Giuseppe Dari Mattiacci * Utrecht University ABSTRACT

Transcription

1 CHAPTER EIGHT NOXAE DEDITIO AND NEGLIGENCE: ROMAN AND MODERN SOLUTIONS TO INEFFICIENT MONITORING UNDER VICARIOUS LIABILITY Giuseppe Dari Mattiacci * Utrect University ABSTRACT Wy is vicarious liability strict for employers and duty-based for parents and supervisors? Wy did Roman law limit paterfamilias vicarious liability to te monetary value of te tortfeasor by means of noae deditio? Te answer to tese two questions is te same: parents, supervisors and patresfamilias do only partially bear te cost of teir agent s precaution. Under an unrestricted strict-liability rule, tey would tend to over-prevent accidents. Tis capter discusses tese and some oter related questions in a formal framework. JEL classification: K13. Keywords: vicarious liability, negligence, liability cap, tresold, negligence, noae deditio, Roman law. * Giuseppe Dari Mattiacci, Economic Institute/CIAV, Utrect University, Kromme Nieuwegract 22, 3512 HH Utrect, te Neterlands; g.darimattiacci@econ.uu.nl. I would like to tank Gerrit De Geest, Willemijn Lindenovius, Jef de Mot and Francesco Parisi for teir elpful comments. Updated versions of tis capter will possibly be available on my web page:

2 CHAPTER Introduction In te Law and Economics literature, vicarious liability is regarded as a system to provide judgment-proof agents wit incentives to take optimal precaution by means of principals monitoring or to enance te efficient allocation of risk between te parties. After te early contributions of Sykes (1981,1984 and 1988) and Kornauser (1982), wo clarified te logic of vicarious liability and delimited its range of application, te literature as mainly been interested in corporate liability, and, in general, in vicarious liability of firms or employers 1, te main concern being te desirability of a vicarious liability rule. Little attention as been devoted to anoter aspect of te problem: te cost borne by te vicariously liable party in order to monitor te potential injurer. Under personal liability, te optimal level of precaution is determined by te equality between te marginal benefit of precaution (te reduction in te epected accident loss) and te marginal cost tereof, wic yields te minimization of total costs. Under vicarious liability, te agent s precaution positively depends on te principal s monitoring ependitures. A reduction in te epected accident loss is attained at iger marginal costs, comprising bot te precaution cost and te monitoring cost. Terefore, te optimal level of precaution under vicarious liability is lower tan under personal liability. Tose principals, wo are only liable for te negligent conduct of teir agents, migt be induced to coose too ig a level of monitoring and teir agents to take overprecaution, if te agents negligence standard is set at a level wic would be optimal under personal liability but is ecessive under vicarious liability. Tis problem can be overcome by setting an appropriate negligence standard to te principal s level of monitoring also or by taking into account te principal s monitoring cost wile setting te agent s standard of negligence. Employers usually bear te precaution costs of teir agents, bot because tey ave to reward te agents for teir efforts and because taking precaution results in an opportunity cost (for instance, agents could produce more instead of preventing accidents). On te contrary, parents (and supervisors in general) migt not completely bear te precaution cost of teir cildren (and of persons under teir supervision), and tey migt be too concerned wit reducing te epected accident loss, regardless of te cost of taking precaution. Again, an appropriate negligence standard for te principal s level of monitoring can solve te problem. Similarly, in Roman family clans te paterfamilias did not bear te full cost of is slaves and family members precaution. As a solution, Roman law provided a maimum upper 1 See Arlen (1994), Capman (1992 and 1996), Coi (1998), Croley (1996), Fiscel and Sykes (1996), Kanna (1996), Kraakman (1984a, 1984b and 1986), Parker (1996), Scwartz (1996a), Savell (1997).

