Northwestern University School of Law

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1 Northwestern University Shool of aw aw and Eonomis Paers Year 2003 Paer 28 Manufaturer iability for arms Caused by Consumers to Others Brue. ay Kathryn E. Sier arvard aw Shool Northwestern University - Kellogg Shool of Management, ksier@law.harvard.edu This working aer is hosted by The Berkeley Eletroni Press beress and may not be ommerially rerodued without the ermission of the oyright holder. htt://law.beress.om/nwws-le/art28 Coyright 2003 by the authors.

2 Manufaturer iability for arms Caused by Consumers to Others Brue. ay and Kathryn E. Sier Abstrat This aer investigates whether manufaturers should be liable if onsumers, through the use of a rodut, ause harm to others. If onsumers have dee okets then onsumer-only liability is soially desirable. With onsumer insolveny, however, onsumer-only liability leads to inadequate onsumer reautions, inadequate safety features, and exessive eonomi ativity. With homogeneous insolvent onsumers, the best rule is residual-manufaturer liability where the onsumer bears rimary resonsibility and the manufaturer bears the shortfall in damages. When onsumers willingness-to-ay is orrelated with soial harm they ause then residual-manufaturer liability distorts the market quantity. When onsumers differ in their wealth then residual-manufaturer liability reates an ineffiient ross-subsidization and an overrovision of safety features. In both ases, onsumer-only liability may be referred to residual-manufaturer liability. Aliations, inluding gun manufaturer liability, are disussed.

3 Manufaturer iability for arms Caused by Consumers to Others Brue ay and Kathryn E. Sier 1 August 13, 2003 This aer investigates whether manufaturers should be liable if onsumers, through the use of a rodut, ause harm to others. If onsumers have dee okets then onsumer-only liability is soially desirable. With onsumer insolveny, however, onsumer-only liability leads to inadequate onsumer reautions, inadequate safety features, and exessive eonomi ativity. With homogeneous insolvent onsumers, the best rule is "residual-manufaturer liability" where the onsumer bears rimary resonsibility and the manufaturer bears the shortfall in damages. When onsumers' willingness-to-ay is orrelated with soial harm they ause then residual-manufaturer liability distorts the market quantity. When onsumers differ in their wealth then residualmanufaturer liability reates an ineffiient ross-subsidization and an overrovision of safety features. In both ases, onsumer-only liability may be referred to residual-manufaturer liability. Aliations, inluding gun manufaturer liability, are disussed. 1 arvard aw Shool and Kellogg Graduate Shool of Management and NBE. The authors thank ik Brooks, oward Chang, Jim Dana, Andy Daughety, Mith Polinsky, Jennifer einganum, Sott Shaefer, seminar audienes at Kellogg and NBE, and eseially Steve Shavell for helful omments and suggestions. 1 osted by The Berkeley Eletroni Press

4 1. Introdution Courts have been alled uon in reent years to deide whether a manufaturer should be liable if a onsumer, through the use of the manufaturer s rodut, auses injury to another erson. The most salient examle is the rash of lawsuits filed against firearms manufaturers, whih seek to hold them liable for the deaths and injuries aused by the riminal use of guns. Suh lawsuits have generally been unsuessful, but the issue of the gun makers liability is still hotly disussed in the legal and olitial arenas. 2 This issue is by no means limited to guns. An automobile, for examle, may hit a edestrian, ylist, or motorist; alohol onsumtion inreases this risk even further. Motorboat engines an laerate swimmers. awnmowers fling rojetiles, harming assersby. Pestiides may oison neighbors' ets and hildren. Cigarette lighters may burn down aartment buildings. And, even more dramatially, some ordinary ro fertilizers when mixed with gasoline beome extraordinarily otent exlosives; this is how the bomb that destroyed the Oklahoma City federal building was made. One an, of ourse, imagine many other roduts whose use by the onsumer reates risks to others, raising the general question whether the manufaturer should be liable for suh risks to nononsumers. 3 2 By and large, the ourts have refused to hold manufaturers liable for the injuries suffered by nononsumers as a onsequene of onsumers use of their roduts. This refusal has been eseially ronouned in ases where the injuries are the result of negligent or riminal ondut by the onsumer. The ourts stane has been that the onsumer alone is resonsible for suh misbehavior. And even in ases where the aident was not the onsumer s fault, the ourts have generally been relutant to hold the manufaturer liable to the nononsumer, unless the rodut malfuntioned. For examle, if a ar s brakes fail and a edestrian is hurt, the edestrian may be able to reover from the manufaturer, rovided that the brake failure is not the onsumer s fault. These limitations on liability have been exliated, and frequently ritiized, by legal ommentators. 3 To take another examle, violent movies or omuter games may insire individuals to ommit murder. These, and eah of the examles given in the reeding aragrah in the text, have led to lawsuits brought against manufaturers by nononsumer vitims of the rodut in question. 2 htt://law.beress.om/nwws-le/art28

