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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

Bilateral precautionBilateral precaution

No liability/strict liability rules underNo liability/strict liability rules under

bilateral precautionbilateral precaution

The problem of efficient tort rules under The problem of efficient tort rules under bilateral precautionbilateral precaution

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Recall that we considered Recall that we considered two classes of risktwo classes of risk

A risk situation is one of A risk situation is one of unilateral precautionunilateral precaution if if onlyonly the potential victim or the potential victim or onlyonly the potential injurer the potential injurer can take precaution but can take precaution but not both.not both.

A risk situation is one of A risk situation is one of bilateral precautionbilateral precaution if if bothboth the potential victim and the potential injurer can the potential victim and the potential injurer can take precaution.take precaution.

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Unilateral PrecautionUnilateral Precaution

The efficient tort rule for risks characterized by The efficient tort rule for risks characterized by unilateral precautionunilateral precaution is: is:

- - if only the if only the potential victimpotential victim can take precaution, then can take precaution, then no no liabilityliability

- if only the - if only the potential injurerpotential injurer can take precaution, then can take precaution, then strict strict liability with perfect damagesliability with perfect damages

RecallRecall

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Bilateral PrecautionBilateral Precaution

There are many risk situations which are not unilateral risk There are many risk situations which are not unilateral risk situations situations

For many types of risk both the potential victim and the For many types of risk both the potential victim and the potential injurer can take precautions potential injurer can take precautions

- driving safely/seatbelts- driving safely/seatbelts- driving safely/bicycle helmets - driving safely/bicycle helmets - walking (not running) over an icy - walking (not running) over an icy sidewalk sidewalk- taking medication as directed- taking medication as directed

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Bilateral PrecautionBilateral Precaution

In such situations, neither the rule of no liability nor the rule of In such situations, neither the rule of no liability nor the rule of strict liability will lead to the ‘efficient’ level of precaution strict liability will lead to the ‘efficient’ level of precaution being taken. being taken.

Both the potential injurer and the potential victim should be Both the potential injurer and the potential victim should be taking precaution – they share control over the risk. taking precaution – they share control over the risk.

But the rules of no liability and strict liability/ perfect damages But the rules of no liability and strict liability/ perfect damages lead to only the potential victim lead to only the potential victim oror only the potential injurer only the potential injurer taking precaution.taking precaution.

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Bilateral PrecautionBilateral Precaution

NOTE: The potential victim’s precaution is different from NOTE: The potential victim’s precaution is different from the potential injurer’s precaution. the potential injurer’s precaution. They are essentially They are essentially different activities.different activities.

Important pointImportant point Getting the potential injurer (victim) to take Getting the potential injurer (victim) to take more precaution when the potential victim (injurer) more precaution when the potential victim (injurer) takes too little precaution will not be takes too little precaution will not be efficientefficient. .

One agent cannot generally compensate for the shortfall of One agent cannot generally compensate for the shortfall of the other agent (the other agent (not in an efficient mannernot in an efficient manner))

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REMINDER: When we say ‘take precaution’ REMINDER: When we say ‘take precaution’ we mean do something (or not do we mean do something (or not do something) that results in a decrease in something) that results in a decrease in the probability of an accident occurring the probability of an accident occurring (lower the risk of an accident). (lower the risk of an accident).

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Recall the social costs of accidents can be expressed as: Recall the social costs of accidents can be expressed as:

SC = wSC = wvv x xvv + w + wi i xxii + p(x + p(xvv, x, xii)A)A

Under unilateral precaution:Under unilateral precaution:

If only the potential victim can control risk, then If only the potential victim can control risk, then

ΔΔp(xp(xvv, x, xii)/)/ΔΔxxi i = 0 = 0 we wrote p(xwe wrote p(xvv, x, xii=0) = p(x=0) = p(xvv))

If only the potential injurer can control risk, then If only the potential injurer can control risk, then

ΔΔp(xp(xvv, x, xii)/)/ΔΔxxv v = 0 we wrote p(x= 0 we wrote p(xvv=0, x=0, xii) = p(x) = p(xii))

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The change in the probability of an The change in the probability of an accident as the amount of accident as the amount of precaution changes precaution changes ΔΔp(xp(xvv, x, xii)/)/ΔΔxxvv

x= xv Precaution

0

p(xv , x, xii))

xv2xv1

p(xv, xi)

ΔΔp(xp(xvv, x, xii))

ΔΔxxvv

p2(xv, xi)

p1(xv, xi)

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But under bilateral precaution:But under bilateral precaution:

ΔΔp(xp(xvv, x, xii)/)/ΔΔxxi i < 0 and < 0 and ΔΔp(xp(xvv, x, xii)/)/ΔΔxxv v < 0< 0

Note: the potential victim and potential injurer control Note: the potential victim and potential injurer control different aspects of the risk (xdifferent aspects of the risk (xv v and xand xii are generally are generally different types of expenditures, actions, etc.)different types of expenditures, actions, etc.)

