentives to) How do we encourage (provide the appropriate incentives to) both the potential injurer and the potential victim to both the potential injurer and the potential victim to internalize the total cost of harm (A) when they decide on internalize the total cost of harm (A) when they decide on the appropriate level of precaution? the appropriate level of precaution?

We know that no liability and strict liability/perfect damages We know that no liability and strict liability/perfect damages will not workwill not work

We know that simply dividing up the cost of harm will not We know that simply dividing up the cost of harm will not work. work.

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What is the efficient amount of precaution for each What is the efficient amount of precaution for each agent?agent?

In order to minimize the expected social costs of accidents In order to minimize the expected social costs of accidents both the potential victim and the potential injurer must both the potential victim and the potential injurer must ‘purchase’ an amount of precaution such that the marginal ‘purchase’ an amount of precaution such that the marginal cost of precaution (cost of precaution (wwv v and wand wii) is just equal to the decrease ) is just equal to the decrease in the expected cost of harm from the expenditure for both in the expected cost of harm from the expenditure for both the potential victim the potential victim

wwv v == - - ΔΔp(xp(xvv, x, xii)/)/ΔΔxxvv A A

and the potential injurer and the potential injurer

wwi i = = - - ΔΔp(xp(xvv, x, xii)/)/ΔΔxxii A A

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But again, But again,

We know that no liability and strict liability/perfect damages We know that no liability and strict liability/perfect damages will not workwill not work

We know that simply dividing up the cost of harm will not We know that simply dividing up the cost of harm will not work. work.

What to do?What to do?

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A Negligence Rule (a legal rule)A Negligence Rule (a legal rule)

A A negligence rulenegligence rule imposes a imposes a standard of carestandard of care on potential on potential injurers and/or potential victims. injurers and/or potential victims.

This This standard of carestandard of care sets the minimum legal level of sets the minimum legal level of precaution that a party must take in order to avoid liability precaution that a party must take in order to avoid liability for an for an accidentaccident. .

If an If an accidentaccident occurs and the injurer and/or victim has taken occurs and the injurer and/or victim has taken the minimum level of precaution, then they cannot be the minimum level of precaution, then they cannot be found to be found to be negligentnegligent (they are not liable). (they are not liable).

If an If an accidentaccident occurs and the injurer and/or victim has not occurs and the injurer and/or victim has not

taken the minimum level of precaution, then they can be taken the minimum level of precaution, then they can be found to be found to be negligentnegligent (they are liable). (they are liable).

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Can a negligence rule provide efficient incentives to Can a negligence rule provide efficient incentives to potential injurers and potential victims?potential injurers and potential victims?

First lets review the concept of First lets review the concept of negligencenegligence

Let x’ represent the Let x’ represent the legal standard of carelegal standard of care – the minimum – the minimum amount of precaution required in order to avoid being found amount of precaution required in order to avoid being found negligent (liable) if an accident occursnegligent (liable) if an accident occurs

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Legal Standard of Care for Continuous PrecautionLegal Standard of Care for Continuous Precaution

Pr(x=0Pr(x=0)) Pr(x=∞)Pr(x=∞)

100%100% 0%0%

ForbiddenForbidden zonezone Permitted zonePermitted zone

x’

x > x’x > x’x< x’x< x’

x’ = standard of carex’ = standard of care

x -----------x -----------

<---------- <---------- Pr. of accidentPr. of accident

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The expected costs of accidents for the potential The expected costs of accidents for the potential injurerinjurer

wwi i xxii + p(x’ + p(x’vv, x, xii)A)A

xxii

PrecautionPrecaution0

$

p(x’p(x’vv, x, xii)A)A

wwi i xxii

xx**ii

wwi i xxii + p(x’ + p(x’vv, x, xii)A)A

Note that we have assumed that the potential Note that we have assumed that the potential victim does not behave negligently xvictim does not behave negligently xvv = x’ = x’vv