5 Manufaturer liability is undesirable when onsumers have adequate finanial resoures and an be held ersonally liable for non-onsumer injuries. In these irumstanes, imosing strit liability on the onsumers alone is the soially otimal liability rule. 4 With onsumer-only liability, onsumers fully internalize the soial harm aused by their rodut use: they bear the ost of their own injuries diretly and ay in full for the injuries suffered by others. Consequently, they will take otimal reautions to redue the robability of aidents, will demand aroriate safety features from the roduts' manufaturers, and will onsume the soially otimal quantities. When onsumers lak the finanial resoures to fully omensate their vitims or are otherwise judgment roof then onsumer-only liability fails to ahieve soial otimality -- insolvent onsumers will demand hea, unsafe roduts and use them dangerously. 5 When onsumers are homogeneous with idential demand urves, finanial assets, and roensities to ause harm the best strit liability rule holds the manufaturer resonsible for the shortfall in See ouvenagle v. Wright, 340 N.W.2d 783 Ia. A automobile; Dauhin Deosit Bank and Trust Co. v. Toyota Motor Cor., 596 A.2d 845 Pa. Su alohol; Fitzatrik v. Madonna, 623 A.2d 322 Pa. Su outboard motor; Dugan v. Sears, oebuk & Co., 447 N.E.2d 1055 Ill. A lawnmower; Masarenas v. Miles, In., 986 F. Su. 582 W.D. Mo estiide; Curtis v. Universal Math Cor., 778 F. Su E.D. Tenn igarette lighter; Gaines-Tabb v. ICI Exlosives, USA, In., 160 F.3d th Cir fertilizer; Byers v. Edmondson, 712 So.2d 681 a. A. 199 violent movie; James v. Meow Media In., Civ. No. 5:99CV W.D. Ky violent omuter game. 4 amada 1976 oints out that onsumer liability for bystander harm works as well when the bystanders an sue the onsumers for damages. Sene 1977 argues out that onsumer liability is less desirable when onsumers misereive the rodut risks. 5 This so-alled "judgment-roof roblem" is formalized in Shavell One ould try to give onsumers a greater inentive to take are by using non-finanial santions, suh as greater use of riminal enalties for areless or maliious rodut use. This strategy might inlude requirements that a onsumer have a liense and/or arry liability insurane, as is done with automobiles. Note, however, that riminal enalties are ostly, and frequently ineffetive. Some individuals are undeterred by any feasible threat of riminal liability. But raising the rie of roduts may restrain these undeterrable individuals, if only by laing some roduts out of finanial reah. The working assumtion in this aer is that the threat of diret liability ivil or riminal is often insuffiient to fore onsumers to take full aount of risks to third arties. 3 osted by The Berkeley Eletroni Press

6 non-onsumer damages not overed by the finanially-onstrained onsumer, a rule that we all "residual-manufaturer liability." 6 Although onsumers still take inadequate reautions when using risky roduts, manufaturers will design and rodue safer roduts. Furthermore, the market rie will neessarily rise to reflet both the additional investments in safety and the exeted future manufaturer liability, leading onsumers to hoose the effiient level of eonomi ativity. 7 esidual-manufaturer liability may be undesirable, however, when onsumers are heterogeneous. Suose that onsumers have heterogeneous referenes and heterogeneous roensities to ause soial harm. esidual-manufaturer liability leads to distortions when the onsumers' elastiity of demand is systematially orrelated with the exeted soial harm that they ause. If onsumers with more elasti demands ause more harm on average, then the ometitive market will oversuly the rodut. If onsumers with less elasti demands ause more harm, then the ometitive market will undersuly the rodut. Indeed, residual-manufaturer liability may deress the level of eonomi ativity so muh that soiety as a whole would be better off with onsumer-only liability. A numerial examle rovides intuition for this result. Suose there is a oulation of onsumers, eah of whom demands at most one unit of the good. Eah unit osts $10 to rodue. Suose that that 99% of the oulation auses no harm but 1% auses harm of $ In a sense, the argument is loosely analogous to that for viarious liability, i.e., holding emloyers liable for the negligene of their emloyees. Sykes, 1998, rovides a survey. See also Mattiai and Parisi, But unlike the viarious liability situation, the manufaturer has little ontrol over how the rodut is used after it is sold. Our aroah in this aer is to analyze the signifiane of suh onsumer heterogeneity for the issue of manufaturer liability for dangerous roduts. 7 As shown by Shavell 1980, the higher rie generally leads to more rudent rodut use. Shavell 1980 does not disuss residual-manufaturer liability or the heterogeneity issues disussed here. 4 htt://law.beress.om/nwws-le/art28

7 Furthermore, suose that the safe onsumers value the rodut less than the harmful onsumers: v = $12.99 and v = $ All onsumers are totally insolvent ex-ost, while manufaturers have dee okets. Finally, we assume that the manufaturers annot disriminate among the different onsumer tyes. 8 Notie that both tyes of onsumer "should" urhase the rodut in this examle: 99% of the oulation reates a surlus of $2.99 while 1% of the oulation reates a soial value of a enny. 9 With onsumer-only liability, ometition drives the rie down to = $10, the manufaturers' marginal ost of rodution. The soially otimal outome is obtained: all onsumers -- safe and unsafe alike -- buy the rodut. Now onsider residual-manufaturer liability. If both tyes of onsumer urhased the rodut the rie would be = $13, above safe onsumers' valuation of $ So the safe onsumers would be driven from the market and the rie would subsequently rise to = $310, the marginal rodution ost of $10 lus the exeted soial harm aused by harmful tyes, $300. Only the harmful 1% of the oulation urhases the rodut, and, for these harmful onsumers, the "soial surlus" is just a enny. Soial welfare has obviously fallen. 10 esidual-manufaturer liability may also fail when onsumers have idential harms and demands but have heterogeneous finanial assets. With onsumer-only liability, the solvent onsumers would internalize the damages aused by their rodut use and would demand safety features and be rudent in their urhase deisions and rodut use. Insolvent onsumers, on the other hand, would urhase unsafe roduts and take too little are. With residual-manufaturer 8 Alternatively, one ould assume that there is a resale market making rie disrimination infeasible: the low harm tyes ould always resell the rodut to the high harm tyes. 9 The soial surlus when the safe onsumers urhase the rodut is $ $10.00 = $2. 99 while the soial surlus for the unsafe onsumers is $ $10.00 $ = $ If the soial surlus for the unsafe onsumers was negative in this examle then the market would ease to exist. 5 osted by The Berkeley Eletroni Press

