Accident analysis: The role of liability rules pecuniary losses.


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1 The role of lablty rules  pecunary losses Accdent analyss: The role of lablty rules pecunary losses. (Draft) Eef Delhaye Center for Economc Studes, K.U.Leuen emal: March INTRODUCTION. Accdents are an mportant socal cost caused by transport. Polcy maers can reduce ths cost by the use of dfferent nstruments such as regulaton (traffc rules, ehcle regulaton ), lablty rules, nfrastructure measures and economc nstruments (subsdes and taxes). The frst opton s called safety regulaton or specfc deterrence and t mposes regulatons on car drng. Thn of speed lmts, safety belts, techncal regulatons The second opton, called general deterrence, consst of confrontng the car drers wth the real costs of ther drng and by that, nfluencng ther behaour. Lablty rules confrm wth ths descrpton. The fact that you could be held lable maes car drng more expense and thus more unattracte. The last nstrument, taxes and subsdes, are not usually used to promote traffc safety. In general, one can try to assess whch nstruments or whch combnatons of nstruments are optmal n order to reduce the sum of the accdent cost and the cost of the accdent preenton. In ths paper we only consder lablty rules and how they nfluence behaour and accdent cost. We frst consder the consequences of dfferent lablty rules n a ctmnjurer model. Then we loo at a model where both partes hae losses. The losses are assumed purely pecunary. For both models we consder the case n whch people are rs neutral and then ntroduce rs adersty and nsurance. For the ctmnjurer model wth rs neutral agents we also loo at what happens f we relax some assumptons. Fnally, we conclude. But we start wth some defntons. 2. DEFINITIONS Vctmnjurer accdent. By a ctmnjurer accdent we thn of an accdent between one njurer and one ctm, n whch only the ctm experences the accdent loss. Thn for example of an accdent between a car and a bcycle. A crash between two cars s an example of an accdent where both partes loose. Partes are assumed to be strangers to each other. Injurers and ctms wll each hae (at least potentally) two nds of decsons to mae. A decson whether, or how much to engage n a partcular actty and a decson oer the degree of care to exercse when engagng n an actty. Injurers and ctms wll be assumed to mae
2 The role of lablty rules pecunary losses 2 ther decsons based on ther expected utlty. If people are rs neutral then ther decsons wll be affected only by ther expected losses. They wll not be nfluenced by the potental magntude of ther losses. Ther utlty of wealth equals ther wealth (or s lnear n ther wealth), so ther margnal utlty of wealth s constant. If people are rs aerse then they are concerned not only about ther expected losses but also about the possble sze of ther losses. Rsaerse partes, n other words, dsle uncertanty about the sze of losses per se. Ther utlty of wealth s ncreasng and strctly concae n ther wealth, that s, ther margnal utlty of wealth s poste but decreasng Lablty Rules. We ge a nonexcluse enumeraton of possble lablty rules. In the analyss, howeer we wll not consder all of them. (1) No Lablty. Each party bears hs/her own losses. (2) Strct Lablty. The njurer must pay for all accdent losses that he caused. (3) Neglgence Rule. The njurer wll be held lable for accdent losses he caused only f he was neglgent, that s, only f hs leel of care was less than a leel specfed by courts, called due care. x : due care leel of njurer njurer at fault ( x < x ) njurer lable njurer faultless ( x x ) njurer not lable (4) Strct Dson of Accdent Losses. Injurer and ctm each bear a poste fracton of any accdent losses that occur. The fracton s assumed to be ndependent of ther leel of care. (5) Strct Lablty wth the Defence of Contrbutory Neglgence. The njurer s lable for the accdent losses he causes unless the ctm s leel of care was less than hs due care leel. x : due care leel of ctm ctm faultless ( x x ) njurer lable ctm at fault ( x < x ) njurer not lable (6) Strct Lablty wth the Defence of Dual Contrbutory Neglgence. The neglgence crteron s appled to both the ctm and the njurer. The ctm only bears the losses f he s neglgent and the njurer taes care, n all the remanng cases the njurer pays. x : due care leel of ctm x : due care leel of njurer
