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1 Contingent Fees for Lawyers: The Impact on Litigation and Accident Prevention Author(s): Thomas J. Miceli and Kathleen Segerson Source: The Journal of Legal Studies, Vol. 20, No. 2 (Jun., 1991), pp Published by: The University of Chicago Press Stable URL: Accessed: 26/06/ :33 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a notforprofit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact The University of Chicago Press is collaborating with JSTOR to digitize, preserve and extend access to The Journal of Legal Studies.
2 CONTINGENT FEES FOR LAWYERS: THE IMPACT ON LITIGATION AND ACCIDENT PREVENTION THOMAS J. MICELI and KATHLEEN SEGERSON* I. INTRODUCTION C ONTINGENTfee arrangements have become the standard form of payment contract between clients and lawyers in tort cases involving personal injuries. Economic analyses of contingent fees have identified several advantages as well as several disadvantages relative to hourly fees.1 Among the purported advantages of contingent fees are that they (1) give individuals with insufficient resources to hire an hourly fee lawyer access to the legal system by allowing them, in effect, to borrow a lawyer's services against their expected award; (2) allow riskaverse individuals to shift the risks of a lawsuit to lawyers who are better able to diversify the risks over their entire caseload; (3) create an incentive for lawyers to work in the best interests of their clients; and (4) eliminate the need to monitor the amount of time a lawyer devotes to a given case. Some of the alleged disadvantages of contingent fees are that they (1) encourage excessive litigation; (2) create an incentive for lawyers to accept settle * Department of Economics, University of Connecticut, Storrs. The authors acknowledge the useful comments of Jerry Sazama and participants in the Economics Colloquium at the University of Connecticut. l Recent articles on contingent fees include Murray Schwartz & Daniel Mitchell, An Economic Analysis of the Contingent Fee in Personal Injury Litigation, 22 Stan. L. Rev (1970); Daniel Mitchell & Murray Schwartz, Theoretical Implications of Contingent Legal Fees, 12 Q. Rev. Bus. & Econ. 69 (1972); Kevin Clermont & John Currivan, Improving on the Contingent Fee, 63 Cornell L. Rev. 529 (1978); P. Halpern & S. Turnbull, Legal Fees Contracts and Alternative Cost Rules: An Economic Analysis, 3 Int'l Rev. Law & Econ. 2 (1983); Patricia M. Danzon, Contingent Fees for Personal Injury Litigation, 14 Bell J. Econ. 213 (1983); Herbert Kritzer, William Felstiner, Austin Sarat, & David Trubek, The Impact of Fee Arrangement on Lawyer Effort, 19 Law & Soc. Rev. 251 (1985); Geoffrey P. Miller, Some Agency Problems in Settlement, 16 J. Legal Stud. 189 (1987); and Joseph Fisher, Contingent and Noncontingent Attorney's Fees in Personal Injury Litigation, 6 Contemp. Pol'y Issues 108 (1988). [Journal of Legal Studies, vol. XX (June 1991)]? 1991 by The University of Chicago. All rights reserved /91/ $
3 382 THE JOURNAL OF LEGAL STUDIES ment offers when it is in their client's best interest to go to trial or, alternatively, to reject settlements when it is in their client's best interest to settle; and (3) produce excessive fees. In this article, we restrict our attention to one of these claims, namely, that contingent fees encourage excessive litigation relative to hourly fees. While this claim has been widely made, little theoretical (or empirical) support for it exists. An exception is Danzon, who develops a theoretical model of contingent fees showing conditions under which the claim is true.2 Her model, however, focuses on the effect of alternative fee arrangements on the lawyer's effort. It ignores the potentially important effect of the fee arrangement on the injurer's incentives to take care to avoid accidents (and thus avoid possible suits). If different fee arrangements imply different incentives to sue, then the probability of a suit being filed if an accident occurs can differ. If this relationship is recognized by potential injurers, a greater incentive to sue will lead to higher expected liability and thus a greater incentive to avoid suits by taking additional care. In this article, we show that, when this indirect effect of fee arrangements is considered, the contingent fee can, in fact, lead to a smaller number of suits being filed overall than an hourly fee would. Thus, in this broader context, there appears to be little theoretical support for the standard claim that contingent fees yield excessive litigation. The article is organized as follows. The next two sections compare the number of suits that would be filed under contingent and hourly fees. Section II compares the two under a rule of strict liability. We begin by describing the model, considering the conditions under which an equilibrium contingentfee arrangement exists and comparing the plaintiff's incentives to sue once an accident has occurred. We then consider the indirect effect of the fee arrangements on the injurer's choice of care and show that the increased threat of suit, given an accident under a contingent fee, creates an incentive for injurers to take more care to prevent accidents. Since the expected number of accidents therefore goes down, on net, the number of suits may be greater or less with contingent fees as compared to hourly fees. Section III compares the two fee arrangements under a negligence rule. The general conclusion is the same as under strict liability, namely, that when the indirect effect of the fee on the injurer's care level is considered, the contingent fee does not necessarily lead to more litigation. Section IV compares the outcome under the two fees to the firstbest outcome and shows that, under a negligence rule, the contingent fee 2 Danzon, supra note 1.