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Will a rule of Will a rule of no liabilityno liability be efficient if the risk requires bilateral be efficient if the risk requires bilateral precaution?precaution?

No, because no liability causes the potential injurer to No, because no liability causes the potential injurer to completely externalize the cost of harm and therefore take completely externalize the cost of harm and therefore take no precaution. no precaution.

Will a rule of Will a rule of strict liability/perfect damagesstrict liability/perfect damages be efficient if the be efficient if the risk requires bilateral precaution?risk requires bilateral precaution?

No, because strict liability/perfect damages causes the No, because strict liability/perfect damages causes the potential victim to completely externalize the cost of harm potential victim to completely externalize the cost of harm and therefore take no precaution. and therefore take no precaution.

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If both the potential injurer and the potential victim control the If both the potential injurer and the potential victim control the risk, risk, efficiencyefficiency will require that both of them take will require that both of them take precaution.precaution.

How much precaution should each take?How much precaution should each take?

That depends on the nature of the risk and the types That depends on the nature of the risk and the types and costs of precaution available.and costs of precaution available.

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The answer to the previously question will differ in each risk The answer to the previously question will differ in each risk situation (for each type of potential accident)situation (for each type of potential accident)

We want We want a general rulea general rule that will ensure that the potential that will ensure that the potential victim and the potential injurer will each take the victim and the potential injurer will each take the efficient efficient amount of precaution for any given type of potential amount of precaution for any given type of potential accidentaccident

Does such a legal rule exist?Does such a legal rule exist?

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

SC = wSC = wvv x xvv + w + wi i xxii + p(x + p(xvv, x, xii)A)A

If we want to minimize the social costs of accidents with respect to both xIf we want to minimize the social costs of accidents with respect to both xv v

and xand xi i our friends in mathematics would say: our friends in mathematics would say:

- take the derivative of SC with respect to x- take the derivative of SC with respect to xvv and set it equal to zero: and set it equal to zero:

wwv v + + ΔΔp(xp(xvv, x, xii)/)/ΔΔxxvv A = 0 A = 0

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

- take the derivative of SC with respect to x- take the derivative of SC with respect to xii and set it equal to zero: and set it equal to zero:

wwi i + + ΔΔp(xp(xvv, x, xii)/)/ΔΔxxii A = 0 A = 0

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

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

Conclusion #1Conclusion #1

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 (ww) is just equal to the decrease in the ) is just equal to the decrease in the expected cost of harm from the expenditure (expected cost of harm from the expenditure (- - ΔΔp(xp(xvv, , xxii)/)/ΔΔxx A A) for each of them.) for each of them.

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

We can divide expression 1) by expression 2) and get:We can divide expression 1) by expression 2) and get:

wwv v / w / wi i = [= [ΔΔp(xp(xvv, x, xii)/)/ΔΔxxvv] / [] / [ΔΔp(xp(xvv, x, xii)/)/ΔΔxxii] ]

oror

[[ΔΔp(xp(xvv, x, xii)/)/ΔΔxxvv] / w] / wv v = [ = [ΔΔp(xp(xvv, x, xii)/)/ΔΔxxii] / w] / wii

Conclusion #2Conclusion #2

The ratio of the prices of a unit of precaution taken by the The ratio of the prices of a unit of precaution taken by the potential victim and that taken by the potential injurer must potential victim and that taken by the potential injurer must equal the inverse of the ratio of marginal declines in the equal the inverse of the ratio of marginal declines in the probability of an accident occurring resulting from an probability of an accident occurring resulting from an additional unit of xadditional unit of xvv and x and xii. .

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

Conclusion to this point:Conclusion to this point:

The efficient level of precaution for the potential victim and The efficient level of precaution for the potential victim and potential injurer will depend on the price of each type of potential injurer will depend on the price of each type of precaution and the nature of the impact of each type of precaution and the nature of the impact of each type of precaution on the probability of an accidentprecaution on the probability of an accident

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A little bit of intuitionA little bit of intuition

Efficiency requires that:Efficiency requires that:

to the extent that the cost of precaution to the potential victim to the extent that the cost of precaution to the potential victim is is relatively inexpensiverelatively inexpensive, or the precaution taken by the , or the precaution taken by the potential victim is potential victim is relatively effectiverelatively effective, the potential victim , the potential victim should take relatively more precaution. should take relatively more precaution.

to the extent that the cost of precaution to the potential to the extent that the cost of precaution to the potential injurer is injurer is relatively inexpensiverelatively inexpensive, or the precaution taken by , or the precaution taken by the potential injurer is the potential injurer is relatively effectiverelatively effective, the potential , the potential injurer should take relatively more precaution.injurer should take relatively more precaution.

