Costly Litigation and Optimal Damages

A basic principle of law is that damages paid by a liable party should equal the harm caused by that party. However, this principle is not correct when account is taken of litigation costs, because they too are part of the social costs associated with an injury. In this article we examine the influence of litigation costs on the optimal level of damages, assuming that litigation costs rise with the level of damages.


Introduction
The standard amount that a party who has been found liable for an injury must pay in damages is the harm caused. 1 Several scholars have pointed out, however, that this basic principle of law is economically problematic because the social cost of a harmful event is not only the harm, but also the associated litigation costs. They have therefore argued that the injurer should bear the harm plus total litigation costs -which implies that the injurer should * Stanford Law School and Harvard Law School, respectively. Both authors are also Research Associates of the National Bureau of Economic Research. Polinsky's research was supported by the John M. Olin Program in Law and Economics at Stanford Law School, and Shavell's by the John M. Olin Center for Law, Economics, and Business at Harvard Law School. 1 See, for example, Restatement (Second) of Torts, § 901, comment a (1979) (". . . the law of torts attempts primarily to put an injured person in a position as nearly as possible equivalent to his position prior to the tort."); Restatement (Second) of Contracts, § 344, comment a (1981) (the court ordinarily awards damages that put the breached-against party "in as good a position as he would have been in had the contract been performed, that is, had there been no breach."). pay damages equal to the harm plus the victim's litigation costs, since the injurer already bears his own litigation costs. 2 We explain here why this conclusion is incorrect when account is taken of the fact that litigation costs generally increase with the level of damages. Consequently, litigation costs can be saved by lowering damages. Due to this consideration, we demonstrate that optimal damages can lie anywhere between zero and the harm plus the victim's litigation costs. The proper level of damages in this range depends on the tradeoff between saving litigation costs and promoting incentives to prevent harm.
The issue we are studying is empirically significant because litigation costs are highon average about two-thirds of harm -and are sensitive to the level of damages. 3 For this reason, we believe that the optimal level of damages will often be less than the harm and, when the incentive effect of damages is low, could be zero.
We derive our results in section 2, illustrate them in section 3, and conclude in section 4.

The Model
We employ the standard model of accidents in which potential injurers take care to reduce the risk of accidents to strangers. 4 We assume that if there is an accident the victim will decide whether to sue the injurer and, if he does, that both parties will bear litigation costs.
These costs include a fixed component and a variable component that rises with the level of 2 See Polinsky and Rubinfeld (1988), Hylton (1990), andShavell (1999). 3 See paragraph (a) in section 4 below. 4 The conclusions that we draw would be expected to carry over to harmful events other than accidents, and notably to breach of contract and violations of property rights. damages. 5 We assume that liability is strict, that is, an injured party will be awarded damages if he brings a lawsuit, regardless of the injurer's level of care. 6 The state selects the level of damages to minimize social costs, which equal the sum of the cost of care, the harm, and litigation expenses.
To obtain damages d after an accident, a victim must sue the injurer, thereby incurring litigation costs of γ v + λ v (d) and causing the injurer to bear litigation costs of γ i + λ i (d). A victim will bring a suit if and only if damages equal or exceed his litigation costs, that is, when or when where d o is the solution to 7 (3) We denote the level of care taken by an injurer by x(d). If d < d o , then x(d) = 0 because no suits will be brought. If d ≥ d o , then suits will be brought and the injurer's costs will be The injurer will choose x(d) so as to minimize (4). This level of precaution is unique since (4) is convex in x. The injurer will choose x(d) = 0 if the derivative of (4) at 0 is non-negative: otherwise x(d) will be positive and determined by It straightforward to show that x′(d) is positive by differentiating (6) with respect to d.
If victims do not bring suits, social costs will be If victims do bring suits, social costs will be Optimal damages, d*, minimize social cost, which is (7) we can assume that d* = 0 because no suits will be brought. Therefore, d* is either 0 or at least d o .
It will be informative to first examine a simplified version of the model in which there are no variable litigation costs.
Proposition 1. When litigation costs are comprised of fixed costs only, optimal damages are either zero or equal to the sum of the harm and the victim's fixed cost of litigation, cannot be optimal because one could achieve the same level of care by the injurer without incurring litigation costs, by choosing d = 0. If x(γ v ) > 0, it is also true that d = γ v cannot be optimal. In particular, (6) must hold, implying that Additionally, the derivative of social costs (8) is Using (9), (10) We now know that d* either is 0 or is greater than d o , in which case it satisfies the firstorder condition  will fully internalize the costs imposed on society whenever an accident occurs, given that a suit will result; there is no need for damages to reflect the injurer's litigation costs because the injurer will naturally bear these costs. On the other hand, if suits are not socially worthwhile because their beneficial effects on the injurer's care decision are offset by their associated litigation costs, optimal damages should be zero in order to forestall suits.
Essentially the same result -that optimal damages are either zero or the sum of the harm and the victim's fixed litigation cost -is shown in Polinsky and Rubinfeld (1988) in a different model of liability for accidents and in Shavell (1999) in a model similar to that considered here.
A closely related result is obtained in Hylton (1990). Variable litigation costs are not considered in these articles.
We now state the main result in our model.  (14) below. Hence, when optimal damages are positive, they are less than the sum of the harm and the victim's litigation costs, d* Proof: We explained above that d* is either zero or at least d o . Clearly, as in Proposition 1, d* = 0 is possible because, if the sum of γ i and γ v is sufficiently large, lawsuits will be undesirable.
That d* can equal d o is demonstrated by an example below. The explanation in essence is that it could be socially desirable to induce suits in order to significantly lower the likelihood of accidents, but not to raise damages any more than is necessary to induce suits because doing so would increase litigation costs more than the additional benefits of risk reduction. To demonstrate that d* < h + γ v + λ v (d*) when d* is positive, first suppose that d* = d o . Then Then d* must satisfy the first-order condition following from (8), Observe that x(d*) > 0, for otherwise the same level of care by the injurer could be obtained without incurring litigation costs by choosing d = 0. Therefore, (6) holds at d*, so that (13) becomes Because