8 liability the solvent onsumers may be driven out of the market. Furthermore, in the searating equilibrium the solvent onsumers are sulied with exessively safe roduts. These distortions may be so severe that it is better to imose liability on the onsumers alone rather than have the manufaturer bear the shortfall in non-onsumer damages. The issues raised here are distint from the large literature that fouses on rodut injuries to onsumers. Where injuries to onsumers are involved, onsumers and manufaturers jointly absorb the osts of suh injuries with the alloation deending on the ontrat struk between them, and so have a natural joint inentive to take otimal reautions against injury. To ut it another way, rodut injuries to onsumers are largely internalized in well-funtioning markets amada, 1976; andes and Posner, 1984 and Even without any manufaturer liability imosed by law, onsumers would be willing to ay a remium for safer roduts that redue their ersonal risk and to use risky roduts rudently. Consequently, the eonomi arguments for roduts liability for onsumer injuries have foused on situations involving transations osts and market imerfetions. Manufaturer liability for onsumer injuries may be desirable, for examle, when onsumers misereive rodut risks Sene, 1977; Ele and aviv, 1978; Polinsky and ogerson, 1983 or manufaturers have rivate information about the safety of their roduts or take unobservable ations that affet rodut safety Daughety and einganum, 1995 and The aer is organized as follows. Setion 2 resents the basi framework with a reresentative onsumer. Setion 3 allows for heterogeneous demand urves and harm roensities, and shows how the desirability of residual-manufaturer liability deends on the orrelation between these to fators. Setion 4 onsiders the distortions assoiated with 11 Early desritive work inludes Calabresi 1961 and MKean htt://law.beress.om/nwws-le/art28

9 heterogeneous solveny among onsumers. Setion 5 onludes. All roofs are given in the aendix. 2. The Basi Framework We begin with the ase of reresentative onsumer urhasing a harmful rodut from a erfetly ometitive market. The robability that a single unit of the good will ause an aident is π x, y, where x 0 is the manufaturer's investments in rodut safety and y 0 is the onsumer's reaution level. The manufaturers' investments in rodut safety are erfetly observable to the onsumer at the time that he makes his urhase deisions. The manufaturers have idential onstant-returns-to-sale rodution tehnologies with marginal rodution ost x we normalize the other rodution osts to zero. We assume that π x, y is dereasing in eah argument and is stritly onvex. 12 Furthermore, we assume that the marginal return from the first dollar of investment is arbitrarily large, imπ 1 x, y = and imπ 2 x, y =. 13 x 0 y 0 Conditional uon an aident ourring, the soial harm is h + d where h > 0 is the harm borne by the onsumer diretly and d > 0 is the harm suffered by third arties. 14 Consumers are said to be insolvent or "judgment-roof" when their future assets, w, are insuffiient to over the damages to third arties, d. 15 In ontrast to the onsumers, manufaturers are assumed to 12 If π 12 x, y > 0 then the reautions are omlements and if π 12 x, y < 0 then the reautions are substitutes where π 12 x, y denotes the ross-artial derivative. 13 We adot the notation that π 1 x, y = π x, y x and π 2 x, y = π x, y y. The assumtion in the text guarantees the existene of an interior solution. 14 If d < 0, so the ativity reates soial benefits, then liability will not hel to enourage the ativity. The "vitims" benefiiaries in this ase would have no inentive to sue. A better oliy might be to subsidize the ativity instead. 15 Note that the rie that the onsumers ay ex ante is not deduted from their future wealth. This assumtion is made mostly for onveniene, and is quite realisti when aidents are low 7 osted by The Berkeley Eletroni Press

10 have dee okets. The reresentative onsumer reeives a marginal benefit P q from onsuming the q th unit of the good. This is the inverse demand urve net of any future aident osts and liability onerns. δ m We onsider the lass of strit liability rules, { δ, }, that alloate damages δ w to m the onsumer and δ to the manufaturer. 16 Note that this lass does not inlude rules where the liability deends on the atual reautions taken by the manufaturer and the onsumer. Negligene rules, and alternative oliies to strit liability, will be disussed in the onlusion. 2.1 The Soial Otimum Soial welfare, whih is a funtion of the market quantity, q, and manufaturer and onsumer reautions, x and y, is: S x, y, q = q [ P z π x, y h + d x y] dz Conditional on reautions x and y, the soially otimal quantity sold is gx,y where: P g x, y = π x, y h + d + x + y. 2 At this quantity, the rivate value of the marginal unit, P g x, y, is exatly offset by the exeted future harm, π x, y h + d, lus the reaution osts, x + y. et { x, y, q } be the first-best outome. 18 robability events. Similar results would be obtained in a world where onsumers have dee okets but there is a low robability of being held resonsible for the damages. This may be due to diffiulties in attributing harm. 16 The astute reader will notie that we are imliitly assuming that only one aident an our for a given onsumer. This is justified if aidents our with a random arrival rate and eonomi ativity eases after the first aident. 17 Some may argue that the benefits to injurers from ertain ativities e.g. rae should not be inluded in the soial welfare funtion. Formally, one ould nullify this onern by adjusting the soial harm for examle. 8 htt://law.beress.om/nwws-le/art28

