Individual or Enterprise Liability? The Roles of Sanctions and Liability Under Contractible and Non-contractible Safety Efforts

Sverre Grepperud

doi:10.1515/rle-2016-0068

Article

Individual or Enterprise Liability? The Roles of Sanctions and Liability Under Contractible and Non-contractible Safety Efforts

Sverre Grepperud

Published/Copyright: March 26, 2020

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From the journal Review of Law & Economics Volume 16 Issue 3

Abstract

This paper analyzes the social effectiveness of fines (sanctions) and awards (liability) where accident risks are influenced by decisions made by both the enterprise and the employees of the enterprise (individuals). The regulator observes a proportion of accidents and the safety decision of the individual can be contractible or non-contractible for the enterprise. All sanction regimes yield the first best, given contractible individual care. The liability regimes, however, produce sub-optimal solutions. Given non-contractible individual care, the combined use of an individual sanction and an enterprise sanction (joint use) produces the first best. The exclusive use of an individual sanction produces the first best if the enterprise does not suffer any direct harm. The exclusive use of an enterprise sanction does not, however, produce the first best. If both decision-makers are solvent and have similar liability probabilities, then individual and enterprise liability do equally well under contractible individual care. Individual liability does, however, best for non-contractible individual care.

Keywords: safety regulation; incentive contracts; enterprise liability; joint liability; strict liability

JEL Classification: D62; D82; K20; K32; I18; L51

Appendix A: Second order conditions for problems (8), (11), (13), (17), (28) and (32)

The second order condition for the problem of the regulator (see 8) is;

d=See′′SeE′′SEe′′SEE′′>0, where d is the determinant of the Hesse matrix.

d=Pee′′PEE′′−PeE′′PEe′′>0 is fulfilled from (3).

The second order condition for the problem of the individual (see 11) is:

Uee′′=−Pee′′(E,e)αD+stαD<0, which is fulfilled from (1) and α>0.

The second order condition for the problem of the firm, when individual effort is non-contractible (see 13), is;

(44)CEE′′(∗)={PEE′′(∗)+[2PEe′′(∗)+Pee′′(∗)eE′(∗)]eE′}Ψ+[Pe′(∗)Ψ+k]eEE′′(∗)>0

Evaluating this condition in optimum using eE′(∗)=−PeE′′(∗)Pee′′(∗) (see footnote 6) leads to the first term in (44) becoming [PEE′′(∗)Pee′′(∗)−(PEe′′(∗))2Pee′′(∗)]Ψ, which from (3) is strictly positive meaning that (44) is always fulfilled for eEE′′(∗)=0. The second term of (44) is evaluated by inserting the first order condition of the individual, PE′(∗)=−kαD+st (see 11), which implies that the second term can be written as follows; −[βD+rT]αD+stkeEE′′(∗). This term is zero for JS (see 19). Thus CEE′′(∗)>0. For EL and IL[βD+rT]αD+st<0, thus a sufficient condition for CEE′′(∗)>0 is eEE′′(∗)≤0.

The second order condition for the problem of the regulator (see 17) is SEE′′>0. Assuming that all third derivatives of the accident probability function are zero yields SEE=PEE′′+Pee′′(eE′)2+2PeE′′eE′D, which from (3) is strictly positive.

The second order condition for the problem of the firm (see 28) is;

dF=Cbb′′CbE′′CEb′′CEE′′>0, where the determinant of the Hesse matrix

dF=Cbb′′CEE′′−CbE′′CEb′′>0. Assuming that all third derivatives of the accident probability function are zero yields the following expressions:

(45)CEb′′=CbE′′=PEe′′−Pee′′eEeb′Ψ=0

(46)Cbb′′=Pee′′(eb′)2Ψ>0

(47)CEE′′=Ψ(PEE′′+Pee′′(eE′)2+2PeE′′eE′)>0.

