NBE WOKING PAPE SEIES MANUFACTUE IABIITY FO AMS CAUSED BY CONSUMES TO OTES Brue ay Kathryn E. Spier Working Paper 10972 http://www.nber.org/papers/w10972 NATIONA BUEAU OF ECONOMIC ESEAC 1050 Massahusetts Avenue Cambridge, MA 02138 Deember 2004 The authors are from the arvard aw Shool and the Kellogg Shool of Management and NBE, respetively. The authors thank ik Brooks, oward Chang, Jim Dana, Andy Daughety, Xinyu ua, Mith Polinsky, Jennifer einganum, Sott Shaefer, seminar audienes at Kellogg and the NBE, and espeially Steve Shavell, Tim Besley, and the referees for helpful omments and suggestions. The seond author thanks the Searle Fund for finanial support. The views expressed herein are those of the author(s) and do not neessarily reflet the views of the National Bureau of Eonomi esearh. 2004 by Brue ay and Kathryn E. Spier. All rights reserved. Short setions of text, not to exeed two paragraphs, may be quoted without expliit permission provided that full redit, inluding notie, is given to the soure.
Manufaturer iability for arms Caused by Consumers to Others Brue ay and Kathryn E. Spier NBE Working Paper No. 10972 Deember 2004 JE No. K13, D62 ABSTACT Should the manufaturer of a produt be held legally responsible when a onsumer, while using the produt, harms someone else? We show that if onsumers have deep pokets then manufaturer liability is not eonomially effiient. It is more effiient for the onsumers themselves to bear responsibility for the harms that they ause. If homogeneous onsumers have limited assets, then the most effiient rule is "residual-manufaturer liability" where the manufaturer pays the shortfall in damages not paid by the onsumer. esidual-manufaturer liability distorts the market quantity when onsumers' willingness to pay is orrelated with their propensity to ause harm. It distorts produt safety when onsumers differ in their wealth levels. In both ases, onsumer-only liability may be more effiient. Brue ay arvard aw Shool Griswold all 401 1563 Massahusetts Avenue Cambridge, MA 02138 hay@law.harvard.edu Kathryn E. Spier Kellogg Shool of Management Northwestern University 2001 Sheridan oad Evanston, I 60208 and NBE k-spier@kellogg.northwestern.edu
1. Introdution Should the manufaturer of a produt be held legally responsible when a onsumer, while using the produt, harms someone else? Manufaturers might be held liable for aidental harms aused by the onsumer, suh as when a lawnmower flings a stone that hits a neighbor in the eye or when a driver of a ar hits a pedestrian. 2 Manufaturers might also be held liable if the onsumer intentionally aused harm, for example when a gun is used to ommit murder. Indeed, reently many lawsuits have been brought reently against firearms manufaturers for the deaths and injuries aused by riminals who use guns. Although suh lawsuits have generally been unsuessful, 3 these issues remain hotly disussed in the legal and politial arenas. 4 We onsider a model of a dangerous produt supplied by a perfetly ompetitive market. The produt s use has some tendeny to harm others -- either aidentally or intentionally -- and both the manufaturers and the onsumers an take ations to redue the likelihood of the harm. For example, gun owners an take greater are while handling and storing their guns to avoid aidental shootings and an refrain from ommitting rimes; likewise, gun manufaturers an make investments in safety features suh as mehanial gun loks (reduing the likelihood that a 2 See Dugan v. Sears, oebuk & Co., 447 N.E.2d 1055 (Ill. App. 1983) (lawnmower) and ouvenagle v. Wright, 340 N.W.2d 783 (Ia. App. 1983) (automobile). awsuits involving other produts suh as alhohol, pestiides, igarette lighters, and omputer games abound. 3 Exeptions involve situations where the onsumer aidentally injured someone as a result of a produt malfuntion. If a ar s brakes fail, for example, the pedestrian may be able to reover from the manufaturer provided that the brake failure is not the onsumer s fault. owever, if the produt funtioned as it was designed to, or if the onsumer deliberately inflited the injury, ourts have traditionally refused to hold the manufaturer liable. 4 A number of lawsuits are pending in federal and state ourts in whih the plaintiffs seek to relax or bypass the traditional rule immunizing manufaturers from deliberately inflited harms. State and federal legislatures have responded by attempting to odify the manufaturers immunity from liability. For example, two bills in Congress,.. 1036 and S. 696, would "prohibit ivil liability ations from being brought or ontinued against manufaturers, distributors, dealers or importers of firearms or ammunition for damages resulting from the misuse of their produts by others." The former bill has made it through the U.S. ouse of epresentatives while the latter is pending in the U.S. Senate. 2
hild inadvertently shoots a sibling) or an refrain from produing highly lethal produts, suh as armor-piering bullets. We show that onsumer liability is more effiient than manufaturer liability when onsumers have deep pokets and an pay for the harms that they ause; solvent onsumers fully internalize the soial risks assoiated with their produt use. This has three desirable effets. First, onsumers take the optimal degree of are when using dangerous produts. Seond, they demand optimal safety features in the produts that they buy. Third, the equilibrium market quantity is effiient beause the market prie plus the onsumer's expeted liability reflets the true soial ost of the dangerous produt. 