3 The role of lablty rules pecunary losses 3 ctm at fault ( x < x ), njurer faultless ( x x ) njurer not lable ctm at fault ( x < x ), njurer at fault ( x < x ) njurer lable ctm faultless ( x x ), njurer at fault ( x < x ) njurer lable (7) Strct Lablty wth the Defence of Relate Neglgence. The njurer s lable for the accdent losses he causes f the ctm too due care. If, howeer the ctm faled to tae due care, the ctm does not bear all the losses; rather he bears only a fracton of them, the fracton dependng on hs actual leel relate to due care. x : due care leel of party njurer at fault ( x < x ), and ctm faultless ( x x ) njurer bears 100% njurer faultless ( x x ), and ctm at fault ( x < x ) ctm bears X%, wth X=f( x / x ) (8) Neglgence rule wth the Defence of Contrbutory Neglgence. The njurer wll not be lable for the accdent losses he causes f he taes at least due care; and een f he does not, he wll stll escape lablty f the ctm faled to tae due care. x : due care leel of party njurer faultless ( x x ) njurer not lable njurer at fault ( x < x ), and ctm at fault ( x < x ) njurer not lable njurer at fault ( x < x ), and ctm faultless ( x x ) njurer lable (9) Comparate neglgence rule. If only one of the partes s at fault, that party bears all the losses. But f both njurer and ctm fal to tae due care, each party bears a fracton of accdent losses, where the fracton s determned by a comparson of the amount by whch the two partes leels of care depart from the leels of due care. x : due care leel of party njurer at fault ( x < x ), and ctm faultless ( x x ) njurer bears 100% njurer faultless ( x x ), and ctm at fault ( x < x ) ctm bears 100% Both at fault [( x < x ),( x < x )] njurer and ctm bear n proporton to neglgence 2.3. Pecunary ersus Nonpecunary Losses. A pecunary loss s the loss of a good, whch has a substtute on the maret. Maret prces therefore determne the alue of the good. An example of a pecunary loss s the materal damage that s caused by the accdent. A nonpecunary loss can be seen as the loss of unque and rreplaceable commodtes. The amount of the loss equals the utlty of the good to the nddual and ths equals the reducton n socal welfare due to the loss of the good. Examples of nonpecunary losses are death, njury, emotonal dstress
4 The role of lablty rules pecunary losses 4 In ths paper we wll only consder pecunary losses. We start wth the smplest case, a ctmaggressor model. 3. VICTIMAGGRESSOR Rsneutral partes. Frst, we consder the case where both njurers and ctms are rs neutral. We wll consder the model of blateral accdents, n whch both njurers and ctms can nfluence the expected accdent losses by ther care and actty leel. Remember that n a ctmaggressor model, only the ctm has losses. We wll base ourseles on Cooter & Ulen (1987), Landes & Posner (1987) and Shaell (1987) The Socal Optmum. Frst we ntroduce some notaton: Subscrpt and stand for the njurer and the ctm, respectely. s s the leel of actty of agent. U ( s ) s the gross utlty of a person of engagng n hs actty at leel s. x s the leel of care of agent per unt of actty. The consumer prce of care s assumed to equal unty and not to be a functon of the leel of care. The expected accdent loss sspx (, x )( l x, x ) mposed on the ctm depends on the actty leel and the leel of care of both agents, wth px (, x ) the probablty of an accdent wth p l < 0 and wth lx (, x ) the losses wth = l 0 x <. Assume that an ncrease n the x x actty leel causes a proportonal ncrease n the expected accdent losses, gen care. We wll denote the expected accdent losses as sslx (, x ) In the socal optmum, the degree of care and the actty leel are such that they maxmse the socal welfare. Ths s the utlty that ctm and njurer dere from the actty mnus the cost of care mnus the expected accdent losses. [ ( ) ] (, ) (1) Max U s sx sslx x =, The frst order condtons. for x and s are: x :1 = sl ( x, x ),n=,; n (2) n x s U s = x + sl x x (3) ' : ( ) (, ),n=; n n Accordng to condton (2), the leel of care should be chosen such that the margnal socal costs of tang care (the prce of x, whch s assumed to be equal to unty) equals the margnal socal benefts (reducton n expected accdent losses). Accordng to (3), the socally optmal actty leel s s that alue such that the socal beneft of actty (margnal utlty from an ncrease n actty leel) equals the margnal socal cost (the sum of the cost of tang optmal care per unt of actty and the ncrease n expected accdent losses).