3 DARI MATTIACCI NOXAE DEDITIO AND VICARIOUS LIABILITY 3 tresold on te damages to be paid by te paterfamilias. Tis mecanism reduced te incentive for precaution, in a similar way to judgment-proofness 2. Te noae deditio provided in fact te paterfamilias wit te possibility to avoid damage compensation by anding over te wrongdoer to te victim s family. Te wrongdoer would ten become te property of te victim s family. Consequently, patresfamilias liability was limited to te monetary value of te wrongdoer. I will also take into account te case tat parents are too indulgent to teir cildren and overestimate teir cost of precaution, wile trying to take tat into account. Negligence can also be a solution to tis problem. Section 8.2 will formalize tese findings and prove tem in a simple model, wic generalizes te results in te case of bilateral-precaution accidents also. Section 8.3 will account for different combinations of te negligence criterion on te principal and/or te agent in employers liability. Section 8.4 will eplore te use of negligence as a solution to over-monitoring and overprecaution wen principals do not bear teir agents precaution cost, and te actual implementation tereof in different legal systems. Section 8.5 will focus on noae deditio in Roman law. Section 8.6 will address some concluding remarks. 8.1.A. A numerical eample Under personal liability, te optimal level of precaution minimizes te sum of te precaution cost and te epected accident loss. Table 1: personal liability Epected accident loss: p Precaution cost: Total costs: +p Under vicarious liability, te optimal level of precaution minimizes te sum of te precaution cost, te epected accident loss and te monitoring cost, and is terefore lower tan te optimal level of precaution under personal liability (20 instead of 30). If te principal bears all tese costs, e will enforce te optimal (under vicarious liability) level of precaution (I). Table 2: vicarious liability wen te principal bears te cost of te agent s precaution. Epected Monitoring Precaution Social cost: Negligence on te Negligence on te 2 Savell (1986).

4 CHAPTER 8 4 accident loss: p cost: m cost: +p+m agent: +p+m if <30 +m if 30 principal: +p+m if m<5 +m if m (I) (III) (II) However, if a negligence standard is set for te agent s precaution, te principal only pays damages if te agent is found negligent. A negligence standard set at te personalliability optimal level (30) does not take te monitoring cost into account and migt induce te principal to require ecessive precaution on te part of is agent (II). In fact, e bears te precaution cost plus te epected accident loss plus te monitoring cost if te agent takes less tan 30, but e only pays te precaution cost and te monitoring cost if te agent takes at least 30. Te problem can be solved eiter by taking te monitoring cost into account wile setting te standard of agent s negligence or by setting an appropriate standard to te principal s monitoring also (III). If te principal does not bear te precaution cost, e will opt for too ig a level of precaution (IV, in table 3), as e minimizes only te sum of te epected accident loss and te monitoring cost. Again, te problem can be solved by a negligence standard concerning te principal s monitoring level (V). Table 3:vicarious liability wen te principal does not bear te cost of te agent s precaution. Epected accident loss: p Monitoring cost: m Precaution cost: Principal s costs: p+m Principal s costs: p+m if m<5 m if m (V) (IV) 17 Roman law adopted a different solution: a maimum upper tresold on te damages to be paid by te principal (noae deditio). In order to clarify tis point, let us assume tat if te agent takes precaution te probability of an accident decreases, wile te arm is eogenous and remains constant. An appropriate upper limit on te damages (300 instead of 1000) makes te principal internalize a portion of te arm only and reduce is level of monitoring, and consequently te agent s level of precaution (VI instead of IV in table 4). Table 4: Noae deditio

5 DARI MATTIACCI NOXAE DEDITIO AND VICARIOUS LIABILITY 5 Epected accident loss: p Monitoring cost: m Precaution cost: Principal s costs: p+m Epected liability: pt Principal s costs: pt+m 10% 1000= % 300= % 1000= % 300= (VI) 6.8% 1000= % 300= % 1000= (IV) 6% 300= Te model 8.2.A. Unilateral accidents We will employ a simple model in order to describe te monitoring decision of a party (te principal), wo is vicariously liable for accident losses caused by anoter party (a judgmentproof agent) 3. We assume tat parties are risk-neutral, rational and utility maimizing. Derivatives are denoted by subscripts. Let: = agent s level of precaution, =[0, ); m() = principal s monitoring ependiture, m=[0, ); m >0; m >0 4 ; p() = probability of an accident occurring, p=[0,1]; p <0; p >0; = arm (eogenous), >0; a = agent s wealt, a< 5 ; w = principal s payment to te agent in a contractual setting; t = maimum upper tresold on te damages to be paid by te principal, t<. Te probability of te accident is a function of te agent s level of precaution only; te principal and te victim cannot reduce it by taking precaution on teir own (bilateral accidents will be considered in section 8.2.B). Te principal can induce te agent to take a certain level of precaution eiter by simply conditioning te agent s payment to tat level, or by enforcing 3 We do not discuss ere weter vicarious liability is preferable to personal liability. We only eamine tose situations in wic tis is te case. Tis question as been te main concern of te literature on vicarious liability. 4 Te causal relationsip between and m is te opposite as a matter of fact. Monitoring induces precaution and not te oter way around. However, writing m() simplifies te model and does not alter te substance of our reasoning at all. Te principal decides ow muc precaution e wants te agent to take, and invests in monitoring so tat tat level of precaution will result. It is simply anoter way of looking at te same relationsip. Te positive second derivative depicts te diminising returns (in terms of precaution) of te investment in monitoring. 5 We do not consider a for te reason tat in suc a case te agent is not judgment-proof and vicarious liability is not a necessary device to induce optimal precaution: personal liability would provide te agent wit perfect incentives.