5 On the other hand, manufaturer liability may be more effiient when onsumers lak the finanial resoures to pay for the harms that they ause. In a representative-onsumer setting, we show that it is more effiient for the onsumer to bear primary responsibility for the damages while manufaturers are held responsible for the shortfall not overed by the onsumer. We all this rule "residual-manufaturer liability." Although onsumers take inadequate preautions when using risky produts, 6 this rule gives manufaturers the orret inentive to design and produe safer produts and insures that the market prie reflets the manufaturers expeted future liability, leading to the effiient market quantity. 7 Importantly, we show that residual-manufaturer liability may distort market outomes when onsumers are heterogeneous. esidual-manufaturer liability leads to quantity distortions, for example, when the onsumers'elastiity of demand is systematially orrelated with the soial harm that they ause. If safe onsumers are more prie sensitive than their 5 See amada (1976). This may not be true if onsumers mispereive risks (Spene, 1977). 6 Shavell (1986) formalizes the so-alled "judgment-proof problem. 7 Shavell (1980) showed that the higher prie leads to a more effiient market quantity but did not disuss residual-manufaturer liability or the heterogeneity issues disussed here. 3
harmful ounterparts, then residual-manufaturer liability may depress the market quantity so muh that soiety as a whole is better off imposing liability on the onsumers alone. 8 esidualmanufaturer liability may also lead to quality distortions. If onsumers have private information about their heterogeneous finanial assets, for example, then the solvent onsumers purhase exessively safe produts in equilibrium. Again, it may be more effiient to impose liability on the onsumers alone than to hold manufaturers liable. The issues raised here are distint from those in the large literature that fouses on produt injuries to onsumers themselves. Simply put, produt injuries to onsumers are largely internalized in well-funtioning markets (amada, 1976; andes and Posner, 1985 and 1987). 9 Even without manufaturer liability imposed by law, onsumers would be willing to pay a premium for safer produts that redue their personal risk and to use risky produts prudently. Consequently, the eonomi arguments for produts liability for onsumer injuries have foused on situations involving transations osts and market imperfetions. Manufaturer liability for onsumer injuries may be effiient, for example, when onsumers mispereive produt risks (Spene, 1977; Epple and aviv, 1978; Polinsky and ogerson, 1983) or when manufaturers have private information about the safety of their produts or take unobservable ations that affet produt safety (Daughety and einganum, 1995 and 1997). 10 Setion 2 highlights the optimality of residual-manufaturer liability in a representative 8 Previous legal ommentators (Note, 1995a and 1995b) have argued in favor of manufaturer liability for gun misuse. With the exeption of ay's (1999) informal analysis, the quantity distortion issue has been unaddressed in the literature. 9 Consumers and manufaturers jointly absorb the osts of injuries (with the alloation depending upon the ontrat struk between them) and therefore have a joint inentive to take optimal preautions. Early desriptive work inludes Calabresi (1961) and MKean (1970). 10 The issues here are reminisent of viarious liability (Sykes, 1998; Mattiai and Parisi, 2002), holding employers liable for the negligene of their employees, for example. Our problem differs in that employers exert some supervision over their employees and an disharge unsatisfatory employees. Manufaturers, on the other hand, typially annot ontrol how their produts are used after the sale. 4
onsumer framework. Setion 3 shows that residual-manufaturer liability an distort the market quantity in an example where onsumers have heterogeneous demand urves and harm propensities. Setion 4 shows that residual-manufaturer liability an distort produt safety in an example where onsumers are privately informed about their wealth levels. Setion 5 onludes. All proofs are given in the appendix. 2. The Basi Framework We begin with the ase of a representative onsumer purhasing a harmful produt from a perfetly ompetitive market. The probability that a single unit of the good will ause an injury is π ( x, y), where x 0 is the manufaturer's investments in produt safety and y 0 is the onsumer's preaution level. Produt safety is perfetly observable to the onsumer at the time that he makes his purhase deisions. The manufaturers have idential onstant-returns-to-sale prodution tehnologies with marginal prodution ost x (we normalize the other prodution osts to zero). We assume that π ( x, y) is dereasing in eah argument, is stritly onvex, and that imπ 1( x, y) = and imπ 2( x, y) =. 11 This last ondition implies that the marginal x 0 y 0 return from the first dollar of investment is arbitrarily large. When injured, the third parties suffer damages d > 0. Consumers are said to be insolvent or "judgment-proof" when their future assets, w, are insuffiient to over d. 12 In ontrast to the onsumers, manufaturers are assumed to have deep pokets. The representative onsumer reeives a marginal benefit P (q) from onsuming the q th unit of the good. This is the 11 π i (x,y) is the derivative with respet to argument i = x, y. 12 Note that the prie that the onsumers pay ex ante is not deduted from their future wealth. This is quite realisti when injuries are low probability events. Similar results would be obtained if onsumers have deep pokets but there is a low probability of being held responsible for the damages. 5
