1. Part D-II The Economics of Tort Law
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2. Objectives Negligence rules Liability rules under bilateral precaution
Efficient tort law under bilateral precaution
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3. We know that simply dividing up the cost of harm will not work.
Risks characterized by bilateral precaution present us with a real problem:
How do we encourage (provide the appropriate incentives to) both the potential injurer and the potential victim to internalize the total cost of harm (A) when they decide on the appropriate level of precaution?
We know that no liability and strict liability/perfect damages will not work
We know that simply dividing up the cost of harm will not work.
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4. What is the efficient amount of precaution for each agent?
In order to minimize the expected social costs of accidents both the potential victim and the potential injurer must ‘purchase’ an amount of precaution such that the marginal cost of precaution (wv and wi) is just equal to the decrease in the expected cost of harm from the expenditure for both the potential victim
wv = - Δp(xv, xi)/Δxv A
and the potential injurer
wi = - Δp(xv, xi)/Δxi A
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5. We know that simply dividing up the cost of harm will not work.
But again,
We know that no liability and strict liability/perfect damages will not work
We know that simply dividing up the cost of harm will not work.
What to do?
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6. A Negligence Rule (a legal rule)
A negligence rule imposes a standard of care on potential injurers and/or potential victims.
This standard of care sets the minimum legal level of precaution that a party must take in order to avoid liability for an accident.
If an accident occurs and the injurer and/or victim has taken the minimum level of precaution, then they cannot be found to be negligent (they are not liable).
If an accident occurs and the injurer and/or victim has not taken the minimum level of precaution, then they can be found to be negligent (they are liable).
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7. Can a negligence rule provide efficient incentives to potential injurers and potential victims?
First lets review the concept of negligence
Let x’ represent the legal standard of care – the minimum amount of precaution required in order to avoid being found negligent (liable) if an accident occurs
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8. Legal Standard of Care for Continuous Precaution
Forbidden zone
Permitted zone
x< x’
x > x’
Pr(x=0)
Pr(x=∞)
100% 0%
x  x’
< Pr. of accident
x’ = standard of care
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9. The expected costs of accidents for the potential injurer
wi xi + p(x’v, xi)A
Note that we have assumed that the potential victim does not behave negligently xv = x’v $
wi xi + p(x’v, xi)A
wi xi
Society wants the potential injurer to choose x*i
p(x’v, xi)A xi
x*i
Precaution
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10. Potential injurer’s cost of accidents under a negligence rule
Forbidden zone xi < x’i
Permitted zone xi > x’i $
wi xi + p(x’v, xi)A
wi xi
Gap
wi xi + p(x’v, xi)A
(negligent – liable)
wi xi (non-negligent – no liability) xi
x’i
Precaution
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11. Potential injurer’s optimal xi under a negligence rule
Potential injurer will choose xi = x’i
negligent xi < x’i
non-negligent xi > x’i $
wi xi + p(x’v, xi)A
wi xi0 + p(x’v, xi0)A
wi xi
wi xi00
wi x’i xi
xi0
x’i
xi00
Precaution
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12. Potential injurer’s optimal xi under a negligence rule
Costs to Potential Injurer under a Negligence Rule
Level of Expected costs:
precaution
precaution liability for Total expected costs expected costs
harm
xi0 < x’i wixi0 p(xi0, xv’)A wixi0 + p(xi0, xv’)A
xi = x’i wix’i nil wix’i
xi00 > x’i wixi nil wixi00
Now from the previous slide wix’i < wixi00 < wixi0 + p(xi0, xv’)A
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13. Potential injurer’s optimal xi under a negligence rule
We can get the potential injurer to choose any level of precaution that we want simply by setting the standard of care under a rule of negligence
The private cost minimizing strategy will always be for the potential injurer to choose a level of precaution (xi) equal to the standard of care (x’i)
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14. Potential injurer’s optimal xi under a negligence rule
Conclusion at this point:
Setting the potential injurer’s standard of care (x’i) at the socially optimal level of care (x*i)
will cause the potential injurer to choose the socially optimal level of care (x*i).
But what about the potential victim?
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15. Potential victim’s optimal xi under a negligence rule
Note the potential victim will assume that the potential injurer will be non-negligent (xi = x’i) since it is in the potential injurer’s self-interest to do so (a little game theory would go in here)
If the potential injurer always meets the standard of care, then the potential injurer will never be found negligent. Therefore, if an accident happens, the potential victim can (and does) expect to suffer the full harm, with no compensation.
