Limiting Limited Liability

Transcription

1 Limiting Limited Liability Giuseppe Dari-Mattiai Amsterdam Center for Law & Eonomis Working Paper No This paper an be downloaded without harge from the Soial Siene Researh Network Eletroni Paper Colletion at: The omplete Amsterdam Center for Law & Eonomis Working Paper Series is online at: For information on the ACLE go to:

2 GEORGE MASON UNIVERSITY SCHOOL of LAW LIMITING LIMITED LIABILITY Giuseppe Dari-Mattiai LAW AND ECONOMICS WORKING PAPER SERIES An eletroni version of this paper an be downloaded from the following websites: Soial Siene Researh Network:

3 LIMITING LIMITED LIABILITY Giuseppe Dari-Mattiai * Universiteit van Amsterdam, ACLE, Rootersstraat 11, 1018 WB Amsterdam, The Netherlands George Mason University, Shool of Law, 3301Fairfa Drive, Arlington, Virginia 22201, USA Abstrat Limited liability may result in ineffiient aident prevention, beause a relevant portion of the epeted harm is eternalized on vitims. This paper shows that under some restritive onditions further limiting liability by means of a liability ap an improve aretaking. Keywords: insolveny, judgment proof, liability, bankrupty, liability ap. JEL lassifiation: K13, K32, L59. * Phone +31 (0) , Fa +31 (0) gdarimat@uva.nl. SSRN author page: The author would like to Eri Langlais and Franeso Parisi for helpful omments on previous versions of this artile. Susan A. Russell provided valuable editorial assistane.

4 G. DARI-MATTIACCI LIMITING LIMITED LIABILITY 2 1 Introdution Limited liability is often blamed for making it too easy for firms to take risks that, if materialized, are eternalized on unaware vitims. The most troubling aspet onerns liability in torts, when aident vitims are not part of any ontrat with the damaging firm, and hene annot negotiate an appropriate level of preaution. Environmental aidents provide many eamples of these types of eventualities. Limited liability usually results in insuffiient aretaking (Summers, 1983; Shavell, 1986). However, Beard (1990) shows that limited liability may result in eessive aretaking, whih in turn auses some otherwise solvent firms (Dari-Mattiai and De Geest, forthoming) to be bankrupt in the ase of an aident. This paradoial result is eplained by noting that a potentially insolvent firm reeives a preaution subsidy when it makes monetary preautionary ependitures. In fat, when preaution osts amount to a monetary investment (e.g. a firm improves funding for its safety division), preautionary ependitures redue the amount of the assets that are available for damage ompensation. After making preautionary ependitures, the firm is left with a smaller amount of assets, and thus is eposed to a redued potential liability. Beause more preautions result in less liability, preautionary ependitures may be said to be partially subsidized by the onsequent redution in epeted liability, possibly yielding to higher levels of preautions than would be soially optimal. With non-monetary preautions, this senario would not arise, as the firm s e post liability would be independent of its e ante preaution deisions. Commentators often advoate piering the veil of orporate liability or imposing stringent finanial requirements as a possible solution to the problems aused by limited liability. 1 Without opposing this view, this paper suggests that the reverse poliy ould also be soially desirable, showing that further limiting a firm s limited liability, by apping the maimum damage award, 2 may improve preaution inentives and, 1 See Beard (1990, p. 633) and Shavell (2005), for a reent ontribution. 2 Boyd and Ingberman (1994) are the first to advoate non-ompensatory damages as a solution to the dilution of inentives aused by insolveny. However, they employ a model in whih preaution