inverse demand urve net of any liability onerns. Soial welfare is given by: 13 S ( x,y,q ) [ P( z ) ( x,y )d x y ]dz. (1) = q 0 The first-best market outome, x, y, and q, are the values that maximize this expression. The ompetitive market hooses these values privately, of ourse, in the shadow of future liability. We onsider the general lass of strit liability rules, { δ, }, that alloates damages δ w to δ m the onsumer and m δ to the manufaturer. 14 We also highlight two speifi rules. With onsumer-only liability the onsumer pays for third-party damages to the point where his or her finanial assets are exhausted, = min{ d,w } and δ = 0. With residual-manufaturer liability the manufaturer is held legally liable for the shortfall in damages, δ min{ d, w} m and δ = d min{ d, w}. Manufaturers ompete by offering prie-safety pairs to attrat the representative onsumer. The manufaturers are the "leaders" (so to speak) hoosing prie and produt safely first while the representative onsumer is a "follower," subsequently hoosing his quantity and preautions. In equilibrium, onsumer surplus is maximized subjet to three onstraints: q Max [ P( z ) ( x,y ) y p ]dz (2) { p,x } 0 m = 13 While our notation naturally reflets aidental harms the framework is also valid for intentional harms, inluding rimes. Even riminals an take ations to redue unneessary losses (ollateral property damage, injuries and deaths) while engaging in riminal ativities and an spend effort searhing for non-riminal alternatives (getting a job, going to shool). Criminals may also borrow or steal guns from onsumers; liability gives onsumers the inentive to safeguard their firearms. The proper treatment of the riminal's utility in the soial welfare funtion is debatable, of ourse, and not addressed here. 14 Note that this lass does not inlude rules where the liability depends on the preautions taken by the manufaturer and the onsumer. Negligene rules are disussed in the onlusion. We are impliitly assuming that only one injury an our for a given onsumer. This is justified if injuries our with a random arrival rate and eonomi ativity eases after the first one. 6
2 = s.t. ( x, y ) 1 0 (3) P( q ) = ( x,y ) + y + p (4) m p x + π ( x, y) δ. (5) The first onstraint reflets that the onsumer hooses his preautions, y, to minimize the expeted private ost assoiated with produt use. The seond onstraint says that the onsumer onsumes to the point where his marginal value of onsumption is exatly offset by his expeted unit ost. The final inequality onstrains manufaturers to earn non-negative profits. Proposition 1: When the representative onsumer is fully solvent then onsumer-only liability ahieves the first-best market outome. When the representative onsumer pays in full for the damages that he auses he will invest optimally in preautions to avoid harming others. Furthermore, the onsumer is willing to pay a premium to manufaturers for optimally safe produts and the ompetitive market delivers exatly what he wants. Finally, the onsumer purhases the soially optimal quantity beause his unit ost reflets the full soial ost: the sum of the marginal ost of prodution, the ost to the onsumer of taking preautions, and the expeted damages to third parties. Next, suppose that onsumers are insolvent. The first-best outome is learly not ahieved with onsumer-only liability. Sine the onsumer bears less than full responsibility for the harms he auses he will take too few preautions to avoid harming others. Sine produts are designed with only the onsumer s preferenes in mind, manufaturers will underinvest in safety features. Finally, the onsumer purhases too muh of the produt as his unit ost of onsumption falls short of the true soial ost. 7
Proposition 2: When the representative onsumer has limited finanial assets then residualmanufaturer liability is optimal within the lass of strit liability rules. It is unavoidable that onsumer preautions fall short of their first-best levels, but putting primary responsibility on the onsumer at least pushes his preautions in the right diretion. Putting residual responsibility on the manufaturer leads the market prie to reflet the manufaturer's share of the expeted future damages in addition to the prodution ost. Consequently, the onsumer's unit ost will fully reflet the soial ost of the risky produt and so the market quantity is soially optimal. Finally, this rule leads the manufaturers to invest effiienty in produt safety. Intuitively, this happens beause the manufaturer and the onsumer together are jointly responsible for the full soial harm to third parties. Other poliy instruments, suh as taxation and mandatory insurane poliies for onsumers, will perform well on some -- but not all -- dimensions. These alternative instruments, if arefully hosen, will ahieve the effiient market quantity. They will not by themselves get onsumers to take additional are or manufaturers to implement soially desirable safety features, however. Taxes would need to be oupled with other instruments -- regulations or negligene-based liability rules perhaps -- in order to mimi all of the benefits of residual-manufaturer liability. The basi model an be extended in number of ways without hanging the basi onlusion. The results hold in situations where onsumers themselves are harmed in addition to the third parties. 15 They also hold when the harms to others stohasti rather than deterministi. 15 The working paper version of this paper, available on SSN, inludes onsumer harm. This feature has been dropped to streamline the exposition. 8