6 CHAPTER 8 6 it directly by means of monitoring te agent s level of precaution and sanctioning noncompliance. Given te magnitude of te sanction, te monitoring cost increases wit te level of precaution tat te principal enforces at an increasing rate. We assume certainty in te principal s enforcement: given a combination of monitoring and sanctions, te required level of te agent s precaution results; as te agent always complies, sanctions are never applied and we do not consider tem into te model A.I. Social optimum Proposition 1. Te optimal level of precaution under vicarious liability is lower tan te optimal level of precaution under personal liability. Wen liability is vicarious, te reduction in te epected accident loss involves not only te agent s precaution cost (as under personal liability) but also te principal s monitoring cost, and ence te same level of precaution will be attained at a iger marginal cost. If liability is personal, te socially optimal level of precaution, p, minimizes te sum of te precaution cost and te epected accident loss. (1) [ p( ) ] min +. As Ep. (1) is conve 7, from te first order condition we ave: (2) p 1 p ( ) = If liability is vicarious te socially optimal level of precaution, *, minimizes te sum of te precaution cost, te epected accident loss and te monitoring cost. (3) min[ p( ) + m( ) ] +. As Ep. (3) is conve 8, from te first order condition we ave: (4) p ( ) + m * = 1. p ( * ) in Eq. (4) is clearly less tan p ( p ) in Eq. (2) 9. As p >0, it follows tat * < p : te optimal level of precaution under vicarious liability is lower tan te optimal level of precaution under personal liability. 6 Tis assumption can be relaed witout undermining te results of te analysis. 7 First order condition: 1+p =0. Second order condition p >0. 8 First order condition: 1+p +m =0. Second order condition p +m >0. 9 and m are bot greater tan zero.

7 DARI MATTIACCI NOXAE DEDITIO AND VICARIOUS LIABILITY A.II. Contractual settings 10 Te principal and te agent are parties to a contract; tey may be, for eample, employer and employee respectively. Te agent as limited wealt, a, and is judgment proof watever payment e receives from te principal, a+w< 11. Te principal is instead solvent. Te contract is Pareto optimal; terefore, it maimizes one party s utility, given te utility of te oter party. Let te agent s utility be w ~, and let te principal maimize is utility by minimizing te payment to te agent plus is epected liability. Let w n denote te payment in te case of no accident, and w te payment in te case of an accident occurring. Te principal sets (5) min [( 1 p( ) ) w + p( ) ( w + ) + m( ) ] w, w, n, n subject to te constraint of constant agent s utility: + 1 ( ) + ( ) = ~ (6) a ( p ) w p w w n Substituting Eq. (6) in Ep. (5), we obtain: (7) min[ w~ a + + p( ) + m( ) ] or min[ + p( ) + m( ) ] Ep. (7), te principal s minimization problem, is te same as in Ep. (3), te social cost minimization problem in te presence of vicarious liability; terefore, te principal will enforce * and bear m( * ) monitoring costs. Proposition 2. If te principal bears te agent s precaution cost, strict liability for bot te principal and te agent acieves te social optimum. In a contractual setting, te principal bears te agent s precaution costs, as e as to compensate te agent for is effort. Strict liability on te principal implies principal s liability regardless of is level of monitoring, m(). Strict liability on te agent implies tat te principal is liable regardless of te agent s level of precaution. Te proof of Proposition 2 immediately follows from te fact tat te principal bears eactly te social cost, Ep. (7). Remark. Te monitoring costs are likely to be zero for te first range on. If te agent s assets plus te payment e receives if te accident does not occur are greater tan zero, e will take some precaution also if te principal does not monitor 12. In suc a case, te agent 10 Te first part of tis section closely follows Savell (1987) at , ecept for te introduction of positive monitoring costs. 11 See Savell (1987) at 182, Sykes (1981). 12 Savell (1987) at 185.