5 G. DARI-MATTIACCI LIMITING LIMITED LIABILITY 3 onsequently, soial welfare. Setion 2 ontains the basi model of potentially insolvent firms with monetary preaution osts. Setion 3 shows that liability aps may improve soial welfare. Setion 4 disusses the optimal setting of the liability ap. Setion 5 provides a onlusion. 2 Model: firm s assets and preaution Building on Shavell (1986), we analyze the preaution deision of a risk-neutral limited liability firm with (eogenously determined) 3 assets a, whih operates under strit liability. 4 The firm s preaution lowers the probability of a single harmful aident involving vitims who are strangers 5 to the firm and annot take any form of preaution in order to protet themselves from harm (e.g. a hemial plant eplosion). All funtions are ontinuously differentiable to any desired order. Let: = the preaution ost, 0; p() = probability of an aident, 0 < p() < 1, p < 0, p > 0; h = magnitude of the harm, h > 0; = the liability ap, h; a = the assets, a > 0. The soial objetive is to minimize the standard (soial) ost funtion: S ( ) = p( ) h + (1) Let * denote the (unique) level of preaution that minimizes (1) and let it be positive; * represents the first-best level of preaution in the absene of limited liability. The firm has limited assets and, following Beard (1990), its preautionary ependitures are monetary, and hene every dollar spent in preaution redues the net assets available for liability by the same amount. Unlike this literature, we also assume that there is a limit (the liability ap) on the amount of damages that vitims will be legally entitled to ependitures do not redue the tortfeasor s liability, and hene disuss a different set of problems. 3 Boyd and Ingberman (1999) study insolveny when assets are endogenous to the model. 4 The negligene rule is also advoated as a solution to the problem (Summers, 1983; Shavell, 1986), although it solves the problem only if the standard of are is perfetly antiipated e ante (Craswell and Calfee, 1986).

6 G. DARI-MATTIACCI LIMITING LIMITED LIABILITY 4 reover from the firm in the ase of an aident. Beause of the liability ap, the firm pays damages equal to h, that is, the damage award may be less than the harm. As a result, if an aident ours, the firm will pay the (possibly apped) damage award if his remaining assets a (that is, the amount of assets left after making preautionary ependitures ) are larger than (or equal to) ; the firm will pay a if its remaining assets are less than. Thus, the firm s liability osts are as follows: { a } L ( ) = p( )min, + (2) If = h, we have the ase analyzed by Beard (1990), in whih it an be proved that the level of preaution taken by the firm may be higher than * (e.g.: when a = h + * ). Some firms, whih would be solvent had they taken the soially optimal level of preaution (in the eample, a * = h), may be indued to take a higher level of preaution, whih is the only ause of their bankrupty and lowers soial welfare. 3 Analysis: liability ap and preaution We will now show that by lowering it is possible to improve soial welfare. From (2), the firm s liability minimization problem an be written as follows: { min[ p( ) + ], min[ p( ) ( a ) + ] } min (3) The problem is onve in. In order to determine the pattern of the firm s preaution as a funtion of, note that the first part in (3) depits the firm s minimization problem when the firm is solvent, that is when a. In this ase, the firm is able to pay the (trunated) damage award. For onveniene, let be the level of preaution that minimizes the firm s liability in this ase. The seond part in (3) depits the liability osts of an insolvent firm, when < a. Let a denote the level of the firm s preaution that minimizes the firm s liability in this ase. Note that a is onstant in and, by the Impliit Funtion Theorem, inreasing in a. On the ontrary, is inreasing in but onstant in a. Therefore, omparing (1) and (3), we have *, as long as h. 5 That is, the vitims annot negotiate the level of preaution with the firm.

7 G. DARI-MATTIACCI LIMITING LIMITED LIABILITY 5 The infra-marginal deision between solveny (taking ) and insolveny (taking a ) depends upon whih of these two possibilities yields the lowest total ost for the firm: 6 ( a a ) a p( ) + <> p( ) (4) a + Using (4) we an determine the level of the firm s assets at whih the firm will swith from a to : a p( ) + = p( ( 1 p( )) a ) By the Envelop Theorem, p( ) + is an inreasing funtion of ; thus, a also inreases in. Therefore, by lowering below h the firm an be indued to take instead of a. This improves soial welfare as long as: p( ) h + < p( ) a a h + a a Figure 1 shows the pattern of the firm s preaution with and without a liability ap. 4 Poliy impliations: the optimal setting of the liability ap In a world with only one firm, the optimal h depends upon the firm s assets a. In general, should be set as high as possible, sine the soial ost dereases in, but not too high, sine we want the firm to prefer to a. Suh a level of satisfies a strit equality in (4) and is an inreasing funtion of a. Figure 2 depits the impat of suh a liability ap on the soial ost. Let ^=^(a) denote this level of. In addition, let a^ be suh that S( (^(a^))) = S( a (a^)). To the right of *, 7 S( a (a)) inreases as a inreases, sine a > * moves further away from *. On the ontrary, S( (^(a))) dereases as a inreases, sine < * moves loser to *. It follows that for a a^ the soial ost is lower when the firm takes than when it takes a. On the ontrary, for a < a^ the soial ost is lower when the firm takes a- than when it takes. At the other end of the spetrum, when a a =h, the firm takes * if no liability ap is applied, while it takes a when a < a =h and no liability ap is 6 For this solution algorithm, see Dari-Mattiai and De Geest (forthoming).