11 2.2 The Cometitive Equilibrium In a ometitive market, reautions x and y and the market quantity q are hosen by rivate arties in the shadow of future liability. Manufaturers omete by offering rie-safety airs, {,x}, to attrat the reresentative onsumer. They are the "leaders," hoosing reautions first, while the onsumers are the "followers," subsequently hoosing their reautions. The ometitive equilibrium, { x ˆ, yˆ, qˆ }, maximizes onsumer surlus subjet to three onstraints: Max {, x} q [ P z π x, y h + δ y ] dz = s.t. π x, y h + δ 1 0 P q = π x, y h + δ + y + m x + π x, y δ. The first onstraint reflets the fat that onsumers hoose their reautions, y, to minimize their exeted rivate osts assoiated with rodut use, π x, y h + δ + y. Under our assumtions the solution to the assoiated first-order ondition is the unique maximum. The seond onstraint reflets the fat that the reresentative onsumer hooses to onsume u to the oint where his marginal value of onsumtion, Pq, is exatly offset by his exeted marginal ost, π x, y h + δ + y +. The final onstraint simly reflets the fat that manufaturers must earn non-negative rofit margins. This rogram gives us imortant insights into the desirability of different liability rules. The first onstraint suggests that the onsumer under-invests in rodut safety when δ d and < 18 The first-order onditions are π x, y h + d 1= 0 for i = 1,2, and q = g x, y. i 9 osted by The Berkeley Eletroni Press

12 over-invests when δ > d. All else equal, onsumers should bear full resonsibility for the third-arty injuries that their rodut use auses. Seond, when the last onstraint binds so manufaturers earn zero rofits then the seond onstraint imlies that the market quantity will satisfy m P q = π x, y h + δ + δ + x + y. Conditional on safety measures x and y, the market quantity or level of eonomi ativity is soially otimal if and only if the third-arty vitim is omensated in full for his damages, m δ +δ = d. In other words, when δ +δ = d m onsumer's total ost of onsumtion reflets all of the ex ost soial osts, inluding the harm to third arties. 2.3 Welfare Analysis Proosition 2.1: If the reresentative onsumer is fully solvent w d then the first-best market outome is ahieved by the erfetly ometitive market if, and only if, the onsumer = alone ays for third-arty damages δ d and δ = 0. If the reresentative onsumer is insolvent w < d then the strit liability rule that ahieves the highest ossible soial welfare uts rimary resonsibility for third-arty harm on the onsumer and residual resonsibility on = the manufaturer, δ w and δ = d w. m m = m The formal roof is given in the aendix. When onsumers are fully solvent, onsumeronly liability δ d and δ = 0 leads the reresentative onsumer to fully internalize the soial ost of their rodut use. e demands the soially otimal safety features from manufaturers, invests otimally in reautions, and engages in the aroriate level of eonomi ativity. Consumer-only liability fails to ahieve desirable outomes when the 10 htt://law.beress.om/nwws-le/art28

13 reresentative onsumer is insolvent: he takes too little are, demands too few safety features, and onsumes too muh. A better rule -- indeed the best rule within the lass of strit liability rules -- is residualmanufaturer liability. The manufaturer who rodued the rodut is held liable for the shortfall in damages when the onsumer who aused the aident has insuffiient assets to omensate the third-arty vitim. More generally, this rule is given by δ min{ d, w} and m δ = d min{ d, w}. When onsumers are insolvent, residual-manufaturer liability leads manufaturers to 1 hoose aroriate manufaturer reautions and 2 set the rie at a level where the market quantity is soially otimal in light of these investments. = 2.4 Disussion The basi model an be extended in number of ways without hanging the onlusion. First, the harms aused by an aident an be stohasti instead of deterministi. The harm borne by the onsumer, h, an simly be reinterreted as the mean or exeted harm and nothing in the exressions would hange. Introduing noise to the third-arty damages, d, omliates the analysis somewhat beause the general liability rule would need to seify the alloation for m eah realization of damages, { δ d, δ d}. esidual-manufaturer liability would still be the otimal rule, however: the onsumer would ay for the third-arty damages to the extent that his wealth allows, δ d = min{ d, w}, and the manufaturer would bear the shortfall, m δ d = d min{ d, w}. Other oliy instruments, suh as taxation and mandatory insurane oliies for onsumers, will erform well on some -- but not all -- dimensions. These alternative instruments, if arefully hosen, will ahieve the desirable level of eonomi ativity. They will 11 osted by The Berkeley Eletroni Press

14 not by themselves get onsumers to take additional are or manufaturers to imlement soially desirable safety features, however. These alternative instruments would need to be ouled with other instruments -- regulations or negligene-based liability rules erhas -- in order to mimi all of the benefits of residual-manufaturer liability. The otimality of residual-manufaturer liability is maintained with some forms of onsumer heterogeneity. Imortantly, the reresentative onsumer's inverse demand urve P q an be reinterreted as reresenting a ontinuum of onsumers who differ in the value they lae on onsuming a single unit of the good. esidual-manufaturer liability is soially desirable so long as the different onsumer tyes all have the same solveny and the same roensity to ause soial harm, h. The next two setions highlight why residual-manufaturer liability may be undesirable when these other forms of heterogeneity are introdued. 3. eterogeneous isk Posed by Consumers This setion fouses on the roblem that arises when onsumers differ in both their willingness to ay for the rodut and also in the soial harm that their rodut use auses. In ontrast to the last setion, where onsumers were homogeneous and residual-manufaturer liability led to soially desirable market outomes, here we show that residual-manufaturer liability distorts the market quantity when onsumers' willingness to ay and the exeted soial harm are orrelated. Indeed, residual-manufaturer liability may reate suh large distortions in the level of eonomi ativity that it would be better to have no manufaturer liability at all. The firearms examle rovides intuition for this last idea. Suose there are two tyes of gun buyers, riminals and law abiders, eah of whom has unit demand. A gun reates more soial harm in the hands of a riminal than in the hands of a law abider. Imagine that riminals 12 htt://law.beress.om/nwws-le/art28