Substituting for eE′ in (45), it follows that CEb′′=CbE′′ = 0. From (46) and (47), it follows that Cbb′′ and CEE′′ are strictly positive. The second order condition is thus fulfilled. The second order condition for the problem of the regulator (see 32) is STT′′(∗)Stt′′(∗)−STt′′(∗)StT′′(∗)>0.

Appendix B: The partial effects of T and t on E

ET′=−CET′′(∗)CEE′′(∗) and Et′=−CEt′′(∗)CEE′′(∗) where CEE′′(∗)>0 (see 44), CET′′(∗)=PE′(∗)+Pe′(∗)eE′(∗)r and CEt′′(∗)=PEE′′(∗)Ψ+Pee′′(∗)eE′(∗)et′+PE′(∗)s+Pe′(∗)Ψ+keEt′′.CET′′(∗) and CEt′′(∗) are indeterminate, thus ET′≥(<)0 and Et′≥(<)0.

Appendix C: The first order conditions for problem (17)

(1)–(5) ensure interior solutions to problem (17). Solving problem (17) yields;

(48)ST′(E,e)=Pe′(∗)D+kET′(∗)eE′(∗)+PE′(∗)D+KET′(∗)=0

(49)St′(E,e)=Pe′(∗)D+kEt′(∗)eE′(∗)+et′(∗)+PE′(∗)D+KEt′(∗)=0

Appendix D: The optimal sanction when the firm issues a sanction being contingent upon the occurrence of accidents

The objective functions of the individual and the firm follows from replacing be in (6) and (7) with zfP(E,e), where z is the probability of the individual being sanctioned by the firm and f is the firm penalty. This procedure yields the following objective functions;

(50)U(E,e)=A−zfP(E,e)−P(E,e)αD−P(E,e)st−ke≥Uˉ

(51)C(E,b)=A+P(E,e)βD+P(E,e)rT+KE

(52)S(E,e)=P(E,e)D+KE+ke

In the final stage, the individual maximizes (50) with respect to e, which yields; Ue′(e;E,b,t)=−Pe′(E,e)(αD+st+zf)−k=0, which again can be expressed as;

(53)−Pe′(E,e)αD+st+zf=k

The first order condition of the individual, (53), defines the following

response function;

(54)e=e(E,t,f)

The firms’ maximization problem becomes;

MinE,bC(E,b,e)=Uˉ+P(E,e)Ω+ke+KEs.t.e=e(E,t,f)whereΩ≡(α+β)D+rT+st.

The first order conditions for this problem become (assuming interior solutions);

(55)Cf′(E,b)=ef′(∗)Pe′(∗)Ω+k=0

(56)CE′(E,f)=PE′(∗)Ω+K+eE′(∗)Pe′(∗)Ω+k=0

By using (53), the two conditions can be expressed as;

(57)zf=βD+rT

(58)PE′(E,e(E,b,t))=−KΩ

Equation (58) defines the response function of the firm;

(59)E=E(T,t)

The regulator minimizes (52) given (54), (57) and (59). Solving this problem

produces the following first order conditions for the regulator;

(60)st+zf−(1−α)D=rT+st−(1−α−β)D=0

By inserting (57), (60) can be expressed as;

(61)st+rT=γD

By inserting (61) into (57), we arrive at the following expression for the

optimal firm sanction;

(62)zf=βD+rT=(1−α)D−st

This regime produces the first best. This is seen by inserting the sanction

levels in (61) and (62) into (53) and (58).

Now consider ES (t = 0). From (61) we get rTˉEL=γD. By inserting this optimal enterprise sanction level into (62), the optimal internal penalty becomes zfˉES=(β+γ)D. For IS (T = 0), the optimal individual sanction level stˉIL=γD (see 61) and the optimal internal penalty is zfˉIS=βD (see 20) and is independent of the optimal individual sanction level.