The framework ould be easily extended to inlude non-finanial santions, suh as riminal penalties for areless or maliious produt use. While useful, these supplements would not generally ahieve the first-best: the ombined threat of ivil and riminal liability is generally insuffiient to indue effiient behavior. Finally, the framework ould be extended to situations where produt safety features interfere with produt use, diluting the value that the onsumer derives from the produt. 16 The optimality of residual-manufaturer liability is maintained with some forms of onsumer heterogeneity. Importantly, the representative onsumer's inverse demand urve P (q) an be easily reinterpreted as representing a ontinuum of onsumers who differ in the value they plae on onsuming a single unit of the good. esidual-manufaturer liability is soially effiient so long as the different onsumer types all have the same wealth level and the same propensity 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. Quantity Distortions: eterogeneous arm evels This setion allows onsumers to differ from one another in both their prie sensitivities and in the soial harms that they ause to third parties. We show that residual-manufaturer liability an distort the market quantity when these parameters are orrelated in the onsumer population. Indeed, residual-manufaturer liability may reate suh large distortions in the market quantity that it would be more effiient to have no manufaturer liability at all. We make two simplifying assumptions here in order to fous attention on quantity 16 The framework ould be extended to onsider imperfet ompetition. esidual-manufaturer liability would learly hange market pries in this ase, too, although the hange may not be effiient. Additional work on these issues is needed. 9
distortions. First, neither the manufaturers nor the onsumers an affet the probability of injuries to others, x = y = 0. Seond, onsumers are assumed to be totally insolvent following these injuries, w = 0. We extend the earlier framework to allow for two types of ustomers, i =,. We will refer to these two types as the "harmful group" and the "safe group," respetively. The expeted soial harm of a single unit of the produt in the hands of a type i onsumer is = d and we assume that > > 0. The inverse demand urve of type i onsumers is i i i P i (q) and the orresponding demand urve is ( p). We assume that it is impossible for manufaturers to distinguish between the two types of ustomers and therefore annot engage in prie disrimination. D i An all-knowing soial planner would, of ourse, set different pries for the two groups of onsumers, but this is infeasible given our assumptions. The appropriate benhmark has the soial planner setting a single prie for both groups. This seond-best prie must reflet the soial harm assoiated with the sale of one additional unit, or the marginal soial harm: 17 p D ( p ) + D ( p ) =. (6) D ( p ) + D ( p ) With residual-manufaturer liability, the ompetitive equilibrium prie reflets the manufaturer's expeted liability assoiated with a sale of one unit, or the average soial harm: 18 p D ( p ) + D ( p ) =. (7) D ( p ) + D ( p ) When the average and marginal harms values diverge, residual-manufaturer liability distorts the 17 Suppose that prie falls so that exatly one more unit is sold. With probability D ( p ) /[ D ( p ) + D ( p )] the additional unit is sold to a type onsumer, and with probability ( p ) /[ D ( p ) + D D ( p )] it is sold to a onsumer of type. Multiplying these probabilities by the assoiated soial harms, and gives the expression. 18 The total soial harm D ( p) D ( p ) + divided by the total quantity D ( p) + D( p). 10
equilibrium market quantity. Proposition 3: If the harmful onsumer group has a more elasti demand urve than the safe onsumer group then the market quantity under residual-manufaturer liability is higher than the seond-best quantity. If the harmful onsumer group has a less elasti demand urve then the equilibrium market quantity is lower than the seond-best quantity. Suppose that the harmful onsumer group has a more elasti demand urve than the safe onsumer group. When the market prie rises, the perentage of harmful onsumers who leave the market is larger than the perentage of safe onsumers who leave. It follows that the marginal purhaser (i.e. the onsumer who is indifferent between buying the gun and not buying the gun at the going prie) is more likely to be a harmful onsumer than the average purhaser in the market. Sine residual-manufaturer liability effetively "taxes" manufaturers for the average soial harm the market prie will be ineffiiently low and the market quantity ineffiiently high. Conversely, when the harmful onsumer group has a less elasti demand urve then when the market prie rises the safe onsumers leave the market at a higher rate than harmful onsumers. The marginal purhaser is more likely to be a safe type than the average purhaser. In this ase, manufaturers are "over-taxed" with residual-manufaturer liability. Proposition 4: When the harmful onsumer group has a more elasti demand than the safe onsumer group then residual-manufaturer liability is more effiient than onsumer-only liability. When the harmful onsumer group has a less elasti demand then residualmanufaturer liability may be more or less effiient than onsumer-only liability. 11
esidual-manufaturer liability an have disastrous onsequenes when the harmful onsumers are less prie sensitive than their safe ounterparts. The onsumers who ause the least soial harm are the first to drop out of the market when the market prie rises while the onsumers who ause the most soial harm are the ones more likely to remain. Consumer-only liability may be more effiient beause it keeps the safe onsumers in the market. This may be seen in a simple numerial example. Suppose there is a population of onsumers, eah of whom demands at most one unit of the good. Eah unit osts $10 to produe. Suppose that 99% of the population auses no harm but 1% auses harm of $300. Furthermore, suppose that the safe onsumers value the produt less than the harmful onsumers: v = $12.99 and v = $310.01. Both types of onsumer "should" purhase the produt in this example: 99% of the population reates a surplus of $2.99 while 1% of the population reates a soial value of a penny. With onsumer-only liability, ompetition drives the prie down to p = $10, the marginal ost of prodution. The soially optimal outome is obtained: all onsumers -- safe and harmful alike -- buy the produt. Now onsider residualmanufaturer liability. If both types of onsumer purhased the produt the prie would be p = $13, above safe onsumers'valuation of $12.99. So the safe onsumers would be driven from the market and the prie would subsequently rise to p = $310, the marginal ost, $10, plus the expeted soial harm aused by harmful types, $300. Only the harmful 1% of the population purhases the produt, and, for these harmful onsumers, the "soial surplus" is just a penny. Soial welfare has obviously fallen. 19 Proposition 5: Suppose that the variane in the population's harms grows while holding the 19 If the soial surplus for the unsafe onsumers were negative then the market would disappear. 12