15 are willing to ay more for firearms than law abiders. Notie that the marginal urhaser i.e. the onsumer who is indifferent between buying the gun and not buying the gun at the going rie is more likely to be a law abider than the average urhaser. It follows that the marginal urhaser auses less soial harm than the average urhaser of the rodut. Sine the strit liability rule "taxes" manufaturers for the average soial harm that their roduts ause assuming they annot distinguish the two onsumer tyes, the market rie will be ineffiiently high and the market quantity ineffiiently low. Taken to the extreme, guns will be driven off the market, even if the ositive soial surlus assoiated with the use of law abiders outweighs the soial losses assoiated with riminal use. 19 To ut it differently, there is a ross-subsidy where low-risk onsumers ay for dangers reated by the high-risk onsumers, and low-risk onsumers will therefore be over-deterred from urhasing and using the rodut The Model Suose there are two tyes of ustomers, i =,. If a tye i onsumer urhases one unit of the rodut, the exeted soial harm to third arties is i. 21 We assume that tye 19 Previous ommentators have argued that manufaturer liability for gun misuse is otimal, beause it will fore riminals to internalize the ost of their ativity. See Note, Absolute iability for Ammunition, 108 arv.. ev ; Note, Manufaturers Strit iability for andgun Injuries: An Eonomi Analysis, 73 Geo..J The roblem with that assertion is that liability will fore law-abiding gun owners to bear muh of the ost of riminal uses, sine that ost will robably be built into the rie of all guns. iability will therefore overdeter law-abiding users. A ritial question is whether that overdeterrent effet outweighs the benefits of liability. With the exetion of ay's 1999 informal analysis, this is unaddressed in the literature. 20 If instead the onsumers' rivate benefits of onsumtion were negatively orrelated with the soial harm -- if law abiders ause more soial harm than riminals -- then the marginal urhaser auses more soial harm than the average urhaser. In this ase, residualmanufaturer liability would lead to a rie that is too low and a quantity that is too high and is better than onsumer-only liability. 21 This orresonds to π d from the last setion. 13 osted by The Berkeley Eletroni Press

16 onsumers ause more soial harm than tye onsumers: > > 0. The inverse demand urve of tye i onsumers is P i q and we let the orresonding demand urve be D i. As in the simle examle above, we assume that onsumers do not suffer ersonal damages from rodut use h = 0 and are all totally insolvent or judgment roof ex ost w = 0. Neither the manufaturer nor the onsumers take reautions here: manufaturing osts are normalized to zero and there is no "moral hazard" roblem for onsumers. Two liability rules will be omared here: residual-manufaturer liability and onsumeronly liability. We will assume that it is imossible for manufaturers to distinguish between the two tyes of ustomers and therefore manufaturers annot rie disriminate. This is imortant beause, under residual-manufaturer liability, manufaturers fae higher exeted liability osts when selling to a tye onsumer. Indeed, if the onsumers' tyes were observable to manufaturers then tye onsumers would be fored to ay a higher rie than their tye ounterarts. 3.2 The Constrained Soial Otimum Suose that a soial lanner an hoose the market rie, but annot disriminate between the two different onsumer tyes. The lanner hooses the rie to maximize soial welfare: D [P 0 D z ]dz + [Pz ]dz 0 Differentiating this exression with reset to the rie,, gives us: D ~ + D ~ ~ = D ~ + D ~ = M ~. 14 htt://law.beress.om/nwws-le/art28

17 This equation has a nie interretation: it says that the seond-best market rie, ~, equals the inremental soial harm assoiated with the sale of one additional unit, or the "marginal soial harm," at that rie, M ~. Intuitively, suose that rie falls ever so slightly so that exatly one more unit is sold. With robability D ~ /[ D ~ + D ~ ] the additional unit is sold to a tye onsumer, and with robability D ~ /[ D ~ + D ~ ] it is sold to a onsumer of tye. Multilying these robabilities by the assoiated soial harms, and, we see that the seond-best market rie, ~, equals the marginal soial ost assoiated with the additional unit. 3.3 The Cometitive Equilibrium With onsumer-only liability, ometition drives the market rie down to the marginal ost of rodution whih we have normalized to zero: = 0. Sine onsumers are insolvent ex ost, the ometitive market does not internalize the soial harm to nononsumers and the market quantity or "level of eonomi ativity" is too high. With residual-manufaturer liability, the ometitive equilibrium rie will rise to reflet the manufaturers' future exeted liability. Sine a manufaturer annot ontrol who buys his rodut the manufaturer's exeted liability for eah unit sold is based on market averages. The average harm aused by eah unit of the rodut sold when the market rie reflets the total soial harm, T = D + D, divided by the total quantity demanded, C D + D. In the ometitive equilibrium, the market rie P reflets the manufaturer's exeted liability assoiated with a sale: D + D = = A. D + D 15 osted by The Berkeley Eletroni Press

18 Comaring this exression with the soial lanner's onstrained otimum shows that residual-manufaturer liability will not generally ahieve the seond-best outome. Sine the average soial harm may exeed the marginal soial harm and vie versa, residual-manufaturer liability an lead to market quantities that are either too high or too low. Indeed, it may be the ase the market quantity is distorted so muh by residual-manufaturer liability that it would be better to have onsumer-only liability instead. 3.4 Welfare Analysis The relative desirability of residual-manufaturer liability hinges on the elastiities of demand for the two onsumer tyes, ε and ε. For the remainder of this setion, we will assume that the two tyes of onsumer an be ranked aording to these elastiities, i.e. Di either ε < ε for all ries,, or the reverse where ε i =. D i emma 3.1: The average harm to third arties exeeds the marginal harm, A > M, if and only if the more harmful onsumer grou has a less elasti demand than the less harmful grou, ε < ε. This result is imortant for assessing the soial desirability of manufaturer liability. If the two grous have the same elastiities, ε ε, then the relative roortions of the two onsumer tyes among all urhasers is the same regardless of the market rie. When the "marginal harm" and the "average harm" are the same, the ometitive manufaturers aroriately internalize the harms that their roduts ause to nononsumers. In this seial 16 htt://law.beress.om/nwws-le/art28