Appendix E: The first order conditions for problem (28)

The first order conditions for problem (28) become;

(63)Cb′(E,b)=eb′(∗)Pe′(∗)Ψ+k≥(<)0

(64)CE′(E,b)=PE′(∗)Ψ+K+eE′(∗)Pe′(∗)Ψ+k≥(<)0

From (1)–(5) and Ψ>0, (63) and (64) are binding. Thus we get;

Pe′(E,e(E,b,t))=−kΨ

PE′(E,e(E,b,t))=−KΨ

Appendix F: The first order conditions for problem (32)

(1)–(5) ensures interior solutions. Solving the problem of (32) therefore yields the following equation system;

(65)ST′(E,e)=Pe′(∗)D+k(ET′(∗)eE′(∗)+eb′(∗)bT′(∗))+PE′(∗)D+KET′(∗)=0

(66)St′(E,e)=Pe′(∗)D+k(Et′(∗)eE′(∗)+eb′(∗)bt′(∗)+et′(∗))+PE′(∗)D+KEt′(∗)=0

References

Abraham, K.S., R.L. Rabin, and P.C. Weiler. 1993. “Enterprise Responsibility for Personal Injury: Further Reflections,” 30 San Diego Law Review 333–364.Search in Google Scholar

Abraham, K.S., and P.C. Weiler. 1994. “Enterprise Medical Liability and the Choice of the Responsible Enterprise,” XX(1&2) American Journal of Law and Medicine 29–36.10.1017/S0098858800006419Search in Google Scholar

Aghion, P., and J. Tirole. 1997. “Formal and Real Authority in Organizations,” 105(1) Journal of Political Economy 1–29.10.1086/262063Search in Google Scholar

Bhole, B., and J. Wagner. 2008. “The Joint Use of Regulation and Strict Liability with Multidimensional Care and Uncertain Conviction,” 28 International Review of Law and Economics 123–132.10.1016/j.irle.2008.02.008Search in Google Scholar

Bisso, J.C., and A.H. Choi. 2008. “Optimal Agency Contracts: the Effect of Vicarious Liability and Judicial Error,” 28 International Review of Law and Economics 166–174.10.1016/j.irle.2008.06.005Search in Google Scholar

Boyer, M., and D. Porrini. 2011. “The Impact of Court Errors on Liability Sharing and Safety Regulation for Environmental/Industrial Accidents,” 31 International Review of Law and Economics 21–29.10.1016/j.irle.2010.11.001Search in Google Scholar

Broussau, E., and J.M. Glachant. 2002. The Economics of Contracts – Theories and Applications. Cambridge: Cambridge University Press.10.1017/CBO9780511613807Search in Google Scholar

Chu, C.Y., and Y. Qian. 1995. “Vicarious Liability under a Negligence Rule,” 13 International Review of Law and Economics 305–322.Search in Google Scholar

Dari-Mattiaci, G., and G. De Geest. 2005. “Judgment Proofness Under Four Different Precaution Technologies,” 161(1) Journal of Institutional and Theoretical Economics 38–56.10.1628/0932456054254470Search in Google Scholar

Dari-Mattiaci, G., and F. Parisi. 2004. “The Cost of Delegated Control: Vicarious Liability, Secondary Liability and Mandatory I Nsurance,” 23 International Review of Law and Economics 453–475.10.1016/j.irle.2003.07.007Search in Google Scholar

De Geest, G., and G. Dari-Mattiaci. 2007. “Soft Regulation, Tough Judges,” 15 Supreme Court Economic Review 119–140.10.1086/656029Search in Google Scholar

Grossmann, S.J., and O. Hart. 1986. “The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration,” 94 Journal of Political Economy 691–719.10.1086/261404Search in Google Scholar

Hart, O. 1995. Firms, Contracts and Financial Structure. Oxford: Oxford University Press.10.1093/0198288816.001.0001Search in Google Scholar