8 CHAPTER 8 8 will coose is level of precaution by maimizing te left-and side of Eq. (6). Te first order condition yields: (8) p 1 a ( ) =, wn w were a is te level of te agent s precaution tat te principal can attain witout monitoring. Te principal can at most offer a contract in wic w =-a, tat is te agent pays is total assets to te principal wen an accident occurs 13. However, we ave assumed at te beginning tat w n +a<; terefore, te level of precaution cosen by te agent is lower tan te optimal level of precaution under personal liability, a < p. Te monitoring cost is, ence, zero for =[0, a ], and starts rising to te rigt of te interval 14. By investing in monitoring, te principal can attain a level of precaution, v, falling between a and p. Te assumptions made assure te conveity of te principal s minimization problem between tose two limits. Terefore, te conclusions reaced supra do not cange. Proposition 3. If te principal bears te agent s precaution cost, strict liability on te principal and duty-based liability on te agent migt yield overprecaution and overmonitoring if te standard of negligence for agent s beavior is set at p. Let p be te standard of negligence for te agent s beavior. After adapting Ep. (7), te principal s minimization problem becomes: (9) p + m( ) if min. p + p( ) + m( ) if < Te principal will coose p 15 if + m( ) < + p + m( ) for <, p p p (10) ( ) and * oterwise 16. From Proposition 1, it follows tat p is too ig a level of precaution and, ence, m( p ) is too ig a level of monitoring. If te standard of agent s negligence under vicarious liability is set at te same level as te standard of agent s negligence under personal liability, principals migt be too strict in order to escape liability, and enforce too ig a level of precaution. 13 Suc a contract would be illegal under many legal systems, as it makes te agent completely judgment proof. Te limit sould terefore be w 0; owever, tat does not cange te result. 14 Hence, m ()=0, m ()=0 for a ; m ()>0, m ()>0, oterwise. 15 Te principal will not coose > p as te first epression in (9) is increasing in. 16 Tis follows from Proposition 2.

9 DARI MATTIACCI NOXAE DEDITIO AND VICARIOUS LIABILITY 9 Neverteless, if te standard of agent s negligence is correctly set at *, as determined by Proposition 1, te outcome will be efficient. Proposition 4. If te principal bears te agent s precaution cost, duty-based liability on te principal acieves te social optimum even if te standard of agent s negligence is set at p. Let us assume tat te standard of principal s negligence is correctly set at m*=m( * ). Te principal s minimization problem is: (11) + m( ) min + p( ) + m( ) if if m m*. m < m* As m( p )>m(*), te principal will coose m(*): any iger level of monitoring would only increase te monitoring cost and tus te precaution cost witout decreasing principal s epected liability, wic is already equal to zero. 8.2.A.III. Non-contractual settings Te concern ere is wit te monitoring decision of a principal wo is not in a contractual relationsip wit te tortfeasor (we sall continue calling im te agent). Parents, supervisors, and patresfamilias are in tis situation. Proposition 5. If te principal only partially bears te agent s precaution cost (or underestimates it), strict liability on bot te principal and te agent yields overprecaution and over-monitoring. If te principal overestimates te agent s precaution costs, strict liability on bot te principal and te agent yields underprecaution and under-monitoring. Wen te parties are not in a contractual relation, te principal migt not internalize te agent s precaution cost perfectly, for e does not ave to compensate te agent for is effort. On te one and, e can use autority over te agent and require a certain level of precaution, witout aving to pay for it. On te oter and, wile trying to take te agent s precaution cost into account, te principal migt over or underestimate tat. Let b denote te portion of tat te principal internalizes. b<1 if te principal does not fully internalize te agent s cost or underestimates tem. b>1if te principal overestimates te agent s cost. (12) min[ b p( ) + m( ) ] +.