5 The role of lablty rules pecunary losses Oerew Results. The njurer and the ctm can tae two decsons, one concernng the leel of care and one concernng the leel of actty. We assume the followng:  If compensaton s pad to the ctm, t s perfect.  The court and the agents are perfectly nformed and the law system functons perfectly. We assume no admnstrate costs or equal admnstrate costs for all rules.  Vctms always sue njurers.  Injurers hae the assets necessary to pay for harm. (1) No Lablty. In ths case the njurer neer has to pay compensaton. He wll not tae nto account the costs he mposes on the ctm. He wll not tae care ( x = 0 whateer x j ) and wll not restrct hs actty leel. The ctm on the other hand bears all the costs. Because x = 0, ctms wll select x j n order to maxmse U( s ) sx ssl(0, x ). He wll tae optmal care and wll engage n the optmal actty leel n order to mnmse hs expected losses. (2) Strct lablty In ths case the njurer s problem becomes: Max Us ( ) sx sslx (, x ) x, s In choosng the actty leel and the leel of care, he wll tae nto account the effect of hs actons on the expected accdent costs. In other words, the margnal socal accdent costs and benefts assocated wth hs transport decsons are completely nternalsed. The ctm nows that he wll be compensated perfectly for the accdent losses, should an accdent occur. Hs net utlty functon therefore s gen by U( s ) sx. He has no ncente to reduce accdent costs under ths rule, snce all accdent costs are borne by the njurer. Consequently, hs leel of care wll be zero and hs actty leel wll be too hgh. He wll not tae nto account the margnal socal benefts of hs precautonary behaour ( sl ( x, x )) and x wll not consder the araton n expected accdent losses due to hs actty ( slx (, x )). (3) Neglgence Under ths rule, the polcy maer mposes a legal standard of care x wth whch the njurer must comply n order to escape lablty. The njurer wll choose to comply wth the legal standard. He wll not choose to tae more care than what s legally requred. If hs leel of care equals x, he wll aod lablty and hs costs wll be sx. Choosng a hgher leel of care would only ncrease hs costs whle not gng hm any addtonal beneft. The net utlty functon of an njurer who taes due care s therefore gen by Us ( ) sx. If the polcy maer sets the legal standard at the effcent leel, t can be shown that ths net utlty s always larger than the net utlty he can attan when he does not comply ( Us ( ) sx sslx (, x )) (gen that the ctm s actty leel s strctly poste). Therefore, he wll choose to comply wth the legal standard. If the legal standard s set at the effcent leel, the njurer wll be nduced to tae the effcent leel of care.
6 The role of lablty rules pecunary losses 6 Graphcally: Cost en losses Socal cost Cost of care Expected cost x Expected accdent losses x Snce the njurer escapes lablty by choosng the due care leel, he wll not tae nto account the effect of hs actty leel on the expected accdent costs. Therefore, hs actty leel wll be too hgh compared to the socal optmum. Of course, ths result would change f the legal standard would be defned not only n terms of leel of care, but also n terms of the actty leel. The ctm nows that the njurer taes the due leel of precauton, and that he wll not recee compensaton for the accdent losses. Therefore, he responds as f there was no lablty and he wll set hs actty leel and leel of care at the effcent leel. (4) Strct lablty wth contrbutory neglgence and comparate neglgence These arants of the neglgence rule ge both partes ncentes for effcent precauton. The mechansm s smlar as n the case of the smple neglgence rule. Under eery arant of the neglgence rule, one party can escape bearng the accdent costs by complyng wth the legal standard. Ths party wll tae due care n order to aod the cost of harm. Howeer, he has no ncente to set hs actty leel at an effcent leel, because, by conformng to the legal standard, he can aod all lablty. Snce the other party bears all accdent costs, ths party has an ncente to set both hs actty leel and hs leel of care at the effcent leel, n order to maxmse hs net utlty. We summarse the effects of dfferent lablty rules on the leel of care and the actty leel. Ths table s based on Cooter&Ulen (1997)