Society wants the potential injurer

to choose x*i

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Potential injurer’s cost of accidents under a Potential injurer’s cost of accidents under a negligence rulenegligence rule

xxii

PrecautionPrecaution0

$

wwi i xxii

x’i

wwi i xxii + p(x’ + p(x’vv, x, xii)A)A

wwii x xii + p(x’ + p(x’vv, x, xii)A)A

(negligent – liable)(negligent – liable)

Permitted zone xi > x’iForbidden zone xi < x’i

wwii x xii (non-negligent – no liability) (non-negligent – no liability)

Negligence rule

Gap Gap

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Potential injurer’s optimal xPotential injurer’s optimal xii under a negligence rule under a negligence rule

xxii

PrecautionPrecaution0

$

wwi i xxii

x’i

wwi i xxii + p(x’ + p(x’vv, x, xii)A)A

Potential injurer will choose xPotential injurer will choose xii = x’ = x’ii

non-negligent xi > x’inegligent xi < x’i

wwi i xxi0i0 + p(x’ + p(x’vv, x, xi0i0)A)A

xi00xi0

wwi i xxi00i00

wwi i x’x’ii

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Potential injurer’s optimal xPotential injurer’s optimal xii under a negligence rule under a negligence rule

Costs to Potential Injurer under a Negligence RuleCosts to Potential Injurer under a Negligence Rule

Level of Level of Expected costs:Expected costs:precaution precaution

precautionprecaution liability forliability for Total expected Total expected costscosts expected expected costs costs

harm harm

xxi0i0 < x’ < x’ii wwiixxi0i0 p(x p(xi0i0, x, xvv’)A’)A w wiixxi0i0 + p(x + p(xi0i0, x, xvv’)A’)A

xxi i = x’= x’ii wwiix’x’ii nil nil wwiix’x’ii

xxi00i00 > x’ > x’ii wwiixxi00i00 nil nil wwiixxi00i00

Now from the previous slide Now from the previous slide wwiix’x’ii < w < wiixxi00i00 < w < wiixxi0i0 + p(x + p(xi0i0, x, xvv’)A’)A

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Potential injurer’s optimal xPotential injurer’s optimal xii under a negligence rule under a negligence rule

We can get the potential injurer to choose any level of We can get the potential injurer to choose any level of precaution that we want simply by setting the precaution that we want simply by setting the standard of standard of care care under a rule ofunder a rule of negligence negligence

The private cost minimizing strategy will always be for the The private cost minimizing strategy will always be for the potential injurer to choose a level of precaution (xpotential injurer to choose a level of precaution (x ii) equal to ) equal to the standard of care (x’the standard of care (x’ii))

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Potential injurer’s optimal xPotential injurer’s optimal xii under a negligence rule under a negligence rule

Conclusion at this point:Conclusion at this point:

Setting the potential injurer’s Setting the potential injurer’s standard of carestandard of care (x’ (x’ii) at the ) at the socially optimal level of caresocially optimal level of care (x* (x*ii))will cause the potential injurer to choose the socially will cause the potential injurer to choose the socially optimal level of care (x*optimal level of care (x*ii).).

But what about the potential victim?But what about the potential victim?

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Potential victim’s optimal xPotential victim’s optimal xii under a negligence rule under a negligence rule

If the potential injurer always meets the If the potential injurer always meets the standard of carestandard of care, then , then the potential injurer will never be found negligent. the potential injurer will never be found negligent. Therefore, if an accident happens, the potential victim can Therefore, if an accident happens, the potential victim can (and does) expect to suffer the full harm, with no (and does) expect to suffer the full harm, with no compensation.compensation.

Note the potential victim will assume that the potential injurer Note the potential victim will assume that the potential injurer will be non-negligent (xwill be non-negligent (xii = x’ = x’ii) since it is in the potential ) since it is in the potential injurer’s self-interest to do so (a little game theory would go in injurer’s self-interest to do so (a little game theory would go in here) here)

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Potential victim’s optimal xPotential victim’s optimal xii under a negligence rule under a negligence rule

What is the potential victim’s private cost minimizing strategy What is the potential victim’s private cost minimizing strategy if he/she expects the potential injurer will not be liable? if he/she expects the potential injurer will not be liable?