Comments:
The explanation of the result that optimal damages must be less than h + γ v + λ v (d*) is as follows. If damages were equal to h + γ v + λ v (d*), then they would fully internalize the costs imposed on society whenever an accident occurs, given that a suit will result. It is desirable to reduce damages from this benchmark because doing so has no first-order effect on socially desirable internalization of social costs but does have a first-order beneficial effect on litigation costs, for they fall as damages are reduced.

An Example
To illustrate our results, let the probability of an accident be q(x) = .01 + .09e -.01x .
Thus, if nothing is spent on care, the probability of an accident is .10, and expenditures on care cause this probability to decline asymptotically to .01. For instance, if $10 is spent on care, the probability of an accident is .09; if $100 is spent, the probability is .04; and if $200 is spent, it is .02. Also, let the fixed litigation costs be γ i = γ v = $2,500 and the variable litigation costs be where 0 < λ i < 1, and where 0 < λ v < 1. Hence, from (3), the threshold value of d below which victims will not sue is . The level of harm h and assumptions about the variable litigation cost parameters λ i and λ v will be discussed below. if h = $25,000, d* = $10,702. Obviously, since optimal damages are less than harm, they are less than the sum of the harm and the victim's litigation costs. 9 These results illustrate Proposition 2.
Note that optimal damages are lower than the harm because of the sensitivity of variable litigation costs to the level of damages. Given λ i = λ v = .3, variable litigation costs decline by 60 cents for every dollar reduction in damages. If λ i and λ v were lower than .3, the motive to lower damages in order to reduce litigation costs would not be as great and, consequently, optimal damages would tend to be higher. Consider the case in which h = $10,000, λ i = λ v = .3, and d* = $5,459. If instead λ i = λ v = .2, d* = $6,663; and if λ i = λ v = .1, d* = $8,590. For optimal damages to exceed the $10,000 harm, λ i and λ v would have to be less than .0532. If, for instance,

Conclusion
We conclude with several remarks about our analysis. 10 See Shavell (2010, pp. 1469-70). 11 Suppose all litigation costs are variable costs and proportional to damages, and that the victim's and the injurer's litigation costs are the same. Specifically, let each party bear litigation costs equal λd. Given the observation that the parties' joint litigation costs equal the amount of damages retained by the victim, the following condition would hold: 2λd = (1 -λ)d. Solving for λ yields λ = 1/3, so 2λ = 2/3. This conclusion would not be affected very much if fixed costs are positive but only a small fraction of total litigation costs. that lowering damages by one percent would lower litigation costs by half of a percent. 12 These observations suggest that lowering damages would often significantly decrease litigation costs.
The countervailing argument to lowering damages is that injurers will have weaker incentives to reduce harm, but this point is not strong in some domains. Notably, incentives to reduce harm would not be affected very much by lower damages when firms face rigorous safety regulation or strong market discipline. Thus, in some important contexts optimal damages may well be less than harm.
(b) Settlements. That most cases settle out of court does not fundamentally alter our conclusions. First, cases that settle tend to involve costs because parties often gather evidence, negotiate with each other, and make certain filings or appearances in court before reaching a settlement. Second, settlement costs would be expected to rise with the level of damages that would be awarded at trial for the same reasons that trial costs would rise. Thus, the motive to lower damages in order to reduce legal costs would remain if settlements were taken into account.
(c) Negligence rule. Although optimal damages depend on litigation costs under strict liability, they do not depend on litigation costs under the negligence rule in the standard model of accidents and liability. The reason is that litigation does not actually occur under the negligence rule, for injurers are led to be non-negligent. 13 Hence, there is no motive to alter damages from harm on account of litigation costs. However, in more realistic models of the negligence rule, litigation would occur and therefore the general points that we have developed here would be relevant.
(d) Alternative ways to control litigation costs. Rather than constraining litigation costs by lowering damages, such costs could be controlled directly by regulating how much parties spend on litigation or by taxing litigation expenditures. However, these alternatives might not be easy to implement because it will often be difficult to identify the resources that parties invest in litigation. Notably, the time devoted to a case by the parties (as opposed to their attorneys) generally will not be observable. Additionally, a lawyer representing a party on a contingency fee basis might not keep a record of how much time he expends on the matter. An advantage of controlling litigation costs by lowering damages is that this method will desirably dampen litigation expenditures even when the parties' investments in litigation cannot be regulated or taxed. A further advantage of using damages rather than regulation to control litigation costs is that the former approach provides flexibility to the parties to allocate their litigation expenditures (for example, between lawyers and experts) in the most efficient way given the circumstances of their case, whereas regulation would impose restrictions on them that are not tailored to their case.