10 CHAPTER 8 10 As Ep. (12) is conve 17, from te first order condition we ave: r (13) p ( ) b + m =, were r is te level of monitoring tat minimizes Ep. (12). If b<1, p ( r ) in Eq. (13) is clearly greater tan p ( * ) in Eq. (4). As p >0, it follows tat r > *, and ence m( r )>m( * ). If te principal does not bear te agent s precaution costs fully, e will spend too muc on monitoring and induce too ig a level of te agent s precaution. On te contrary, if b>1, r < *, and, ence m( r )<m( * ). If te principal overestimates te agent s precaution cost, e will spend too little on monitoring and induce too low a level of te agent s precaution. Proposition 6. If te principal only partially bears te agent s precaution cost (or underestimates tem), duty-based vicarious liability or an appropriate maimum upper tresold on damages acieves te social optimum. If te principal overestimates te agent s precaution cost, duty-based vicarious liability acieves te social optimum under certain restrictive conditions. Te inefficient-monitoring / inefficient-precaution problem described in Proposition 5 can be dealt wit by introducing a negligence standard concerning te principal s monitoring level or a maimum upper tresold on principal s liability. Under duty-based liability, if te standard of negligence is correctly set at m*=m(*) 18, te principal s minimization problem is: (14) b + m( ) min b + p( ) + m( ) if if *. < * If b<1, ten r > *, and te principal will coose *: any iger level of precaution would only increase te cost of monitoring witout decreasing te epected liability, wic is already equal to zero. Terefore, duty-based vicarious liability solves te overprecaution / over-monitoring problem completely. If b>1, ten r < *, and te principal will coose * only if b*+* b r +p( r )+m( r ). Consequently, duty-based vicarious liability does not always solve te underprecaution / under-monitoring problem. Let us now turn to te second proposed solution. If a tresold t< is introduced on 17 First order condition: b+p +m =0. Second order condition: p +m >0. 18 Note tat te standard of principal s negligence can be epressed indifferently in terms of m or. We sall use te latter as it simplifies te analysis.

11 DARI MATTIACCI NOXAE DEDITIO AND VICARIOUS LIABILITY 11 principal s liability, te principal s minimization problem becomes 19 : (15) min[ b p( ) t + m( ) ] +. Te level of t sould be set so tat * minimizes Ep. (15). As Ep. (15) is conve 20, from te first order condition we ave: (16) p ( ) b + m =. t By substituting te rigt-and side of Eq. (16) in te left-and side of Eq. (4), we obtain: v b + m ( *) (17) t =. 1+ m ( *) It is clear tat t< can yield * only if b<1. Hence a maimum upper tresold can only solve te overprecaution / over-monitoring problem, but would be an inappropriate solution for te case of underprecaution / under-monitoring. 8.2.B. Bilateral accidents Let us now consider te case of victims being able to take some precautions in order to curtail te probability of accidents. In addition to wat as already been specified for te case of unilateral accidents, let: y = victim s level of precaution, y=[0, ); p(,y) = probability of an accident occurring, p=[0,1]; p <0; p y <0; p >0; p yy > B.I. Social optimum If liability is personal, te socially optimal level of precaution, ( p, y p ), minimizes te sum of te precaution cost and te epected accident loss. (18) min[ y p(, y) ] +, y +. As Ep. (18) is conve 21, from te first order condition we ave: 19 Te result would be te same even if we considered a stocastically variable and eogenous arm. Te formal analysis would only sligtly cange. 20 First order condition: b+p t+m =0. Second order condition: p t+m >0. 21 First order conditions: 1+p =0 and 1+p y =0. Second order conditions p >0 and p yy >0.

12 CHAPTER 8 12 (19) p p y ( ( p p, y, y p p 1 ) =. 1 ) = If liability is vicarious, te socially optimal level of precaution, (*, y*), minimizes te sum of te precaution cost, te epected accident loss and te monitoring cost. (20) min[ y + p(, y) + m( )] +., y As Ep. (20) is conve 22, from te first order condition we ave: (21) p p y ( *, y *) ( *, y *) 1+ m = 1 =, were (*, y*) is te level of precaution wic minimizes Ep. (20) and is clearly different from ( p, y p ). Two possible solutions are compatible wit Eq. (19) and (21). (i) (*< p, y* y p ) (ii) (* p, y*>y p ) Confronting te first Eq. in (21) and in (19), we ave *(y)< p (y) for any y. Hence, if y* y p also *< p. If y*>y p, ten again * p, as (y*>y p, *> p ) cannot be a solution: under vicarious liability te marginal benefit of precaution is te same as under personal liability but te marginal costs are iger, ence at least precaution level of eiter party must be lower under vicarious liability tan under personal liability B.II. Contractual settings In a contractual setting, a negligence rule can induce bot parties to take te optimal level of precaution. From te analysis under te former section it is clear tat if te standard of negligence is set at te personal-liability level for eiter or bot te agent and te victim, te result will be inefficient. Hence, any negligence rule ougt to be implemented by setting a due level (for te victim, y*, or te agent, *) tat takes te monitoring cost into account. 8.2.B.III. Non-contractual settings In a non-contractual setting te principal only partially bears, te agent s cost of precaution. Terefore, te minimization problem is: 22 First order conditions: 1+p +m =0 and 1+p y =0. Second order conditions p +m >0 and p yy >0. 23 If (y*, * p ) were a solution, ten p +y p +p( p,y p )+m( p )>*+y*+p(*,y*)+m(*), wic can be rewritten as p +y p +p( p,y p )>*+y*+p(*,y*)+m(*)-m( p ), wic is not possible as m(*)-m( p ) 0 and