19 ase, strit liability yields the seond-best market outome beause the ometitive market sets the orret market rie. When ε ε, however, then the marginal harm and the average harm will tyially diverge and so the seond-best is not obtained. Proosition 3.2: The equilibrium market ries under onsumer-only liability residual-manufaturer liability C and may be ranked with reset to the onstrained soial otimum ~. When ε ε, we have C = ~ > ; when ε > ε we have ~ C > > ; and when ε ε < we have C > ~ >. When ε > ε then the harmful onsumers have a more elasti demand urve than the less harmful grou. Aording to the lemma, the average harm is less than the marginal harm. The ometitive market is being "under-taxed" so to seak for the rodut and so the equilibrium rie is too low. Although the seond-best outome is not ahieved, it is easy to see that residual-manufaturer liability is referred to onsumer-only liability. Although it does not ahieve the first-best outome, residual-manufaturer liability erforms better than onsumeronly liability. When ε < ε, on the other hand, the more harmful onsumer grou has a less elasti demand urve than the less harmful grou. The average harm exeeds the marginal harm in this ase and so the manufaturers are being "over-taxed" under residual-manufaturer liability. The equilibrium market rie is too high and the equilibrium market quantity is too low. To ut it another way, the low risk onsumers are being ineffiiently driven out of the market beause they are fored to subsidize their high-risk ounterarts. The next roosition 17 osted by The Berkeley Eletroni Press

20 states that onsumer liability beomes more desirable relative to residual-manufaturer liability when the distane between the harm levels aused by the two tyes inreases. Proosition 3.3: If rises and falls while holding the average harm A at rie fixed, then i soial welfare under onsumer-only liability rises if and only if ε < ε and ii soial welfare under residual-manufaturer liability is unhanged. 3.5 Disussion We have seen that residual-manufaturer liability an have disastrous market onsequenes when the harmful onsumers are less rie sensitive than their less harmful ounterarts. This is quite intuitive. When the harmful onsumers have a relatively inelasti demand, the harm aused by the average onsumer who urhases the rodut exeeds the harm aused by the marginal onsumer. The residual-manufaturer liability rule indues the ometitive manufaturers to raise the rie above the soially otimal level, reating a hilling effet on eonomi ativity. The onsumers who ause the least soial harm are the first to be driven from the market; the onsumers who ause the most soial harm are the ones more likely to remain. In these situations, onsumer-only liability may be referable beause it kees the less harmful onsumers in the market. 22 Soial welfare would of ourse be higher if an all-knowing soial lanner ould fine-tune the oliies to reflet the marginal harms instead. Damage multiliers ould rovide suh an instrument: the multilier would be less than one when onsumers with less elasti demands 22 Consumer-only liability may, of ourse, have a host of unfortunate onsequenes as well. As shown in setion 2, manufaturers will take insuffiient safety reautions in designing their roduts and the onsumers level of eonomi ativity will be too high. 18 htt://law.beress.om/nwws-le/art28

21 ause more soial harm and greater than one when the less elasti onsumers ause less soial harm. Alternatively, the soial lanner ould imose a tax on the market to reflet the marginal soial harm. Both oliies would require that the ourt understand a host of market harateristis inluding the nature of demand urves, harm levels, and orrelations, et. Furthermore, both alternatives would omromise the desirable imat manufaturer liability has on the design of rodut safety features. 4. eterogeneous Finanial Assets This setion introdues a seond kind of onsumer heterogeneity: heterogeneous finanial assets. Proortion θ of the onsumer oulation, the "tye 0" onsumers, are omletely insolvent following an aident w 0. Proortion 1 θ of the onsumer oulation, the 0 = "tye 1" onsumers, are fully solvent w 1 > d. Following the notation from Setion 2, the soially-effiient reautions are the same for the two grous, 0 x1 x x = = and 0 y1 y y = =. Finally, we assume that the robability of an aident is additively searable in manufaturer and onsumer reautions, or equivalently π x, y 0. This assumtion simlifies the analysis 12 = beause a onsumer's hoie of reautions, y, is indeendent of the rodut's safety features, x. As in Setion 2, onsumers are both about rie and rodut safety features. We will haraterize inentive-omatible airs of rodut offerings,, } and, }, where the { 0 x 0 { 1 x1 judgment-roof onsumers selet the former rodut and the solvent onsumers selet the latter rodut. A air of rodut offerings is a ometitive equilibrium if no manufaturer an earn ositive rofits by deviating to a different rie-safety ombination. The equilibrium is said to be ooling when, x } = {, } and searating otherwise. { x1 19 osted by The Berkeley Eletroni Press

22 4.1 Examle To start, let's ignore reautions and assume that the robability of an aident is exogenously given and idential for solvent and insolvent onsumers: π = 1/ 3. Suose further that the onsumers all have unit demands with valuation v whih we will vary. The onsumers do not bear any diret harm from an aident, h = 0, but third-arties suffer damages in the event of an aident, d = 12. Finally, suose that half of all onsumers are insolvent θ = 1/ 2. We will see that both onsumer-only liability and residual-manufaturer liability are ineffiient and lead to very different eonomi distortions. et's start with the ase of onsumer-only liability. The ometitive manufaturers drive the rie down to marginal ost, normalized to zero. A solvent onsumer internalizes all of the soial harm that his rodut use auses and urhases when v π d = 4, the soially effiient outome. The insolvent onsumers do not internalize the third-arty harms, urhasing the rodut whenever v > 0. In other words, onsumer-only liability leads to an effiient level of eonomi ativity for the solvent onsumers but an exessive level for the insolvent onsumers. esidual-manufaturer liability, on the other hand, leads to the effiient outome for the insolvent onsumers but insuffiient quantities for the solvent onsumers. To see why, suose that both tyes of onsumers are served in the ometitive equilibrium. The equilibrium rie would reflet the average manufaturer liability, or = θπ d = 2. The solvent onsumers are willing to urhase the rodut when v π d + θπd = 6. This deision rule is soially ineffiient beause onsumers "should" urhase the rodut when v > π d = 4. Intuitively, a distortion arises beause the solvent onsumer ays twie for the third-arty harm: through his own ersonal liability ex ost, and also through the inflated rie. If all of the solvent onsumers are 20 htt://law.beress.om/nwws-le/art28