average harm onstant at prie p. If the harmful onsumer group has a less elasti demand urve than the safe onsumer group then onsumer-only liability beomes more effiient relative to residual-manufaturer liability. When the two onsumer types are equally harmful, residual-manufaturer liability learly dominates onsumer-only liability on effiieny grounds (indeed, it ahieves the seond-best market outome; see Proposition 3). When the variane in harms grows, however, then residualmanufaturer liability diverges from the seond-best and beomes relatively less effiient. The proposition holds soial welfare under residual-manufaturer liability fixed (by holding average harm onstant at p ) and performs the omparative stati on onsumer-only liability. Alternatively, one ould hold soial welfare fixed under onsumer-only liability and show that residual-manufaturer liability beomes relatively less effiient although this is less straightforward to prove. Our analysis has restrited attention to two speifi liability rules: residual-manufaturer and onsumer-only liability. Soial welfare would of ourse be higher if the soial planner ould fine-tune the rule. Damage multipliers would be valuable supplementary instrument to residualmanufaturer liability, for example. The optimal multiplier would be less than one when onsumers with less elasti demands ause more soial harm, effetively lowering the manufaturers liability to reflet marginal harm. Similarly, it would be greater than one when the less elasti onsumers ause less soial harm. Alternatively, the soial planner ould impose a diret tax on the manufaturers refleting the marginal soial harm of the ativity. These poliies would of ourse require that the ourt understand a host of market harateristis inluding the nature of demand urves, harm levels, and orrelations, et. They would also 13
ompromise the positive impat manufaturer liability has on produt design. 4. Quality Distortions: eterogeneous Finanial Assets This setion introdues a seond kind of onsumer heterogeneity: heterogeneous finanial assets. Proportion θ of the onsumer population, the "type 0" onsumers, are ompletely insolvent following an injury ( w 0 = 0 ). Proportion 1 θ of the onsumer population, the "type 1" onsumers, are fully solvent ( w 1 > d ). Finally, we assume that the probability of harm is additively separable in manufaturer and onsumer preautions, π ( x, y) 0. 20 We will 12 = haraterize inentive-ompatible pairs of produt offerings, p, } and p, }, where the { 0 x0 { 1 x1 insolvent onsumers selet the former and the solvent onsumers selet the latter. The pair of produt offerings is a ompetitive equilibrium if no manufaturer an earn positive profits by deviating to a different prie-safety ombination. Finally, the equilibrium is said to be pooling when p, x } = { p, } and separating otherwise. { 0 0 1 x1 As before, we fous on two basi liability rules. With onsumer-only liability the damages are paid by the onsumer when he is fully solvent and go unompensated otherwise, m { 1 1 d { 0 δ m 0 = δ, δ } = {,0} and δ, } {0,0}. With residual-manufaturer liability the damages are paid by the onsumer when he is fully solvent but are paid by the manufaturer if the onsumer is m { 1 1 d m { 0 0 d insolvent, δ, δ } = {,0} and δ, δ } = {0, }. Proposition 6: With onsumer-only liability, the solvent onsumers purhasing deisions and preautions are at their first-best levels. The insolvent onsumers purhase unsafe produts, take 20 This implies that a onsumer's hoie of preautions is independent of produt safety features. 14
too few preautions, and onsume too muh. As in Setion 2, the insolvent ustomers do not are enough about safety and the ompetitive market gives them exatly what they want: a heap and relatively dangerous produt. They subsequently put in too little are to avoid harming others and overonsume the produt. The fully solvent onsumers, on the other hand, are held personally aountable for any third-party damages and therefore demand safer produts from the manufaturers and use them prudently. In short, the ompetitive market supplies the solvent onsumers "effiiently." emma 7: Suppose the onsumers'types are observable and prie disrimination is feasible. With residual-manufaturer liability, all onsumers purhase optimally safe produts. The prie paid by the solvent onsumers reflets marginal prodution osts only while the insolvent onsumers pay a premium that reflets the manufaturer s future liability. Conditional on produt safety and onsumer preautions, effiient market quantities are obtained. This full-information benhmark may be understood intuitively. Solvent onsumers demand optimally safe produts beause primary liability fores them to internalize the soial harms they ause. Insolvent onsumers do not personally internalize the harm, but the manufaturers supplying them are fored to internalize the harm through residual-manufaturer liability (as in Setion 2). The solvent onsumers pay ex post for the harm that they ause while the insolvent onsumers pay ex ante through a higher market prie. This benhmark is not sustainable when the onsumer are privately informed. Sine the insolvent onsumers pay a higher prie than their solvent ounterparts the insolvent onsumers 15
