Paul Calcott

Abstract:

Liability for environmental harm is often capped when precaution meets a minimum requirement and is often applied in conjunction with regulations. The correct setting for such regulations depends on the approach that courts take to evaluating the minimum requirement. It may also depend on which of the minimum requirement and capped liability is the more pressing consideration for the firm. Regulatory design is more straightforward when it is capped liability that is more pressing.

JEL Classification: K32; Q58

Appendix

A Lemma 1

Proof. The argument proceeds in two steps. First, we establish that the firm’s choice of risk level is nonincreasing in θ. Let e=x+y and Z be the set of π,e for which π=π(x,y) for some x,yX×Y. Given the objective θπ+e, the marginal rate of substitution between π and e is θ. Therefore π is nonincreasing in θ by the Spence-Mirrlees condition.

The second step is to establish that reduced risk is achieved with more x. Assume the contrary. Then the change in precaution that delivers the reduction in risk can be decomposed into two movements. The first is an increase in y, holding x constant, which increases πx/πy by eq. 3. The second is a movement around the new isorisk curve, increasing y and decreasing x. This increases πx/πy by quasi-convexity. But problem 4 implies that πx/πy should be unchanged, so the assumption that x has reduced can be rejected.

B Three Proofs

B.1 Preliminaries

The impact on expected costs from a marginal increase in x along y=Y(x;θf+θl),l{c,d} is:

[(θf+θj)πx+1]+[(θf+θj)πy+1]Y(x;θc+θl)x,

where j=h for social costs and j=c for private costs under capped liability. For points on y=Y(x;θf+θl), we can substitute in (θf+θl)πy+1=0 and rearrange to get:

(26)[(θf+θl)πx+1]+(θjθl)πx+πyY(x;θc+θl)x,

where πx+πyY/x<0 by eq. 3.

B.2 Lemma 8

Proof. Consider the impact on social costs (j=h) of a movement along the firm’s best response under capped liability (l=c). Then θjθl>0 in eq. 26. Moreover, at the initial point the firm chooses x to minimize private costs, so (θf+θl)πx+1=0 and eq. 26 is locally negative by eq. 3. Consequently, welfare would be improved so long as the firm continues to comply with the regulation. Moreover, the firm would strictly prefer to comply with the duty when θd<θc, by Lemma 6. Consequently, it would also plan to comply with a regulation that only required incrementally more x than the cost minimizing way to reach the threshold, Xˆ(θf+θd).

B.3 Lemma 11

Proof. First, as θc<θd and costs are quasi-convex, the firm will want to keep y as low as is consistent with reaching the threshold, i. e., y=Y(xˉ;θf+θd). Now consider the impact on private costs (j=c) of increasing x above xˉ along y=Y(xˉ;θf+θd) (l=d). Then θjθl<0 in eq. 26. Moreover, [(θf+θl)πx+1]0 at the initial point so eq. 26 is locally positive.

B.4 Lemma 12

Proof. Consider the impact on social costs (j=h) of a movement along the threshold function (l=d). Then θjθl>0 in eq. 26. The initial point is the least-cost way to reach the threshold, so (θf+θd)πx+1=0. Then eq. 26 can be signed by Lemma 2 and assumption 8.

B.5 Heterogeneous Firms

Section 4.3 acknowledged heterogeneity of firms. In particular, θf was drawn from a continuous distribution with support [α,β]. Imagine that the initial setting for the regulation was at the lowest level of x that would be chosen without regulation, xˉ=Xˆ(α+θc). An incremental increase in xˉ would be socially beneficial for the firms that are induced to change precaution, by Lemma 8, and neither beneficial or harmful to the others. Consequently, it would be beneficial on balance.

C Example

C.1 Assumptions

Let π(x,y)=(ax)2+(ay)22, where X=Y=[0,a],a=1. Then Xˆ(θ)=aθ1 and Yˆ(θ)=Y(x;θ)=aθ1. Assume as in Section 3 and Section 4.1 that θc<θd<θh and so:

θc1>θd1>θh1.

For simplicity, let θf1=0.

C.2 No Beneficial Regulation

Because x,y are independent, πxy=0, the regulator’s preferred point on y=Y(x;θc) is Xˆ(θh),Yˆ(θc). If this point violates the general criterion, πˉπ(x,y) i. e., if θd2(θh2+θc2)/2, then no regulation can be beneficial. The reason is that the regulator prefers the intersection of πˉ=π(x,y),y=Y(x;θc) to any other implementable point on y=Y(x;θc) by eq. 26 with l=c,j=h. Moreover, Xˆ(θd),Yˆ(θd) is the least cost way to attain πˉ=π(x,y), and this is attainable without regulation.

A similar argument holds for the biased general criterion of Section 4.1. If ϕˉ<ϕ(Xˆ(θh),Yˆ(θc)), then the best outcome attainable with regulation is on ϕˉ=ϕ(x,y), and so is dominated by the outcome without regulation.