7 The role of lablty rules pecunary losses 7 Table 1: Effcency of ncentes created by lablty rules. Care Actty leel Injurer Vctm Injurer Vctm No lablty no yes no yes Strct lablty yes no yes no Neglgence yes yes no+ yes Strct Lablty + contrbutory neglgence yes yes yes no+ Comparate Neglgence yes yes no+ yes Source: Couter & Ulen (1997) yes = effcent ncentes no = neffcent ncentes (gen behaour of other party) = f the leel of due care equals the socal optmal leel. += f the standard of behaour used to determne neglgence s defned only n terms of care. Frstly, we can conclude that certan lablty rules lead to an effcent leel of care by both partes. Ths s the case for all rules nolng neglgence. Secondly, we see that there exsts no lablty rule that always results n optmal leels of actty for both partes. Ths s caused by the fact that lablty rules do not allow both players to carry the accdent cost. To correct for ths, seeral approaches hae been suggested. Shaell(1987) suggests that njurers pay n the case of an accdent a fne equal to the expected accdent losses to the state and that ctms are not gen compensaton next to a neglgence rule. One could also use a neglgent rule to nduce effcent care and complement t wth a tax, whch should prode ncentes for effcent actty choces. Goere (2001) proposes the use of monetary fnes, whch are not related to the occurrence of an accdent. Thn of fnes for speedng, parng offences, He shows that n order to obtan an effcent outcome, the standards hae to be excesse. Whch lablty rule to use depends on the persons that need to tae care. If, for nstance, t s optmal that only the njurer taes care, strct lablty can lead to an effcent outcome. If both hae to tae care, the rule chosen should depend on whose actty leel matters the most Relaxng the assumptons. In ths paragraph we leae our deal world and loo at what happens f our assumptons are relaxed. Frst, we loo at the consequences of errors, made by the court or by the njurer. Next, the nfluence of ague standards and uncertanty s dscussed. Thrdly, we relax the assumpton of no or equal admnstrate cost and fnally, the effect of nonunform agents s consdered. We base ourseles on Cooter & Ulen (1997), Emons (1990,1991), Endres (1991), Landes & Posner (1987) and Shaell (1987). (1) Errors. By errors we mean mstaes on the extent of harm, the cause of the accdent and the actor s fault. These errors wll nfluence the ncentes. The nfluence wll depend on the rule used. () Mstaes n estmatng harm by court
8 The role of lablty rules pecunary losses 8 Strct lablty. If the compensaton s smaller than the harm, part of the accdent cost s external to the njurer. Hs care leel wll be lower than optmal and hs actty leel hgher. If the compensaton he has to pay s larger, he wll rase hs care leel aboe optmal. We see that the njurers precauton responds n the same drecton as the error. Neglgence rule. The njurer wll not adapt hs care leel to small court errors (poste or negate) n settng the damages. If the error s large, ths s, f he only has to pay a small fracton of the accdent losses, t could be optmal to olate the standard. Endres (1991) shows that n ths later case the njurer could be nduced to tae due care by a tax proportonal to the degree of neglgence. Graphcally: Suppose B s the true cost. Small errors such as A and C hae no effect on the leel of care. Large errors such as D affect the leel of care. Note that f there s an error n estmatng the harm, due care s probably also set wrong. Ths s because court estmates due care usng estmated harm. Cost A B Expected cost C D x Note that the conclusons stay f we nterpret ths problem as njurers mang mstaes n estmatng the expected harm. x () Mstaes n fndngs of neglgence Strct lablty. If neglgent njurers are not found lable, the expected lablty lowers. Ths cause njurers to lower ther care. In general, the njurer wll respond n the same drecton as the error. Neglgence rule. We agan fnd that njurers do not respond to small errors. We can use the same graph as before, but wth a dfferent nterpretaton. () Errors n settng legal standards In realty due care does not equal optmal care. If due care s too small, the party wll confrm wth ths leel and hence exercse suboptmal care. If due care s too large, we obtan ether complance or dsobedence. Whether the njurer decdes to eep the standard depends on a comparson of the cost of care when eepng the standard and the mnmal total cost when olatng t.