13 DARI MATTIACCI NOXAE DEDITIO AND VICARIOUS LIABILITY 13 (22) min[ b y + p(, y) + m( )] +., y As Ep. (22) is conve 24, from te first order condition we ave: (23) p p y r r (, y ) r r (, y ) b + m = 1 =, were ( r, y r ) is te level of precaution wic minimizes Ep. (22), and it is clearly different from (*, y*). If b<1, two possible solutions are compatible wit Eq. (21) and (23): (i) ( r >*, y r y*) (ii) ( r *, y r <y*) Confronting te first Eq. in (21) and in (19), we ave r (y)>*(y) for any y. Hence, if y* y r also *< r. If y*<y r, ten again r *, as ( r <*, y r <y*) cannot be a solution: in a noncontractual setting te marginal benefit of precaution is te same as in te social optimum, but marginal costs are lower, ence at least te precaution level of eiter party must be iger in a non-contractual setting tan in te social optimum 25. If b>1, te feasible solutions are: (i) ( r <*, y r y*) (ii) ( r *, y r >y*) Te reason is opposite to te one given above. As in te unilateral precaution case, negligence or a maimum upper tresold can be implemented as solutions to te problem under te conditions already discussed Different combinations of te negligence criterion in employers liability Te foregoing analysis suggests tat if te principal is eld liable for negligent agents torts only, e will enforce too ig a level of te agent s precaution unless: (i) Wile setting te due level of te agent s precaution, monitoring costs are also taken into account (te due level is set at *); (ii) Monitoring is inepensive (*= p ); (iii) A duty-based vicarious liability rule is implemented and an appropriate due level of monitoring is set [m*=m(*)]. P +y P +p( p,y p )<*+y*+p(*,y*). Hence, *< p. However, bot y*>y p and y* y p are possible. 24 First order conditions: b+p +m =0 and 1+p y =0. Second order conditions p +m >0 and p yy >0. 25 If (y r, r *) were a solution, ten b r +y r +p( r,y r )+m( r )<b*+y*+p(*,y*)+m(*); it follows tat b r +y r +p( r,y r )+m( r )<b*+y*+p(*,y*)+m(*)+(1-b)(*- r ), as (1-b)(*- r ) 0; te former can be rewritten as r +y r +p( r,y r )+m( r )<*+y*+p(*,y*)+m(*).tis is not possible as (*,y*) minimizes te epression by

14 CHAPTER 8 14 (iv) Te situation can be modeled as suggested by Grady (1983) and Kaan (1990); see my concluding remarks on tis point. If none of tese conditions is fulfilled, a due level of te agent s precaution p tat would be optimal under personal liability is ecessive under vicarious liability. Unless monitoring is inepensive, vicarious liability corrects te inefficiency due to personal liability of judgmentproof agents at te price of lower accident prevention. Tis framework can be applied to te study of te different legal solutions adopted by various legal systems and to teir efficiency evaluation. German law implements a duty-based liability for employers, wile Frenc and Anglo-American law generally opt for strict employers liability (see Eörsi, 1975). A toroug comparative analysis sould also take into account judicial decisions and te caracteristics of te contets in wic employers liability takes place (as indicated by points (ii) and (iv) above), but it would eceed te scope of tis capter. Here I simply suggest a teoretical framework wic can be implemented in suc an analysis Vicarious liability of parents and supervisors: negligence as a solution for overdemanding principals If te principal only partially bears te agent s cost of precaution, e will enforce too ig a level of precaution. In a non-contractual setting, te principal does not ave to reward te agent for is effort. Te relationsips between parents and teir cildren and between supervisors and te persons under teir supervision resemble tis situation. Parent will only partially take into account te cost of precaution borne by teir cildren. Similarly, supervisors will not internalize te full cost of precaution borne by te supervised persons. Bot of tem will enforce too ig a level of precaution. It is also possible tat parents and supervisors attempt to consider te costs of precaution tat tey impose on teir cildren / supervisees, wile taking teir decisions concerning monitoring. If tey overestimate tose costs (tey are too indulgent), ten underprecaution will result. An appropriate negligence standard can always solve te first problem and will sometimes solve te second as well. Te liability of parents and supervisors is negligencebased in most legal systems (see le Gall, 1976). In te ligt of my analysis, tis seems to be an efficient solution. definition of te social optimum level of precaution. Hence, r >*. However, bot y r y* and y r <y* are possible.