The potential victim should choose a level of precaution (xThe potential victim should choose a level of precaution (xvv) ) just as he/she would do under a rule of no liability because just as he/she would do under a rule of no liability because that is exactly the situation that the potential victim faces.that is exactly the situation that the potential victim faces.

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The expected costs of accidents for the potential The expected costs of accidents for the potential victimvictim

xv

PrecautionPrecaution0

$

p(xp(xvv, x’, x’ii)A)A

wwv v xxvv

x*v

Society wants the potential victim to

choose x*v

wwv v xxvv + p(x + p(xvv, x’, x’ii)A)A

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The expected costs of accidents for the The expected costs of accidents for the potential victimpotential victim

xv

Precaution0

$

wwv v xxvv

x*v

wwv v xxvv + p(x + p(xvv, x’, x’ii)A)A

Since the potential victim expects the potential Since the potential victim expects the potential injurer will not be liable, the potential victim treats injurer will not be liable, the potential victim treats the expected cost of accidents as wthe expected cost of accidents as wvv x xvv + p(x + p(xvv, x, xii)A)A

xv00xv0

wwv v x*x*vv+ p(x*+ p(x*vv, x’, x’ii)A)A

The potential victim will always

choose x*v

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Will the social cost of accidents be minimized under a Will the social cost of accidents be minimized under a negligence rule that sets x’negligence rule that sets x’ii = x* = x*ii ? ?

SC = wSC = wvv x* x*vv + w + wi i x*x*ii + p(x* + p(x*v v , x*, x*ii)A)A

Yes, because the negligence rule with the Yes, because the negligence rule with the correctcorrect standard of care (x’standard of care (x’ii) causes the potential injurer to ) causes the potential injurer to minimize his private cost of accidents by choosing x*minimize his private cost of accidents by choosing x* i i

- it provides the socially optimal incentives to the - it provides the socially optimal incentives to the potential injurer. potential injurer.

The potential victim knowing that it is in the potential The potential victim knowing that it is in the potential injurer’s own self-interest to choose xinjurer’s own self-interest to choose xii = x’ = x’i i will assume will assume that the potential injurer will not be found negligent. If that the potential injurer will not be found negligent. If an accident does happen there will be no compensation an accident does happen there will be no compensation and as a result the potential victim assumes a rule of no and as a result the potential victim assumes a rule of no liability applies and takes the socially optimal level of liability applies and takes the socially optimal level of precaution.precaution.

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Alternatively we can state:Alternatively we can state:

A A negligence rulenegligence rule with a with a correctly set standard of carecorrectly set standard of care provides the correct incentives to the potential injurer, provides the correct incentives to the potential injurer, inducing her to choose the socially optimal level of inducing her to choose the socially optimal level of precaution in order to avoid liability.precaution in order to avoid liability.

This in turn provides the correct incentive to the potential This in turn provides the correct incentive to the potential victim (no liability) causing him to choose the socially victim (no liability) causing him to choose the socially optimal level of precaution.optimal level of precaution.

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Do we get all of the nice results that the math tells Do we get all of the nice results that the math tells us we need ? us we need ?

wwv v = - = - ΔΔp(xp(xvv, x, xii)/)/ΔΔxxvv A A 1)1) andand

wwi i = - = - ΔΔp(xp(xvv, x, xii)/)/ΔΔxxii A A 2) 2)

Yes, both the potential injurer and the potential victim are Yes, both the potential injurer and the potential victim are induced (through self-interested cost minimization) to induced (through self-interested cost minimization) to internalize the expected cost of harm (and of course internalize the expected cost of harm (and of course precaution cost) precaution cost)

Both the potential victim and the potential injurer Both the potential victim and the potential injurer ‘purchase’ an amount of precaution such that the ‘purchase’ an amount of precaution such that the marginal cost of precaution (marginal cost of precaution (ww) is just equal to the ) is just equal to the decrease in the expected cost of harm (decrease in the expected cost of harm (- - ΔΔp(xp(xvv, x, xii)/)/ΔΔxx AA) for each of them.) for each of them.