9 The role of lablty rules pecunary losses 9 Also note that care can be defned n dfferent dmensons. If the due leel of care does not coer all these dmensons, the njurer wll only comply wth the effcent leel for the dmensons coered. (2) Vague standards and Uncertanty. We wll consder how people react under legal uncertanty. Assume that courts mae purely random errors, or, what comes down to the same thng, that njurers mae purely random errors n predctng what the court wll do. () Random errors by the court computng damages/by the njurer predctng errors Purely random errors wll hae no effect on the expected lablty. Hence, there wll be no effect on the leel of care under any lablty rule. () Random errors n settng due care Under a smple neglgence rule the court can mae random errors n settng the due leel of care or n comparng the leel of actual care wth the standard or the njurer can mae random errors n predctng the due leel of care. Ths causes uncertanty for the njurer. Rasng hs care leel costs relately lttle and he wll rase hs care leel to aod beng held lable. () Stochastc element of care Care often has a stochastc element. We can say that realsed care ε IID(0, ) σ. Ths means that x = x + ε wth Ex ( ) = x. If ε < 0 as the accdent happens, the njurer wll be found neglgent. It s possble that the njurer wll rase hs leel of care to aod beng neglgent by accdent. We summarse these frst two ponts wth a table, based on Cooter & Ulen (1997) Table 2: The effect of errors and uncertanty. Lablty rule Court s error Injurer s error Effect on njurer Strct lablty Excesse damage Oerestmates damage Excesse precauton Neglgence Excesse damage Oerestmates damage None Neglgence Excesse legal standard Oerestmates due care Excesse precauton Strct lablty Random error n damage Random error n damage None Neglgence Random error n due care Random error n due care Excesse precauton (3) Admnstrate costs An accdent causes three costs to arse: a precautonary cost, the cost of accdental harm and an admnstrate cost. A no lablty rule leaes the accdent losses where t falls, there s no reallocaton. Hence, there are no admnstrate costs for reallocaton. Under strct lablty and neglgence there s an admnstrate cost. Neglgence wll n general be more expense per case than strct lablty, but there are less cases under the neglgence rule. There s also a dfference n costs between unform rules and case by case n whch the former s edently
10 The role of lablty rules pecunary losses 10 less expense. Wth nonunform partes, howeer, a unform rule s dstorte, as we wll see n (4) Note also that hgh ltgaton costs can cause the ctm to mae fewer clams. Hence, the njurer gets no sgnal that he s dong somethng wrong and he wll tae less precauton. If t s expense for the njurer to ltgate, he wll tae more precauton than optmal. We cannot be sure of the net effect. (4) Non unform partes In general courts use an aerage man concept of neglgence, because of the nformaton cost. Howeer the socal optmal leel of care depends on the cost of tang care. Ths means that due care should ary. It s possble that the effcent leel for a certan person s lower than the standard. Hence f ths person exercses hs optmal care leel, he wll be found neglgent n the case of an accdent. Emons (1990,1991) shows that lablty rules that exhbt sharng features are superor to neglgence rules f ndduals are not dentcal Rsaerse partes and nsurance. Wth rs aerse agents the socal optmum noles not only the reducton of accdent losses but also the protecton of rs aerse partes aganst rs. We want to now how ths nfluence the ncentes assocated wth lablty. We wll consder a unlateral ctmnjurer model. We assume that only the njurers decsons hae an mpact on the probablty of an accdent and not on the seerty. We wll base ourseles on Arlen (1990), Mattacc (?), Posner (1998), Shaell (1987,2000) and Van den Bergh (1998) The Socal Optmum. The presence of rsaerse partes means that the dstrbuton or allocatons of rs wll n t self affect socal welfare. Socal welfare s rased not only by the complete shftng of rss from the more to the less aerse or to the rs neutral, but also by the sharng of rss among rsaerse partes. Sharng rss reduces the magntude of the potental loss that any one of them mght suffer. Ths s why we ntroduce nsurance. By ntroducng nsurance, we also hae to ntroduce moral hazard. Moral hazard exsts when people can nfluence the rs. In ths setup, they can nfluence the probablty of an accdent happenng by the choce of ther leel of care and actty. If nsurers hae perfect nformaton at no cost about the nsureds rs reducng actons, then there s no problem. The nsurers can ln the terms of the polcy to the nsureds rs reducng actons. If, on the other hand, nsurers are not nformed, as they wll be n realty, then the nsureds ownershp of nsurance wll affect ther ncentes to reduce rs. If the nsured posses complete coerage, the problem wll be more serous, for they wll hae no reason to aod losses. The exstence of nsurance thus can hae a great mpact on the preente role of lablty. Frst, we consder the careaspect. If an actor does not hae to pay for hs losses or hs lablty hmself because he s nsured, he wll not tae these costs nto account when determnng hs behaour. The care ncentes then hae to be proded by the nsurance company. Ths s not always possble under each rule as we wll see. In general, the nsurance company can mpose a