15 DARI MATTIACCI NOXAE DEDITIO AND VICARIOUS LIABILITY Noae deditio as a Roman law solution for over-demanding vicariously liable patresfamilias In Roman families, te paterfamilias (te principal) did not ave to reward is agents (te slaves and te members of is family, filiifamilias) for teir efforts. If e ad been obliged to pay any arm caused by any of tem to anoter family clan, e would ave enforced too ig a level of precaution (at too ig a monitoring cost). Noae deditio limited is responsibility to te monetary value of te wrongdoer, wo could be anded over to te victim as a form of compensation. Tis solution rougly corrects te overprecaution/over-monitoring problem. Te istorical evolution of noae deditio confirms tese teoretical predictions. Originally, it was a form of vengeance on te injurer s body. Te tortfeasor was anded over to te victim s family in order to be punised. Te tortfeasor was often killed by is family and is corpse was anded over to te victim s family, for te only purpose of redressing te wrong committed. Te same can be found in te actio de pauperie, wic provided a similar solution for damages caused by animals: vengeance was directed against te body of te animal. At a later stage, wen tort law evolved from its early criminal law matri, noae deditio remained in force but canged its function. It simply meant te transfer of te property rigt on te slave or te member of te family to te victim s family. Our framework applies at tis stage. Te possibility of escaping liability by anding over te tortfeasor to te victim generated a sort of limited liability: te paterfamilias bore te lower cost between damage compensation and te market value of te slave / member of te family. I ave eplained tis peculiar system by noticing tat te paterfamilias was likely to internalize only a portion of te slaves efforts, and terefore under full liability e would ave been too severe on tem. Te limitation on paterfamilias liability mitigated tis effect. In a later period, wen filiifamilias liability could be personal for te eistence of a personal patrimony (peculium), noae deditio lost its function and tended to disappear, wile it was retained for slaves. Tis is consistent wit my eplanation, as, wen liability can be personal, te need for vicarious liability fades and te function of noae deditio as a corrective device for te principal s enforcement level also disappears. In modern societies, noae deditio does not occur for two reasons. First, wen te principal-agent relationsip is based upon a contract, principals internalize te agents precaution cost. I ave demonstrated tat, in suc cases, since te principal as to reward te agent for is effort, e will consider te cost of precaution wile setting te level tereof. Terefore, tere is no need for a corrective device. Second, wen te principal-agent relationsip is non-contractual, in modern societies te

16 CHAPTER 8 16 principal s enforcement migt also lead to too ig a level of precaution. However, a better solution is available: negligence rules. Negligence rules, if appropriately set, are more precise a mecanism to deal wit te over-monitoring / overprecaution problem tan noae deditio, wic only provided a roug correction of te problem, for it limited principal s liability to te market value of te slave, wic did not necessarily correspond to te optimal limit. On te contrary, negligence rules can be set eactly at te optimal level and correct te vicarious liability rule perfectly. Neverteless, te application of a negligence rule triggers iger administrative costs tan noae deditio, as it requires an analysis of te level of precaution actually taken by te parties and of te precaution and monitoring tecnology. Tose costs are likely to be lower in modern societies tan in ancient societies, for a muc more developed judicial system is available, te cost of acquiring information is lower, te understanding of te laws of nature is more precise and systems of records are more common Concluding remarks Some of te results of tis analysis crucially depend on te discontinuity created by te application of a negligence rule to te injurer s cost function. Suc discontinuity is due to te fact tat negligent injurers also pay damages for te accidents tat would ave occurred anyway, even if tey ad been non-negligent. Grady (1983) and Kaan (1990) ave demonstrated tat, if suc discontinuity is eliminated, a due level of precaution tat is iger tan te optimal level does not induce overprecaution. However, a due level of precaution tat is lower tan te optimal level of precaution yields underprecaution just as in te standard model. It follows tat te first part of tis analysis does not old true in te Grady-Kaan model: principals will coose te optimal level of precaution even if te agents standard of negligence is too ig. Neverteless, te second part of te analysis still olds true: tose principals, wo do not bear te full cost of te agent s precaution, will monitor ecessively and a negligence rule can lower teir monitoring levels References Arlen, Jennifer H. (1994), Te Potentially Perverse Effects of Corporate Criminal Liability, 23 Journal of Legal Studies, See Posner (1980).