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16. Potential victim’s optimal xi under a negligence rule
What is the potential victim’s private cost minimizing strategy if he/she expects the potential injurer will not be liable?
The potential victim should choose a level of precaution (xv) just as he/she would do under a rule of no liability because that is exactly the situation that the potential victim faces.
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17. The expected costs of accidents for the potential victim
Society wants the potential victim to choose x*v $
wv xv + p(xv, x’i)A
wv xv
p(xv, x’i)A xv
x*v
Precaution
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18. The expected costs of accidents for the potential victim
Since the potential victim expects the potential injurer will not be liable, the potential victim treats the expected cost of accidents as wv xv + p(xv, xi)A
The potential victim will always choose x*v $
wv xv + p(xv, x’i)A
wv xv
wv x*v+ p(x*v, x’i)A xv
x*v
xv0
xv00
Precaution
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19. SC = wv x*v + wi x*i + p(x*v , x*i)A
Will the social cost of accidents be minimized under a negligence rule that sets x’i = x*i ?
SC = wv x*v + wi x*i + p(x*v , x*i)A
Yes, because the negligence rule with the correct standard of care (x’i) causes the potential injurer to minimize his private cost of accidents by choosing x*i
- it provides the socially optimal incentives to the potential injurer.
The potential victim knowing that it is in the potential injurer’s own self-interest to choose xi = x’i will assume that the potential injurer will not be found negligent. If an accident does happen there will be no compensation and as a result the potential victim assumes a rule of no liability applies and takes the socially optimal level of precaution.
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20. Alternatively we can state:
A negligence rule with a correctly set standard of care provides the correct incentives to the potential injurer, inducing her to choose the socially optimal level of precaution in order to avoid liability.
This in turn provides the correct incentive to the potential victim (no liability) causing him to choose the socially optimal level of precaution.
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21. Do we get all of the nice results that the math tells us we need ?
wv = - Δp(xv, xi)/Δxv A )
and
wi = - Δp(xv, xi)/Δxi A )
Yes, both the potential injurer and the potential victim are induced (through self-interested cost minimization) to internalize the expected cost of harm (and of course precaution cost)
Both the potential victim and the potential injurer ‘purchase’ an amount of precaution such that the marginal cost of precaution (w) is just equal to the decrease in the expected cost of harm (- Δp(xv, xi)/Δx A) for each of them.
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22. Examples
Doctor must meet the standard of care of the medical profession in prescribing your medications.
Pharmacist must meet the standard of care of the pharmacy profession in selling you the medicine.
If the Doctor or Pharmacist makes an avoidable error in prescribing the medication (ie. fails to carry out a standard test - gives you the wrong medicine) they could be found negligent and required to pay compensation for any resulting mishap.
Beyond that, you are responsible for taking precaution with respect to the use and storage of the medication. If you inappropriately mix the medication with alcohol or allow it to become accessible to a child, you are totally responsible and suffer whatever harm results.
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23. A game theory version - the ‘negligence game’
Let’s consider what we know in the form of a ‘payoff matrix’: the value to each player for each of the possible outcomes (each possible combination of choices of precaution)
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24. Potential victim’s decision purchase x*v purchase xv<,>x*v
PAYOFF MATRIX
Potential victim’s decision
purchase x*v purchase xv<,>x*v
Potential injurer’s decision
Behave non-negligently ( wix’i , θ*) ( wix’i , θ)
Behave negligently ( β* , wvx*v) ( β , $0)
(first entry in the round brackets represents potential injurer’s payoff second entry represents potential victim's payoff)
where β = wixi0 + p(xi0, xv)A > β* = wixi0 + p(xi0, x*v)A > wix’i
wvx*v < θ* = wv x*v + p(x*v, x’i)A < θ = wv xv + p(xv, x’i)A
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25. What will each player do
What will each player do? Consider the ‘extensive form’ or a ‘decision tree’
Potential Injurer
If potential victim purchases x*v
and potential injurer is non-negligent wix’i
and potential injurer is negligent β*
If potential victim does not purchase x*v
and potential injurer is negligent β
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26. β = wixi0 + p(xi0, xv)A > β* = wixi0 + p(xi0, x*v)A > wix’i
But
β = wixi0 + p(xi0, xv)A > β* = wixi0 + p(xi0, x*v)A > wix’i
So the potential injurer will always behave non-negligently (purchase x’I) and the potential victim can recognize this as the potential injurer’s dominant strategy – what the potential injurer will do no matter what the potential victim decides to do.
This is the equilibrium solution to the ‘negligence game’
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