23 driven out of the market, the market rie rises to = π d = 4 to reflet the liability ost assoiated with insolvent onsumers only and the insolvent onsumers subsequently make the effiient urhase deision. This examle suggests that residual-manufaturer liability will be referred when there are many insolvent onsumers in the oulation, but is inferior when the roortion is low. The next sub-setions extend this basi insight to the more general ase where the reautions of the manufaturers and onsumers are hoie variables and demand urves are downward sloing. 4.2 Consumer-Only iability With onsumer-only liability onsumers are resonsible for third-arty injuries to the extent that their wealth allows. The third-arty vitim is made whole when the onsumer is fully m { 1 1 d solvent, δ, δ } = {,0}, but goes unomensated when the onsumer is insolvent, { 0 δ m 0 = δ, } {0,0}. As a benhmark, suose that there is omlete information about the onsumers' tyes. From Setion 2 we know that, for the solvent onsumers, the reaution levels x, minimize the total soial osts assoiated with a sale, π x, y h + d + x + y. The reaution levels for the insolvent onsumers, on the other hand, would minimize the total rivate osts assoiated with a y sale, π x, y h + x + y and so the equilibrium reautions, x, y, are too low. The next roosition states that this outome is obtained with inomlete information as well. Proosition 4.1: In the unique ometitive equilibrium with onsumer-only liability, the solvent C C 1 1 x onsumers urhase {, x } = { x, } and the insolvent onsumers urhase 21 osted by The Berkeley Eletroni Press

24 C C 0 x {, x0 } = { x, } where x < x. The solvent onsumers take the effiient reautions, 1 y y C 1 = y, and onsume the right amount, q C = g x,. The insolvent onsumers underinvest in reautions, 0 y y y C = <, and onsume too muh, q C = g x,. 0 y The insolvent ustomers do not are enough about safety and the ometitive market gives them exatly what they want: a hea and relatively dangerous rodut. They subsequently ut in too little are to avoid aidents and onsume too muh. The fully solvent onsumers, on the other hand, are held ersonally aountable for any third-arty damages and therefore demand safer roduts from the manufaturers, x C 1 = x, and use them rudently, 1 y y C =. The ometitive market sulies the solvent onsumers "effiiently." When θ = 0 all onsumers are fully solvent and onsumer liability alone ahieves the first-best market outome. Soial welfare is learly falling in θ, the roortion of insolvent onsumers. 4.3 esidual-manufaturer iability Suose instead that the manufaturer is resonsible for the shortfall in damages not aid by the insolvent onsumer. The third-arty vitim is omensated in full by the onsumer if the m { 1 1 d onsumer is fully solvent, δ, δ } = {,0}, and is omensated in full by the manufaturer if the m { 0 0 d onsumer is insolvent, δ, δ } = {0, }. As a benhmark, suose that there is full information and that the ometitive manufaturers an disriminate between the two onsumer tyes, setting a different safety-rie air for eah. 22 htt://law.beress.om/nwws-le/art28

25 emma 4.2: Suose the onsumers' tyes are observable. With residual-manufaturer liability, 1 1 x { 0 x0 the market offers {, x } = { x, } to the solvent onsumers and, } = { x + π x, y d, x } to the insolvent onsumers. The fully solvent onsumers take the effiient level of reautions, y 1 = y, while the insolvent onsumers take too few reautions, 0 y y y = <. Conditional on the reautions levels, the effiient market quantities are obtained. With full information and residual-manufaturer liability, the ometitive firms hoose the soially otimal reautions, x 0 x1 = x =, but set different ries for the two grous. The fully solvent onsumers are hea to serve beause there is no future "shortfall" for the manufaturers to ay. Consequently, 1 reflets the marginal rodution ost only. Insolvent onsumers, on the other hand, are exensive to serve sine the manufaturer is liable for the soial harm that the insolvent onsumers ause. The rie that the insolvent onsumers must ay, x + π x, y d, inludes a remium to reflet the antiiated future liability of the manufaturer. To ut it somewhat differently, solvent onsumers ay ex ost for the harm that they ause while the insolvent onsumers ay ex ante through a higher market rie. This full-information benhmark is not sustainable when the onsumers' tyes are unobservable. Sine the insolvent onsumers ay a higher rie than their solvent ounterarts, 0 1 >, the insolvent onsumers would obviously retend to be solvent in order to seure the lower rie. In other words, the full-information outome in emma 4.2 is not inentive omatible. 23 osted by The Berkeley Eletroni Press

