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Negligence as Determined by the Marginal Hand Rule

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Consider a barge owner who is deciding whether to post an attendant on his barge to make sure that it remains properly moored to the pier. The following table gives the total cost of hiring the attendant,the probability of an accident, and the ...xed cost of an accident:
Cost of care Probability Damage
No attendant posted $0 0.25 $400
Attendant posted for 24 hours $94 0 $400

(a) Calculate the marginal cost and marginal bene...t of posting the attendant. According to the marginal Hand Rule, would the barge owner be found negligent for failing to post an attendant?
Now suppose that the barge owner had a third option: post the attendant only during the day. The data for this option are as follows: Cost of care $50, Probability of an accident 0.10, and Damages $400.
(b) Assume that the barge owner's only two options are "no attendant"and "post an attendant during the day." In this case, would the owner's failure to post an attendant be judged negligent by the marginal Hand Rule?
(c) Assume that, prior to the accident, the owner had posted an attendant during the day. Suppose that the victim claims that the owner is negligent for not having posted the attendant for 24 hours. Use the marginal Hand Rule to evaluate the merits of this claim.
(d) For each of the three options: "no attendant," "attendant during the day,"and "attendant for 24 hours," calculate total expected costs (costs of care plus expected damages). Which option minimizes this total? Reconcile the result with your answers to (a)-(c).

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Negligence as determined by the marginal Hand Rule.

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The Hand Rule for determining negligence was formulated by Judge Learned Hand in U.S. v. Carroll Towing Co. The defendant is considered negligent if the burden of the undertaken precaution is less than the expected harm. The marginal Hand Rule states that the defendant is negligent if the marginal cost of the precaution against damage is less than the resulting marginal benefit. Mathematically, this is stated as B <PL, where B is the burden (marginal cost) of the precaution, P is the marginal probability of damage, and L is the liability (cost of the accidental harm).

In the first case the cost of marginal social benefit of ...

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