References

Abelkop A. 2014. “Tort Law as an Environmental Policy Instrument.” Oregon Law Review 92:2.Search in Google Scholar

Abraham K. S. 2001. “The Relation between Civil Liability and Environmental Regulation: An Analytical Overview.” Washburn Law Journal 41:379.Search in Google Scholar

Bartsch E. 1997. “Environmental Liability, Imperfect Information, and Multidimensional Pollution Control.” International Review of Law and Economics 17 (1):139–146.Search in Google Scholar

Bennear L. S. 2015. “Offshore Oil and Gas Drilling: A Review of Regulatory Regimes in the United States, United Kingdom, and Norway.” Review of Environmental Economics and Policy 9 (1):2–22.Search in Google Scholar

Bhole B., Wagner J. 2008. “The Joint Use of Regulation and Strict Liability with Multidimensional Care and Uncertain Conviction.” International Review of Law and Economics 28 (2):123–132.Search in Google Scholar

Burrows P. 1999. “Combining Regulation and Legal Liability for the Control of External Costs.” International Review of Law and Economics 19 (2):227–244.Search in Google Scholar

Calcott P., Hutton S. 2006. “The Choice of a Liability Regime When There Is a Regulatory Gatekeeper.” Journal of Environmental Economics and Management 51 (2):153–164.Search in Google Scholar

De Geest G., Dari-Mattiacci G. 2007. “Soft Regulators, Tough Judges.” Supreme Court Economic Review 15 (1):119–140.Search in Google Scholar

Grady M. 1989. “Untaken Precautions.” Journal of Legal Studies 18:139–156.Search in Google Scholar

Grady M. F. 1983. “A New Positive Economic Theory of Negligence.” Yale Law Journal 92(5)799–829.Search in Google Scholar

Hart O., Moore J. 1988. “Incomplete Contracts and Renegotiation.” Econometrica 56(4) 755–785.Search in Google Scholar

Hause J. 2006. “Offsetting Behavior and the Benefits of Safety Regulations.” Economic Inquiry 44 (4):689–698.Search in Google Scholar

Henderson J. Managing the Negligence Concept: Respect for the Rule of Law. In: Madden M. S., editors. In Exploring Tort Law. Cambridge, New York: Cambridge University Press, 2005.Search in Google Scholar

Hiriart Y., Martimort D., Pouyet J. 2004. “On the Optimal Use of Ex Ante Regulation and Ex Post Liability.” Economics Letters 84 (2):231–235.Search in Google Scholar

Innes R. 2004. “Enforcement Costs, Optimal Sanctions, and the Choice between Ex-Post Liability and Ex-Ante Regulation.” International Review of Law and Economics 24 (1):29–48.Search in Google Scholar

Jain S., 2014 Economic Analysis of Liability Rules. New Delhi: Springer India.Search in Google Scholar

Jain S. K. 2006. “Efficiency of Liability Rules: A Reconsideration.” Journal of International Trade & Economic Development 15 (3):359–373.Search in Google Scholar

Klein B., Crawford R. G., Alchian A. A. 1978. “Vertical Integration, Appropriable Rents, and the Competitive Contracting Process.” The Journal of Law & Economics 21 (2):297–326.Search in Google Scholar

Koch B., 2008 Economic Loss Caused by Genetically Modified Organisms: Liability and Redress for the Adventitious Presence of GMOs in Non-GM Crops. Vienna: Springer Vienna. Tort and Insurance LawSearch in Google Scholar

Kolstad C. D., Ulen T. S., Johnson G. V. 1990. “Ex Post Liability for Harm vs. Ex Ante Safety Regulation: Substitutes or Complements?” American Economic Review 88(4) 888–901Search in Google Scholar

Louka E., 2006 International Environmental Law: Fairness, Effectiveness, and World Order. Cambridge, UK: Cambridge University Press.Search in Google Scholar

Park P., 2002 Energy Law and the Environment, Boca Raton, Florida: Taylor & Francis.Search in Google Scholar

Pistor K., Xu C. 2002. “Incomplete Law.” NYU Journal of International Law & Policy 35:931.Search in Google Scholar

Posner R. A. Regulation (Agencies) versus Litigation (Courts): An Analytical Framework. In: Kessler D., editor. In Regulation vs. Litigation: Perspectives from Economics and Law, Chicago: University of Chicago Press, 2010:11–26.Search in Google Scholar

Schmitz P. W. 2000. “On the Joint Use of Liability and Safety Regulation.” International Review of Law and Economics 20 (3):371–382.Search in Google Scholar

Shavell S. 1984. “A Model of the Optimal Use of Liability and Safety Regulation.” RAND Journal of Economics 15 (2):271–280.Search in Google Scholar

Tan A., 2005 Vessel-Source Marine Pollution: The Law and Politics of International Regulation Cambridge, UK: Cambridge University Press.Search in Google Scholar

Trebilcock M., Winter R. 1997. “The Economics of Nuclear Accident Law.” International Review of Law and Economics 17:215–243.Search in Google Scholar

Twerski A. D., Henderson J. A. 2015. “Fixing Failure to Warn.” Industrial Law Journal 90:237.Search in Google Scholar

Williamson O. E. 1979. “Transaction-Cost Economics: The Governance of Contractual Relations.” The Journal of Law & Economics 22 (2):233–261.Search in Google Scholar

Published Online: 2016-11-12
Published in Print: 2016-10-1