26 emma 4.3: Suose the onsumers tyes are not observable. A ooling equilibrium does not exist with residual-manufaturer liability. This result is quite intuitive. If a ooling equilibrium did exist, the market rie would have to be inflated to reflet the manufaturers' liability assoiated with the insolvent onsumers. Consumers who are solvent fae ersonal liability of third-arty harm, and therefore lae greater weight on rodut safety than their insolvent ounterarts. A lever manufaturer ould skim off these safety-sensitive onsumers in the following way: offer a safer rodut at a rie that only the solvent onsumers would refer. The manufaturer would then avoid future liability himself and earn a ositive rofit margin. This intuition is aliable in understanding the searating equilibrium as well. The market sulies a rodut with otimal built-in manufaturer reautions to the insolvent onsumers who ay for manufaturers' future liability u front through an inflated rie. If the solvent onsumers urhased this rodut, too, they would effetively have to ay twie for liability: one u front through the market rie and then later on when a third arty is suffers damages. But the ometitive market sulies the solvent onsumers with a very different rodut -- a safer rodut at a higher rie. This ultra-safe rodut is ried "fairly" -- the solvent onsumers are only aying the manufaturing osts and so their urhase deisions are effiient given the safety measures. But the safety measures themselves are ineffiiently high. Proosition 4.4: Suose that onsumers' tyes are unobservable. With residual-manufaturer liability there exists a unique searating equilibrium when θ, the roortion of insolvent { 1 1 x onsumers, is not too small. The fully solvent onsumers urhase, x } = { x, } where 24 htt://law.beress.om/nwws-le/art28

27 x 0 0 x x > and the insolvent onsumers urhase {, x } = { x +π x, y d, }. 23 The fully solvent onsumers take the effiient reautions, y 1 = y, while the insolvent onsumers take too few reautions, 0 y y y = <. Conditional on the reaution levels, the effiient market quantities are obtained. When θ, the roortion of insolvent onsumers, is small then a ometitive equilibrium fails to exist. The reason is simle: a lever manufaturer ould rofitably deviate from the searating equilibrium and offer a rodut with otimal safety features x and a relatively low rie that both onsumer tyes would refer. This is analogous to othshild and Stiglitz's 1976 famous result that ometitive insurane markets may have no equilibrium. Many authors have suggested hanges to the othhild-stiglitz timing that serve to restore the existene of equilibrium. iley 1979 roosed a dynami adjustment roess where firms ould modify their rodut offerings in light of a deviation. Our searating equilibrium in Proosition 4.4 is a so-alled "eative Equilibrium" when θ is low as well. The idea behind this is that if a deviator did indeed make an offer that both tyes of onsumer referred, then another firm ould reat to this deviation and skim off the solvent onsumers along the lines of emma 4.3. The robustness of the searating equilibrium for low θ is sensitive to the artiular dynami roess, however. Indeed, Wilson 1977 restored the existene of a ooling equilibrium in othshild-stiglitz by allowing the non-deviating firms to withdraw, but not modify, their offers in light of a deviation. These extensions, and other refinements, are surveyed in iley The value x is endogenous and imliitly defined by The roof is given in the aendix. π x + π x, y h + d = x + x, y h. 25 osted by The Berkeley Eletroni Press

28 4.4 Disussion We end this setion by omaring the outomes in Proositions 4.1 and 4.4. With onsumer-only liability the ometitive market rovided the solvent onsumers with effiient safety features, x1 C = x, but the insolvent onsumers with ineffiiently low levels of safety features, x0 C = x. On the other hand, with residual-manufaturer liability the market sulies effiient safety features to the insolvent onsumers, x0 = x, but exessive safety features to the solvent ustomers, x1 = x. Not surrisingly, the former outome is referred when there are suffiiently many solvent onsumers in the oulation but not when the oulation is dominated by insolvent onsumers. Proosition 4.5 There exists a utoff, θ 0, 1. If the roortion of insolvent onsumers is above this utoff, θ > θ, then the searating outome with residual-manufaturer liability is stritly referred to the equilibrium with onsumer-only liability. If the roortion of insolvent onsumers is below this utoff, θ θ, then onsumer-only liability is referred. 5. Conlusion There are sound eonomi reasons to hold manufaturers liable for the injuries that their roduts ause to non-onsumers. Sine onsumers tyially annot be held resonsible for 100% of the harms that they ause, laing liability on onsumers alone will lead to the overonsumtion of roduts with inadequate safety features. In a reresentative-onsumer framework, the best strit liability rule holds the onsumer liable for third-arty damages u to 26 htt://law.beress.om/nwws-le/art28

29 the oint that their finanial assets allow, and then holds the manufaturer liable for the shortfall in damages. 24 owever, when onsumers are heterogeneous, residual-manufaturer liability an lead to undesirable distortions in the market quantities and safety features. The formal analysis in this aer ignored the osts of the legal system and assumed that vitims were automatially omensated for their losses. olding manufatures liable would only make ratial sense if the shortfall in damages not aid by onsumers and the assoiated benefits of manufaturer liability was large enough to justify the added exense and transations osts assoiated with the litigation roess. esidual-manufaturer liability may also bakfire if overly-symatheti juries grant astronomial jury awards, hilling the eonomi ativity. Note, however, that damage as may ontrol runaway jury awards and restore the roer market outomes. As mentioned earlier, taxes may be a viable alternative to residual-manufaturer liability. 25 The otimal tax, whih would reflet the marginal soial harm, ould be imosed on either the manufaturers or the onsumers. Although taxation may have lower transations osts than residual-manufaturer liability, it has several imortant drawbaks. First, the lanner would require both the time and the ability to fine-tune the taxes on a market-by-market basis. Seond, a tax by itself would rovide inadequate inentives for manufaturers to design safer roduts. A negligene rule that holds manufaturers liable if their safety features fall short of aetable levels -- or regulations geared at rodut safety diretly -- may rove useful sulements to taxation. Note, however, that liability has the advantage of utting resonsibility for safety in 24 The asymmetry in the treatment omes from the assumtion that onsumers observe rodut attributes at the time of urhase but manufaturers annot observe or ontrol onsumer are. 25 See Carlton and oury, 1980 and amilton, 1998, for disussions of Pigouvian taxation in the liability ontext. 27 osted by The Berkeley Eletroni Press