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Such a general rule will need to account for Such a general rule will need to account for

wwvv and w and wi i

- how much each type of precaution cost- how much each type of precaution cost

andand

ΔΔp(xp(xvv, x, xii)/)/ΔΔxxii and and ΔΔp(xp(xvv, x, xii)/)/ΔΔxxvv

- the marginal effect of the alternative types - the marginal effect of the alternative types of of precaution on the probability of an accident precaution on the probability of an accident

Does such a general rule exist?Does such a general rule exist?

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Again, will a rule of Again, will a rule of no liabilityno liability be efficient if the risk requires be efficient if the risk requires bilateral precaution?bilateral precaution?

No, because no liability causes the potential injurer to No, because no liability causes the potential injurer to completely externalize the cost of harm and therefore take completely externalize the cost of harm and therefore take no precaution. no precaution.

Will a rule of Will a rule of strict liability/perfect damagesstrict liability/perfect damages be efficient if the be efficient if the risk requires bilateral precaution?risk requires bilateral precaution?

No, because strict liability/perfect damages causes the No, because strict liability/perfect damages causes the potential victim to completely externalize the cost of harm potential victim to completely externalize the cost of harm and therefore take no precaution. and therefore take no precaution.

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We need both the potential victim and potential injurer to We need both the potential victim and potential injurer to internalize the full cost of harm internalize the full cost of harm

p(xp(xvv, x, xii)A)A

When they determine how much precaution to take When they determine how much precaution to take

xxvv and and xxii

So no liability and strict liability/perfect damages will not be So no liability and strict liability/perfect damages will not be efficient tort rules – they will create the wrong incentives efficient tort rules – they will create the wrong incentives

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An intuitive rule that won’t workAn intuitive rule that won’t work

Since both the potential injurer and the potential Since both the potential injurer and the potential victim can take precaution, why not just set victim can take precaution, why not just set damages at 50% of harm for each?damages at 50% of harm for each?

This means that the potential victim and the potential injurer This means that the potential victim and the potential injurer will each bear 50% of the cost of harm. will each bear 50% of the cost of harm.

Under this rule of liability/damages Under this rule of liability/damages D = 0.5 AD = 0.5 A

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What is the cost of accidents to the potential victim?What is the cost of accidents to the potential victim?

wwvv x xvv + p(x + p(xvv, x, xii)(0.5A) )(0.5A) since D = 0.5 Asince D = 0.5 A

What is the optimal amount of precaution for the potential What is the optimal amount of precaution for the potential victim to take? What will be in the potential victim’s own victim to take? What will be in the potential victim’s own self-interest? Keep ‘buying’ precaution until, self-interest? Keep ‘buying’ precaution until,

wwvv = - = - Δ Δ p(xp(xvv, x, xii)/)/ΔΔxxv v (0.5A)(0.5A)

Potential victim’s Potential victim’s = 0.5 of the potential victim’s = 0.5 of the potential victim’s

marginal cost ofmarginal cost of marginal benefit marginal benefit

precautionprecaution from precaution from precaution

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What is the cost of accidents to the potential injurer?What is the cost of accidents to the potential injurer?

wwii x xii + p(x + p(xvv, x, xii)(0.5A) )(0.5A) since D = 0.5 Asince D = 0.5 A

What is the optimal amount of precaution for the potential What is the optimal amount of precaution for the potential injurer to take? What will be in the potential injurer’s own injurer to take? What will be in the potential injurer’s own self-interest. Keep ‘buying’ precaution until, self-interest. Keep ‘buying’ precaution until,

wwii = - = - Δ Δ p(xp(xvv, x, xii)/)/ΔΔxxi i (0.5A)(0.5A)

Potential injurer’s Potential injurer’s = 0.5 of the potential injurer’s = 0.5 of the potential injurer’s

marginal cost ofmarginal cost of marginal benefit marginal benefit

precautionprecaution from precaution from precaution

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What’s wrong with this outcome?What’s wrong with this outcome?

The potential victim and the potential injurer are each The potential victim and the potential injurer are each minimizing their private costs of accidents (the portion of minimizing their private costs of accidents (the portion of the cost that they are responsible for) the cost that they are responsible for) but they are ignoring but they are ignoring 50% of the cost of harm50% of the cost of harm – the 50% for which they are not – the 50% for which they are not liable. liable.

Each of them is only internalizing 50% of the expected cost of Each of them is only internalizing 50% of the expected cost of harm – harm – they will only make half an effort at precautionthey will only make half an effort at precaution

A simple 50%/50% rule (or any other arbitrary split of the A simple 50%/50% rule (or any other arbitrary split of the liability) results in each agent only internalizing their liability) results in each agent only internalizing their assigned share of the cost of harm.assigned share of the cost of harm.

There will be too little precaution taken by both the potential There will be too little precaution taken by both the potential victim and the potential injurervictim and the potential injurer

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We have a real problem. We have a real problem.

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

Simply dividing up the cost of harm will not work. Simply dividing up the cost of harm will not work.