would obviously pretend to be solvent in order to seure the lower prie. In other words, the fullinformation benhmark is not inentive ompatible. Proposition 8: Suppose that onsumers'types are private information. With residualmanufaturer liability a pooling equilibrium does not exist. There does exist a unique separating equilibrium when the proportion of insolvent onsumers, is not too small. The fully solvent onsumers purhase exessively safe produts and the insolvent onsumers purhase optimally safe produts. Conditional on the preaution levels, the effiient market quantities are obtained. A detailed proof is given in the appendix, but the main ideas may be understood intuitively. If a pooling equilibrium did exist, the market prie would have to be inflated to reflet the manufaturers'liability assoiated with the insolvent onsumers. Consumers who are solvent fae primary liability for third-party harm and therefore plae greater weight on produt safety than their insolvent ounterparts. A lever manufaturer ould skim off these safetysensitive onsumers in the following way: offer a safer produt at a prie that only the solvent onsumers would prefer. The manufaturer would avoid future liability himself and earn a positive profits. This intuition is appliable in understanding the separating equilibrium as well. The market supplies a produt with optimal built-in safety features to the insolvent onsumers who pay for manufaturers'future liability up front through an inflated prie. If the solvent onsumers purhased this produt, too, they would effetively have to pay twie for liability: one up front through the market prie and then later on when a third party suffers damages. But the ompetitive market supplies the solvent onsumers with a very different produt -- a safer 16
produt at a higher prie. This ultra-safe produt is pried "fairly" -- the solvent onsumers are only paying the manufaturing osts and so their purhase deisions are effiient given the safety measures. -- but the safety measures themselves are ineffiiently high. When θ, the proportion of insolvent onsumers, is small then a ompetitive equilibrium fails to exist. The reason is simple: a lever manufaturer ould profitably deviate from the separating equilibrium and offer a produt with soially optimal safety features and a relatively low prie that both onsumer types would prefer. This Proposition is analogous to othshild and Stiglitz's (1976) famous result that ompetitive insurane markets may have no equilibrium. Many authors have suggested hanges to othhild and Stiglitz s timing to restore the existene of equilibrium. iley (1979) proposed a dynami adjustment proess where firms ould modify their produt offerings in light of a deviation. The separating equilibrium desribed above 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 types of onsumer preferred, then another firm ould reat to this deviation and skim off the solvent onsumers. 21 (A similar logi was used to break the pooling equilibrium.) Proposition 9: If the proportion of insolvent onsumers is above a utoff then the separating outome with residual-manufaturer liability is more effiient than the equilibrium with onsumer-only liability. If the proportion of insolvent onsumers is below the utoff then onsumer-only liability is more effiient. 21 The robustness of the separating equilibrium for low θ is sensitive to the partiular dynami proess, however. Indeed, Wilson (1977) restored the existene of a pooling 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 (2001). 17
From Proposition 6, onsumer-only liability ahieves the first-best outome for solvent types while the insolvent types over-onsume unsafe produts and take too little are while using them. esidual-manufaturer liability, on the other hand, distorts the produt safety supplied to the solvent ustomers in the separating equilibrium (Proposition 8). It follows that onsumeronly liability is more effiient when there are suffiiently many solvent onsumers in the population but not when the population is dominated by insolvent onsumers. 5. Conlusion There are sound eonomi reasons to hold manufaturers liable for the injuries that their produts ause to non-onsumers. Sine onsumers typially annot be held responsible for 100% of the harms that they ause, plaing liability on onsumers alone will lead to the overonsumption of produts with inadequate safety features. In a representative-onsumer framework, the most effiient strit liability rule holds the onsumer liable for third-party damages up to the point that their finanial assets allow, and then holds the manufaturer liable for the shortfall in damages. 22 owever, when onsumers are heterogeneous, residualmanufaturer liability an lead to undesirable distortions in the market quantities and produt safety features. The formal analysis in this paper ignored the osts of the legal system and assumed that vitims were automatially ompensated for their losses. olding manufaturers liable would only make pratial sense if the shortfall in damages not paid by onsumers (and the assoiated benefit of residual-manufaturer liability) was large enough to justify the added expense and transations osts assoiated with the litigation proess. Additional problems would arise if 22 The asymmetry in the treatment omes from the assumption that onsumers observe produt attributes at the time of purhase but manufaturers annot observe or ontrol onsumer are. 18