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ExamplesExamples

Doctor must meet the Doctor must meet the standard of carestandard of care of the medical of the medical profession in prescribing your medications.profession in prescribing your medications.

Pharmacist must meet the Pharmacist must meet the standard of carestandard of care of the pharmacy of the pharmacy profession in selling you the medicine. profession in selling you the medicine.

If the Doctor or Pharmacist makes an avoidable error in If the Doctor or Pharmacist makes an avoidable error in prescribing the medication (ie. fails to carry out a standard prescribing the medication (ie. fails to carry out a standard test - gives you the wrong medicine) they could be found test - gives you the wrong medicine) they could be found negligentnegligent and required to pay compensation for any and required to pay compensation for any resulting mishap.resulting mishap.

Beyond that, you are responsible for taking precaution with Beyond that, you are responsible for taking precaution with respect to the use and storage of the medication. If you respect to the use and storage of the medication. If you inappropriately mix the medication with alcohol or allow it inappropriately mix the medication with alcohol or allow it to become accessible to a child, you are totally responsible to become accessible to a child, you are totally responsible and suffer whatever harm results. and suffer whatever harm results.

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A game theory version - the ‘negligence game’A game theory version - the ‘negligence game’

Let’s consider what we know in the form of Let’s consider what we know in the form of a ‘payoff matrix’: the value to each a ‘payoff matrix’: the value to each player for each of the possible outcomes player for each of the possible outcomes (each possible combination of choices of (each possible combination of choices of precaution)precaution)

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PAYOFF MATRIXPAYOFF MATRIX

Potential victim’s decisionPotential victim’s decision

purchase x*purchase x*vv purchase purchase xxvv<,>x*<,>x*vv

Potential injurer’s decisionPotential injurer’s decisionBehave non-negligentlyBehave non-negligently ( ( wwiix’x’ii ,, θθ*)*) ( ( wwiix’x’ii , , θθ))

Behave negligentlyBehave negligently ( ( ββ* , * , wwvvx*x*vv)) ( ( ββ , $0) , $0)

(first entry in the round brackets represents potential injurer’s payoff (first entry in the round brackets represents potential injurer’s payoff second entry represents potential victim's payoff)second entry represents potential victim's payoff)

where where ββ = = wwiixxi0 i0 + p(x+ p(xi0i0, x, xvv)A > )A > ββ* = * = wwiixxi0 i0 + p(x+ p(xi0i0, x*, x*vv)A > w)A > wiix’x’ii

wwvvx*x*v v < < θθ** = w = wv v x*x*vv + p(x* + p(x*vv, x’, x’ii)A < )A < θθ = w = wv v xxvv + p(x + p(xvv, x’, x’ii)A )A

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What will each player do? Consider the ‘What will each player do? Consider the ‘extensive extensive formform’ or a ‘’ or a ‘decision treedecision tree’’

Potential InjurerPotential Injurer

If potential victim purchases x*If potential victim purchases x*vv

and potential injurer is non-negligentand potential injurer is non-negligent wwiix’x’ii

and potential injurer is negligent and potential injurer is negligent ββ**

If potential victim does not purchase x*If potential victim does not purchase x*vv

and potential injurer is non-negligentand potential injurer is non-negligent wwiix’x’ii

and potential injurer is negligent and potential injurer is negligent ββ

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But But

ββ = = wwiixxi0 i0 + p(x+ p(xi0i0, x, xvv)A > )A > ββ* = * = wwiixxi0 i0 + p(x+ p(xi0i0, x*, x*vv)A > w)A > wiix’x’ii

So the potential injurer will always behave non-negligently (purchase So the potential injurer will always behave non-negligently (purchase x’x’II) ) and the potential victim can recognize this as the potential injurer’s and the potential victim can recognize this as the potential injurer’s dominant strategydominant strategy – what the potential injurer will do no matter what the – what the potential injurer will do no matter what the potential victim decides to do. potential victim decides to do.

This is the equilibrium solution to the ‘negligence game’This is the equilibrium solution to the ‘negligence game’