Kolstad, C.D., T.S. Ulen, and G.V. Johnsen. 1990. “Ex Post Liability for Harm vs. Ex Ante Safety Regulation: Substitutes or Complements,” 80(4) American Economic Review 888–901.10.4324/9781315197296-16Search in Google Scholar

Kornhauser, L., and R. Revesz. 1989. “Sharing Damages Among Multiple Tortfeasors,” 98 Yale Law Journal 831–884.10.4324/9781315188133-15Search in Google Scholar

Kornhauser, L., and R. Revesz. 1990. “Appointing Damages Among Potentially Insolvent Actors,” 19(2) Journal of Legal Studies 617–651.10.1086/467864Search in Google Scholar

Kornhauser, L.A. 1982. “An Economic Analysis of the Choice between Enterprise and Personal Liability for Accidents,” 79 California Law Review 1345–1387.10.2307/3480271Search in Google Scholar

Landeo, C.M., M. Nitkin, and S. Baker. 2007. “Deterrence, Lawsuits, and Litigation Outcomes under Court Errors,” 23 Journal of Law, Economics and Organization 57–97.10.1093/jleo/ewm003Search in Google Scholar

Landes, W.M., and R.A. Posner. 1980. “Joint and Multiple Tortfeasors: An Economic Analysis,” 9(3) Journal of Legal Studies 517–555.10.1086/467651Search in Google Scholar

McLean, T.R. 2002. “Crossing the Quality Chasmml: Autonomous Physician Extenders Will Necessitate a Shift to Enterprise Liability Coverage for Health Care Delivery,” 12 Health Matrix 239–296.Search in Google Scholar

Newman, H.A., and D.W. Wright. 1990. “Strict Liability in a Principal-Agent Model,” 10 International Review of Law and Economics 219–231.10.4324/9781315188133-8Search in Google Scholar

Peter, P.G., Jr. 2008 “Resuscitating Hospital Enterprise Liability,” 73 Missouri Law Review 369–398.Search in Google Scholar

Polinsky, A.M., and S. Shavell. 1993. “Enforcement Costs and the Optimal Magnitude and Probability of Fines,” 35(1) Journal of Law and Economics 133–148.10.3386/w3429Search in Google Scholar

Sage, W.M., K.E. Hastings, and R.A. Berenson. 1994. “Enterprise Liability for Medical Malpractice and Health Care Quality Improvement,” XX(1&2) American Journal of Law and Medicine 1–28.10.1017/S0098858800006407Search in Google Scholar

Schmitz, P.S. 2000. “On the Joint Use of Liability and Safety Regulation,” 20 International Review of Law and Economics 370–382.10.1016/S0144-8188(01)00051-5Search in Google Scholar

Shavell, S. 1984. “Liability for Harm versus Regulation of Safety,” 15 Rand Journal of Economics 271–280.10.3386/w1218Search in Google Scholar

Shavell, S. 1993. “The Optimal Structure of Law and Enforcement,” 36(1) Journal of Law and Economics 255–287.10.1093/acprof:oso/9780198765295.003.0011Search in Google Scholar

Shavell, S. 1997. “The Optimal Level of Corporate Liability Given the Limited Ability of Corporations to Penalize Their Employees,” 17 International Review of Law and Economics 203–213.10.1016/S0144-8188(97)00003-3Search in Google Scholar

Sykes, A.O. 1981. “An Efficiency Analysis of Vicarious Liability under the Law of Agency,” 91 Yale Law Journal 168–206.10.2307/795853Search in Google Scholar

Young, R., M. Faure, P. Fenn, and J. Willis. 2007. “Multiple Tortfeasors: An Economic Analysis,” 3 Review of Law and Economics 111–132.10.2202/1555-5879.1093Search in Google Scholar

Published Online: 2020-03-26

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https://doi.org/10.1515/rle-2016-0068

Keywords for this article

safety regulation; incentive contracts; enterprise liability; joint liability; strict liability