overly-sympatheti juries grant astronomial jury awards, hilling the eonomi ativity. Taxes may be a viable alternative to residual-manufaturer liability. 23 The optimal tax, whih would reflet the marginal soial harm, ould be imposed on either the manufaturers or the onsumers. Although taxation may have lower transations osts than residual-manufaturer liability, it has several important drawbaks. First, the planner 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 provide inadequate inentives for manufaturers to design safer produts. A negligene rule that holds manufaturers liable if their safety features fall short of aeptable levels -- or regulations geared at produt safety diretly -- may prove useful supplements to taxation. Note, however, that liability has the advantage of putting responsibility for safety in the hands of experts. Manufaturers are likely to be better informed about the feasibility of produt modifiations than regulators. Foring onsumers to purhase insurane poliies when they own dangerous produts is another possibility. This may suffer from the same problems as residual-manufaturer liability. If insurane providers annot disriminate among the different types of onsumers then the ompetitive insurane premiums would reflet the average rather than the marginal harm and the market quantity would be distorted. Furthermore, in the absene of manufaturer liability and other regulations produt safety regulations, manufaturers would have insuffiient inentives to produe safer produts. 24 In this way, mandatory insurane has the same problems as taxation. The results of this paper raise the natural question -- and onern -- about where the hain of orporate responsibility should end. The model assumed a single manufaturer, but harmful ativities will often involve multiple produts and multiple suppliers. Guns, for example, are 23 See Carlton and oury, 1980 and amilton, 1998, for disussions of Pigouvian taxation and liability. 24 Indeed, one an interpret manufaturer liability as bundling the produt with an insurane poliy. 19
espeially dangerous when they are loaded with bullets. Should the ammunition manufaturer be held liable for deaths and injuries as well? Timothy MVeigh reated the bomb that destroyed the Oklahoma City Federal Building by loading a mixture of fertilizer with diesel fuel -- purhased at a Conoo servie station -- into a rented yder truk. Should the fertilizer manufaturer, Conoo and yder all be held responsible for the 168 lives that were lost? 25 These issues remain fruitful for further researh. 6. eferenes Calabresi, G., "Some Thoughts on isk Distribution and the aw of Torts," Yale aw Journal, Vol. 70 (4), 1961, pp. 499-553. Carlton, Dennis W. and Glenn oury, "The imitations of Pigouvian Taxes as a ong-un emedy for Externalitites," Quarterly Journal of Eonomis, Vol. 95(3), 1980, pp. 559-566. Andrew F. Daughety and Jennifer F. einganum, "Everybody Out of the Pool: Produts iability, Punitive Damages, and Competition," Journal of aw, Eonomis, and Organization, Vol. 13 (2), 1997, pp. 410-432. Andrew F. Daughety and Jennifer F. einganum, "Produt Safety: iability, &D, and Signaling," Amerian Eonomi eview, Vol. 85(5), 1995, pp.1187-1206. Epple, Dennis and Artur aviv, "Produt Safety: iability ules, Market Struture, and Imperfet Information," Amerian Eonomi eview, Vol. 68 (1), 1978, pp. 80-95. amada, Koihi. "iability ules and Inome Distribution in Produt iability," Amerian Eonomi eview, Vol. 66 (1), 1976, pp. 228-234. amilton, Stephen F., "Taxation, Fines, and Produer iability ules: Effiieny and Market Struture Impliations," Southern Eonomi Journal, Vol. 65 (1), 1998, pp. 140-150. ay, Brue, "Manufaturer iability to Nononsumers." arvard aw Shool Mimeo, 1999. andes, William, and ihard Posner, "A Positive Eonomi Analysis of Produts iability," Journal of egal Studies, Vol 14(3), 1985, pp. 535-567. 25 See Gaines-Tabb v. ICI Explosives, USA, In., 160 F.3d 613 (10th Cir. 1998) for a ase against fertilizer manufaturers. 20
andes, William, and ihard Posner, The Eonomi Struture of Tort aw, arvard University Press, Cambridge, 1987. Mattiai, Giuseppe Dari, and Franeso Parisi, "The Cost of Delegated Control: Viarious iability, Seondary iability, and Mandatory Insurane," George Mason University Shool of aw, aw & Eonomis Working Paper Series, 02-27, 2002. MKean, oland N. "Produts iability: Impliations of Some Changing Property ights," Quarterly Journal of Eonomis, Vol. 84(4), 1970, pp. 611-26. Note, "Absolute iability for Ammunition," arvard aw eview, Vol. 108, pp. 1679-1696, 1995. Note, "Manufaturers Strit iability for andgun Injuries: An Eonomi Analysis," Georgetown aw Journal, Vol. 73, pp. 1437-1462, 1995. Polinsky, A. Mithell, "Strit iability vs. Negligene in a Market Setting," Amerian Eonomi eview, Vol. 70 (2), 1980, pp. 363-367. Polinsky, A. Mithell, and William P. ogerson, "Produts iability, Consumer Mispereptions, and Market Power," Bell Journal of Eonomis, Vol. 14 (2), 1983, pp. 581-89. iley, John G., "Informational Equilibrium," Eonometria, Vol. 47(2), 1979, pp. 331-359. iley, John G., "Silver Signals: Twenty Five Years of Signaling and Sreening," Journal of Eonomi iterature, Vol. 39(2), 2001, pp. 432-478. othshild, Mihael, and Joseph Stiglitz, "Equilibrium in Competitive Insurane Markets," Quarterly Journal of Eonomis, Vo. 90, 1976, pp. 629-650. Shavell, Steven, "Strit iability versus Negligene," Journal of egal Studies, Vol. 9(1), 1980, pp. 1-25. Shavell, Steven. "The Judgment Proof Problem," International eview of aw and Eonomis, Vol. 6(1), 1986, pp. 45-58. Sykes, Alan O., "Viarious iability." In Peter Newman, ed., The New Palgrave Ditionary of Eonomis and the aw, Mamillan eferene imited, 1998. Spene, A. M., "Consumer Mispereptions, Produt Failure, and Produer iability," eview of Eonomi Studies, Vol. 44 (3), 1977, pp. 561-572. Wilson, Charles A., "A Model of Insurane Markets with Inomplete Information," Journal of Eonomi Theory, Vol. 16, 1977, pp. 167-207. 21