8 G. DARI-MATTIACCI LIMITING LIMITED LIABILITY 6 applied. Therefore, in the range a^ < a < a =h the optimal liability ap is ^(a) < h, sine the firm s preaution an be improved by making it take instead of a. Outside this range = h is optimal, either beause the firm already has inentives to take * (upper end) or beause a results in lower soial osts than any feasible (lower end). Let us now onsider a world in whih many firms eist with different assets, where the liability ap affets all firms at the same time. Given a distribution of firm types between a and a, with density f(a) 0 over the relevant region and umulative distribution F(a), with F( a ) = 0 and F( a ) = 1, we have the following restatement of the soial ost in (1) as a funtion of : min a ( ) a ( ( a) ) df( a) ( ) ( ( ) df( S a + S ) a a where firms with assets below a take a, while firms with assets above a take. A hange in affets the level of preaution taken by the latter group of firms and, at the same time, also affets the omposition of both groups, sine a varies with. Assuming onveity, the optimal setting of the liability ap solves the following FCO: ds( ( )) da [ 1 F( a ( )) ] = [ S( () ) S( a ( a ( )) )] f ( a ( d )) (5) d Epression (5) is readily interpreted. The LHS an be seen as the marginal benefit of raising the liability ap, thereby inreasing the levels of preautions taken by all firms to the right of a. Reall that by raising we bring loser to *, thereby reduing the soial ost. The RHS depits instead the marginal benefit of lowering the liability ap: the marginal firm (with assets equal to a ) is indued to take < * instead of a >, in so doing, possibly reduing the soial ost. The optimal liability ap balanes these opposite effets and depends upon the distribution of the firm types. a) 5 Conlusions A potentially insolvent firm may be indued to take more preaution than is soially 7 To the left of * a liability ap would only worsen aretaking.

9 G. DARI-MATTIACCI LIMITING LIMITED LIABILITY 7 optimal. This is due to an impliit preaution subsidy generated by monetary preautionary ependitures, whih redue the amount of the firm s assets eposed to liability. This inrement in preaution inreases the total soial ost of aidents. We have shown that apping the firm s liability an redue both the firm s preaution and the soial ost of aidents. Liability aps are limits on the firm s liability eposure set by law. Contrary to the firm s assets, liability aps are independent from the firm s preautionary ependitures. An inrease in the firm s preaution redues the firm s assets but does not affet the liability ap. For this reason, liability aps are not vulnerable to the perverse inentives reated by monetary preautionary ependitures and an effetively ounter eessive preaution, thereby giving the opportunity to improve soial welfare. In a world in whih many firms eist with different assets, liability aps ome at some osts, as they also lower the level of preaution of some solvent firms. Optimal liability ap poliies balane these osts against the benefits we have emphasized above in this paper. Referenes Beard, T. R. (1990). Bankrupty and Care Choie. Rand Journal of Eonomis, 21, Boyd, J., & Ingberman, D. E. (1994). Nonompensatory Damages and Potential Insolveny. Journal of Legal Studies, 23, Boyd, J., & Ingberman, D. E. (1999). Do Punitive Damages Promote Deterrene? International Review of Law and Eonomis, 19, Craswell, R. & Calfee, J. E. (1986). Deterrene and Unertain Legal Standards. Journal of Law, Eonomis, and Organization, 2, Dari-Mattiai, G., & De Geest, G. (forthoming). When Will Judgment Proof Injurers Take too muh Preaution? International Review of Law and Eonomis. Shavell, S. (1986). The Judgment Proof Problem. International Review of Law and Eonomis, 6, Shavell, S. (2005). Finanial Responsibility Rules: Minimum Asset Requirements and Compulsory Liability Insurane. Forthoming in RAND Journal of Eonomis. Summers, J. (1983). The Case of the Disappearing Defendant: An Eonomi Analysis. University of Pennsylvania Law Review, 132,

10 G. DARI-MATTIACCI LIMITING LIMITED LIABILITY 8 a * (with < h) a* a <h a =h a FIGURE 1: Liability ap and firm s preaution

11 G. DARI-MATTIACCI LIMITING LIMITED LIABILITY 9 S() S( a ) S( ) S(*) a* a^ a =h a FIGURE 2: Soial ost and liability ap

12 G. DARI-MATTIACCI LIMITING LIMITED LIABILITY 11