17 DARI MATTIACCI NOXAE DEDITIO AND VICARIOUS LIABILITY 17 Capman, Bruce (1992), Limited Auditors Liability: Economic Analysis and te Teory of Tort Law, 20 Canadian Business Law Journal, Capman, Bruce (1996), Corporate Liability and te Problem of Overcompliance, 69 Soutern California Law Review, Coi, Stepen (1998), Market Lessons for Gatekeepers, 92 Nortwestern University Law Review, 916 ff. Cu, C.Y. Cyrus and Qian, Yingy (1995), Vicarious Liability under a Negligence Rule, 15 International Review of Law and Economics, Croley, Steven P. (1996), Vicarious Liability in Tort: On te Sources and Limits of Employee Reasonableness, 69 Soutern California Law Review, Eörsi, Gyula (1975), Private and Governmental Liability for te Torts of Employees and Organs, in André Tunc (ed.), Torts, International Encyclopedia of Comparative Law, Tübingen, Mor. Fiscel, Daniel R. and Sykes, Alan O. (1996), Corporate Crime, 25 Journal of Legal Studies, Grady, Mark F. (1983), A New Positive Economic Teory of Negligence, 92 Yale Law Journal, Kaan, Marcel (1989), Causation and Incentives to Take Precaution under te Negligence Rule, 18 Journal of Legal Studies, Kanna, V.S. (1996), Corporate Criminal Liability: Wat Purpose does it Serve?, 109 Harvard Law Review, Kornauser, Lewis A. (1982), An Economic Analysis of te Coice between Enterprise and Personal Liability for Accidents, 70 California Law Review, Kraakman, Reinier H. (1984a), Te Economic Functions of Corporate Liability, in Hopt, Klaus J. and Teubner, Gunter (eds), Corporate Governance and Directors Liabilities, New York, de Gruyter, Kraakman, Reinier H. (1984b), Corporate Liability Strategies and te Costs of Legal Controls, 93 Yale Law Journal, Kraakman, Reinier H. (1986), Gatekeepers: Te Anatomy of a Tird-Party Enforcement Strategy, 2 Journal of Law, Economics, and Organization, Landes, William M. and Posner, Ricard A. (1987), Te Economic Structure of Tort Law, Cambridge (MA), Harvard University Press. Le Gall, Jean-Pierre (1976), Liability for Persons under Supervision, in André Tunc (ed.), Torts, International Encyclopedia of Comparative Law, Tübingen, Mor. Levmore, Saul (1995), Gomorra to Ybarra and More: Overetraction and te Puzzle of Immoderate Group Liability, 81 Virginia Law Review, Newman, Harry A. and Wrigt, David W. (1990), Strict Liability in a Principal-Agent Model, 10 International Review of Law and Economics, Parker, Jeffrey (1996), Doctrine for Destruction: Te Case of Corporate Criminal Liability, 17 Managerial and Decision Economics, Posner, Ricard A. (1980), A Teory of Primitive Society wit Special Reference to Law, 23 Journal of Law and Economics, Scwartz, Gary T. (1996a), Te Hidden and Fundamental Issue of Employer Vicarious Liability, 69 Soutern California Law Review,

18 CHAPTER 8 18 Savell, Steven (1986), Te Judgment Proof Problem, 6 International Review of Law and Economics, Savell, Steven (1987), Economic Analysis of Accident Law, Cambridge (MA), Harvard University Press. Savell, Steven (1997), Te Optimal Level of Corporate Liability Given te Limited Ability of Corporations to Penalize Teir Employees, 17 International Review of Law and Economics, Sykes, Alan O. (1981), An Efficiency Analysis of Vicarious Liability Under te Law of Agency, 91 Yale Law Journal, Sykes, Alan O. (1984), Te Economics of Vicarious Liability, 93 Yale Law Journal, Sykes, Alan O. (1988), Te Boundaries of Vicarious Liability: An Economic Analysis of te Scope of Employment Rule and Related Legal Doctrines, 101 Harvard Law Review,