7. Appendix Proof of Propositions 1 and 2: As a benhmark, suppose a soial planner hooses x, q, and δ. The onsumer hooses y to minimize his expeted osts: ( x,y ) + y. Our earlier assumptions guarantee that this y is positive and unique. Impliitly, y = f ( x, δ ) where f ( x, δ ) > 0 δ. olding x fixed, if < > δ d ( δ d ) then the onsumer under-invests (over-invests) relative to what a soial planner would do. The most effiient liability rule is δ min{ d, w}. Substituting into (1), the soial planner would hoose x and q to maximize: q 0 [ P( z) π ( x, f ( x,min{ d, w})) d x f ( x,min{ d, w})] dz. The benhmark solution satisfies x = arg min π ( x, f ( x, min{ d, w})) d + x + f ( x, min{ d, w}), x y = f ( x,min{ d, w}), P + ( q ) = π ( x, y ) d + x y. = Claim: The ompetitive equilibrium is the benhmark, {ˆ, x yˆ, qˆ} = { x, y, q }, if and only if = δ min{ d, w} and δ = d min{ d, w}. m Proof of laim: Inequality (5) learly binds, m p = x + π ( x, y) δ. Substituting this and y = f ( x, δ ) into (2) and (4) gives an equivalent program: Max x q [ P( z ) ( x, f ( x, 0 ))( m + ) x f ( x, )]dz s.t. P( q ) = ( x, f ( x, ))( + ) + x + f ( x, ) Using the envelope theorem we find the ompetitive equilibrium { x ˆ, yˆ, qˆ } satisfies m xˆ = arg min π ( x, f ( x, δ ))( δ + δ ) + x + f ( x, δ ), yˆ = f ( xˆ, δ ), x m P( qˆ) = π ( xˆ, yˆ)( δ + δ ) + xˆ + yˆ. m 22
{ x ˆ, yˆ, qˆ} = { x, y, q } with residual-manufaturer liability. With δ d and δ = 0, {ˆ, x yˆ, qˆ} = { x, y, q }. = m Proof of Proposition 3: D D ( p) + ( p) + D D( p) > ( p) D ( p) + D ( p) D ( p) + D ( p) if and only if D ( p )D ( p ) < D ( p )D( p ). Dividing both sides by D ( p) D( p) and multiplying by p shows this is equivalent to ε ( p) < ε ( p). This orders the pries under residual-manufaturer liability and the benhmark. The order of the quantities follows. Proof of Proposition 4: With onsumer-only liability, the prie p = 0. When C ε ( p) > ε ( p) then p > p > p ε ( p < p then C ; when ) ε ( ) from the quasionavity of soial welfare. p > C > p p. The result follows Proof of Proposition 5: olding the average harm, p, fixed in equation (7) we may define as a funtion of : ( ) where d ( d ) D ( p = D ( p ). Soial welfare with onsumer- ) D ( 0 ) only liability ( p = 0 ) may be written [ P ( z ) ]dz + [ P ( z ) ( )]dz. D ( 0 ) 0 0 Differentiating with respet to and substituting the derivative of ( ) gives d ( ) D ( p ) D ( 0 ) D(0 ) D (0 ) D( 0 ) d D( p ) = +. This is positive if D ( p ) / D( p ) is inreasing in prie or equivalently ε ( p) < ε ( p). Proof of Proposition 6: Suppose perfet prie disrimination is possible. It follows from Proposition 1 that the solvent onsumers will be effiiently supplied, x 1 = x and y 1 = y. For the insolvent onsumers the market outome is x 0 = y 0 = 0. The market prie is p 1 = x for the solvent onsumers and p 1 = 0 for the insolvent onsumers. Inentive ompatibility is satisfied so this is also the equilibrium with inomplete information. 23
Proof of emma 7: For the solvent onsumers, residual-manufaturer liability is equivalent to onsumer-only liability so by Proposition 1 they are supplied effiiently. From the proof of Propositions 1 and 2, the insolvent onsumers take zero preautions y0 = 0 and manufaturer preautions satisfy effiient levels. x0 = arg min π ( x,0) d + x. Therefore x x 0 = x and P ( q + x 0 ) = π ( x,0) d, the Proof of Proposition 8: Suppose a pooling equilibrium, { p ˆ, xˆ }, does exist and let θˆ be the proportion of insolvent types. Zero-profits implies pˆ = xˆ + ˆ( xˆ,0 ) d. Consider a deviation to { p~,x ~ } = { pˆ +,xˆ + }. The insolvent onsumers prefer { p ˆ, xˆ } to { ~ p, ~ x} and the solvent onsumer prefers ~, ~ { p x} to { p ˆ, xˆ } when 0 < < [( xˆ, y ) ( xˆ +,y )] d. The deviator reeives positive profits when ~ p > ~ x or ρ > xˆ + ε p ˆ. Substituting for pˆ gives > ˆ( xˆ,0 )d. When ε is suffiiently small then this ondition is satisfied for any ρ > 0. { 1 x 1 { 0 x 0 Claim: In any separating equilibrium, p, } and p, }, 1 x1 p = and p 0 0 + 0 = x ( x,0 )d. Proof of laim: Suppose p 0 0 + 0 { 0 0 > x ( x,0 ) d. By deviating to p ρ, x } a manufaturer ould profitably apture the type 0 market. (If he attrats the solvent onsumers too, all the better.) Suppose that p1 x1 >. The inentive ompatibility onstraint for the insolvent onsumer holds that 0 p1 p. By deviating to a slightly higher safety level, { p1, x1 + }, a manufaturer ould profitably apture the entire type 1 market. Claim: 0 x x =. Proof of laim: { p, x } = { x + π ( x,0) d, } is the outome with perfet prie disrimination. { 0 x 0 0 0 x If p, } did not have this form, then a deviator would steal the entire type 0 market { 0 0 p +,x } (if the type 1 onsumers aept, too, all the better for the deviator.) 24
Claim: x = x + ( x,0) d. 1 π Proof of laim: Given the two laims proved earlier, the IC onstraints for the two types are: (IC 0 ): x ( x,0) d x1 + π, (IC 1 ): x 1 1 + + ( x,y )d x + ( x,0 )d ( x,y ) d. (IC 0 ) implies that x 1 > x. If (IC 0 ) were slak, then the type 1 onsumers ould be made better off by lowering x 1 loser to x. If (IC 0 ) binds then (IC 1 ) is slak. Claim: When θ is suffiiently large there is no unilateral deviation that both types would prefer. Proof of laim: Suppose { ~ p, ~ x} is preferred by both types and let ~ θ be the proportion of insolvent types at that deviation. Positive profits for the deviator implies deviation is preferred by the insolvent onsumers when together, we have p~ x~ + ~ ( p x + ( x,0) d p0 x~,0 ) d. The ~ π =. Taken ~ ~ x ( ~ ~ + θ π x,0) d x + π ( x,0) d. When θ = 1 then θ = 1 as well, so this inequality is only satisfied when ~ p, ~ x } = { p, x }. We have already seen that the type 1 { 1 x 1 { 0 0 onsumers would prefer p, }, a ontradition. Continuity ompletes the proof. Proof of Proposition 9: et j S i be the soial welfare assoiated with liability regime j for a representative onsumer of type i. Consumer-only liability is preferred if θ C C S0 ( 1 θ ) S1 + > θs 0 (1 θ ) S1 C C ( 1 1 0 0 +, or 1 θ )( S S ) > θ ( S S ). Note that C 1 S1 S > beause solvent onsumers are served effiiently under onsumer-only liability (Proposition 6) but not under residual-manufaturer liability (Proposition 8). C S S0 0 > beause manufaturers supply effiient safety features to the insolvent onsumers under residual-manufaturer liability and the market quantity is optimal. The result follows. 25