11 The role of lablty rules pecunary losses 11 fxed amount whch can not be recoered or use a bonusmalus system 1. As for the actty leel, t mght be possble to nfluence the actty leel of partes through the nsurance polcy. For nstance, the premum could be lned to the number of lometres dren n a year. Socal welfare s agan defned as the sum of the partes expected utlty. Shaell (1987) shows that under the socally deal soluton to the accdent problem, partes wll mae decsons about engagng n acttes and about ther exercse of care n the way that was earler descrbed. In addton, rsaerse partes be they ctms or njurers wll not bear rss, whch s to say, ther rss wll be perfectly spread trough nsurance arrangements or wll be shfted to rsneutral partes Oerew Results. We assume that:  njurers are always sued by ctms  njurers hae assets necessary to pay for harm  nsurance premums are actuarally far, set by a compette nsurance ndustry. (1) No Lablty. If njurers are not lable for accdent losses, they generally wll not reduce rss approprately. They may engage n too much rsy acttes and wll hae no mote to tae care. We wll not hae a socal optmum. Vctms are left bearng all the rss f accdent nsurance s not aalable. Ths s socally undesrable f ctms are rs aerse. If accdent nsurance s aalable, rsaerse ctms wll purchase full nsurance f they can. Full coerage wll be offered because n ths settng the ctm does not nfluence the probablty of an accdent. (2) Strct Lablty. Under strct lablty ctms are compensated for any losses; t s the njurers who bears the rs. If the njurers are rs neutral, they wll tae optmal care, as we saw before. If they are rs aerse, socal welfare wll be lowered relate to the deal f njurers engage n an actty not only because njurers wll bear rs, but also because they may exercse too much care to aod lablty. In addton, njurers may be dscouraged from engagng n an actty n the frst place een though dong so would be socally optmal. The way of solng ths s to reduce the magntude of lablty or to allow njurers to nsure themseles. In the case that nsurance s aalable we should dstngush between two cases. In the frst case the nsurers can determne the njurers leel of care. Vctms wll be protected aganst rs by defnton of strct lablty and njurers, f rs aerse, wll purchase lablty nsurance. And snce nsurers can obsere the leel of care, full coerage wll be offered and prosons wll be ncluded to nduce optmal care. The premums pad wll equal expected losses. Note that the outcome s socally optmal because ctms can not nfluence the accdent rs. If nsurers cannot obsere the njurers leel of care, polces wll usually be less than complete coerage. 1 A bonusmalus system can nfluence the leel of care, but s not perfect. Ths s because there s not enough dersfcaton n the system.
12 The role of lablty rules pecunary losses 12 The premum rate wll be lower than the premum for full coerage. But f the njurers are rs aerse and cannot buy full coerage, ths means that the socal outcome wll not be optmal. In addton, the fact that they are not responsble for all of the losses nduces them to tae less than optmal care. The concluson howeer stays that the aalablty of lablty nsurance wll stll be socally desrable. We reason as follows: snce ctms are always compensated under strct lablty the exstence or nonexstence of a lablty nsurance does not affect ther socal welfare. Hence the only thng on whch the lablty nsurance has an nfluence s on the welfare of the njurers. Snce njurers choose to buy nsurance, t must be that the nsurance maes them better off. (3) Neglgence rule. In ths case njurers wll not bear rs proded they tae due care, whch they wll decde to do. Hence there are no partcular problems when njurers are rs aerse, and they wll not exercse excesse care or be dscouraged from engagng nto a socally desrable actty. Ther actty leel wll een be too hgh. Vctms on the other hand wll bear ther losses and as a consequence socal welfare wll be lowered f ctms are rs aerse and not nsured. If nsurance s aalable, ctms wll buy full accdent nsurance coerage 2. Injurers wll not buy nsurance because the premum would be too hgh to mae t worth buyng. Snce all njurers who would own an nsurance would act neglgently, nsurers cost and the premum would equal the leel of expected accdent losses produced by neglgent behaour. Injurers would therefore be better of not to buy nsurance but to tae due care. We summarse wth a table: Table 3: : Effcency of ncentes created by lablty rules Care Leel of actty Insurance Injurer Injurer Injurer Vctm No lablty No No No Full nsurance Strct lablty Yes a Yes a Partal nsurance b No Neglgence Yes Excesse No Full nsurance a: f rs neutral or full nsurance; too much care and too lttle actty f rs aerse and no nsurance b: If nsurers cannot obsere the leel of care : f due care= socally optmal care We see that n a unlateral ctmnjurer model we can obtan a socal optmum under strct lablty f the njurer s rs neutral or f nsurers hae perfect nformaton. 2 Vctms can buy ths, because they cannot nfluence the accdent rs. In a blateral settng and because n general, nsurance companes cannot obsere the leel of care, ctms wll only be able to buy partal coerage.
13 The role of lablty rules pecunary losses BOTH PARTIES HAVE LOSSES. We ll base ourseles on Boyer & Donne (1987) and Landes & Posner(1987) Rs neutral partes The Socal Optmum. The socal optmum stays the same as n the ctmaggressor model. Care and actty should be such that they maxmse the utlty that the ctm and the njurer 3 dere from the actty mnus the cost of care mnus the expected accdent losses. The two partes now share expected accdent losses. Denote λ the losses of the njurer and whch s the same as before. =, λ, the losses of the ctm, where λ λ 1 Max U ( s ) sx λ sslx (, x ) [ ] = Max U ( s ) sx sslx (, x ) =, + =. We get (4) Oerew results. We assume the followng:  If compensaton s pad, t s perfect.  The court and the agents are perfectly nformed and the law system functons perfectly. We assume no admnstrate costs or equal admnstrate costs for all rules.  Partes hae enough assets necessary to pay for the harm. (1) No lablty Partes wll tend to mnmse λ sspx (, x )( lx, x ) + sx. Snce partes do not carry all the losses, they wll not tae optmal care and wll be engaged n too much actty. (2) Strct lablty. Under strct lablty, partes compensate each other. Both are fully compensated so they wll not tae optmal care nor actty leel. (3) Neglgence. Under the neglgence rule, the losses le where they fall f both are neglgent or f both tae care. Neglectng actty for a moment, we get the followng problem: Care of the ctm C ar e 0 x x 3 We wll eep the njurerctm notaton, although both nfluence the accdent losses and both loose.
14 The role of lablty rules pecunary losses x λ sslx x + sx x sx (, ), λ sslx (, x ) + sx 0 0 0, sslx (, x ) + sx 0 0 sslx x 0 0 (, ) + sx, sx λ sslx (, x ) + sx, λ sslx (, x ) + sx If the njurer taes due care, the ctm wll also choose due care and ce ersa. If the njurer taes less than due care, the ctm wll compare λ sslx (, x ) + sx >< sx. If λ s small 0 and sx sx s large, then the ctm wll prefer 0 0 x. If the ctm chooses x, the njurer wll mae the same calculaton. On frst sght t loos as f there are two equlbrum, ( x, x ),( x, x ), but ( x, x ) s not an equlbrum. Snce λ sslx (, x ) + sx < sx + λ sslx (, x ) + sx < sx sslx (, x ) + sx + sx < sx + sx x and x mnmze Lx (, x ) 0 0 ( x, x) can not be an equlbrum Intutely, f the ctm taes less than due care, the njurer chooses due care because then the costs are shfted to the ctm. The ctm also nows ths and wll tae due care. The same apples to the njurer. We summarse: Table 4: Effcency of ncentes created by lablty rules. Care Actty leel Injurer Vctm Injurer Vctm No lablty no no no no Strct lablty yes no yes no Neglgence yes yes no+ no+ yes = effcent ncentes no = neffcent ncentes (gen behaour of other party) = f the leel of due care equals the socal optmal leel. += f the standard of behaour used to determne neglgence s defned only n terms of care. We see that although neglgence nduces optmal care by both partes, the actty leels of both partes s not optmal. 5. CONCLUSION. Transport causes accdents, whch are an mportant socal cost. There are dfferent nstruments to reduce ths cost. In ths paper we only looed at one nstrument, lablty rules. They confront drers wth the real cost of ther actty. We looed at the nfluence of dfferent lablty rules
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