4 CONTINGENT FEES 383 always permits attainment of the firstbest while the hourly fee may or may not. II. THE IMPACT OF CONTINGENT FEES UNDER STRICT LIABILITY Consider a simple model of accident claims along the lines of Shavell3 in which a rule of strict liability prevails. Assume that accident victims (also referred to hereafter as plaintiffs) are risk neutral and that they file suit provided the expected payoff exceeds their litigation costs. Let there be a continuum of plaintiff types who are distinguished by the size of their expected payoffs from filing suit, denoted J,4 where J is distributed by F(J) on the interval [0, J].5 Assume that legal suits are complex procedures for which expert counsel is required. Hence, both plaintiffs and defendants hire a lawyer. The costs of litigation incurred by the plaintiff's and the defendant's lawyers are denoted Cp and Cd, respectively. Lawyers in turn are paid a fee for their efforts. Assume that defendants pay their lawyer an hourly fee (or fee for service) equal to the lawyer's costs (due to competition among lawyers). For plaintiffs, we will consider two types of fees: an hourly fee,6 and a contingent fee that depends on the plaintiff's payoff. For both types of fees we assume that lawyers are risk neutral and competitive and hence only expect to cover their costs.7 We also assume that lawyers cannot observe a plaintiff's type with certainty before accepting a case, they can do so only after having expended some litigation costs. (This will be especially important for contingentfee lawyers, as will be seen shortly.) Lawyers know the distribution of J, however. 3 Steven Shavell, Economic Analysis of Accident Law (1987). 4 Although we treat J as the plaintiff's expected judgment at trial, we could equally well interpret it as her expected settlement amount. See I. P. L. Png, Litigation, Liability, and Incentives for Care, 34 J. Pub. Econ. 61 (1987), for a model that explicitly incorporates the plaintiff's decision to settle or go to trial along with the injurer's (defendant's) choice of care. 5 We assume that for any individual J is exogenous. In particular, it does not depend on the actions of either the plaintiff or the lawyer. For an examination of how alternative fee arrangements might affect awards, see Danzon, supra note 1. 6 We do not explicitly introduce the choice of hours by lawyers or the ability of clients to monitor the number or quality of their lawyer's hours. For analyses of these issues, see Schwartz & Mitchell, supra note 1; Mitchell & Schwartz, supra note 1; Danzon, supra note 1; and Fisher, supra note 1. We simply assume that the number of hours required for each case is the same and that the total cost under an hourly fee is Cp for plaintiffs and Cd for defendants. 7 See Frederick B. MacKinnon, Contingent Fees for Legal Services (1964), for a discussion of competition among contingentfee lawyers.
5 384 THE JOURNAL OF LEGAL STUDIES A. The Existence of Equilibrium ContingentFee Arrangements Before examining the effects of contingent fees, we first ask whether or under what conditions an equilibrium contingentfee arrangement will exist, given the heterogeneity of plaintiffs. As noted above, the assumption that lawyers cannot observe a plaintiff's J before incurring litigation costs is crucial. It implies the existence of asymmetric information, similar to that discussed in Rothschild and Stiglitz.8 When asymmetric information exists, one party has an incentive to withhold that information for her own gain. Here, the plaintiff might initially withhold certain facts of the case that bear on the plaintiff's actual damages so that the lawyer will accept the case. By doing so, the plaintiff gains a chance at a positive return that would be unavailable if the case is not accepted. Since the lawyer may not learn the full facts until after the case is accepted and litigation costs have been incurred, unprofitable cases cannot be completely weeded out at the time of acceptance.9 Lawyers are willing to accept some proportion of such cases, however, as the cost of locating cases with merit, given imperfect information. More formally, given risk neutrality, a lawyer will be willing to accept contingent fee cases if and only if the expected return across all accepted cases at least covers litigation costs, that is, if and only if10 3E(J) Cp  O, (1) where,b is the fraction of the plaintiff's award paid to the lawyer as the lawyer's fee.11 By competition, (1) holds with equality; hence, under an 8 Michael Rothschild & Joseph Stiglitz, Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information, 90 Q. J. Econ. 629 (1976). 9 Note, however, that under a contingent fee the remaining set of suits that are accepted could still include as a subset nuisance suits, that is, those suits for which J < Cp. (See, for example, David Rosenberg & Steven Shavell, A Model in Which Suits Are Brought for Their Nuisance Value, 5 Int'l Rev. L. & Econ. 3 (1985); and Lucian Bebchuk, Suing Solely to Extract a Settlement Offer, 17 J. Legal Stud. 437 (1988).) Also note, however, that some suits with merit (J > Cp) end up being unprofitable under a contingent fee (if,bj < Cp). Thus, they would not have been accepted by contingentfee lawyers if the lawyer knew J ex ante. 10 We assume that lawyers have no fixed costs of pursuing a claim. 11 This assumes that the lawyer's fraction is constant across all plaintiff types, that is, that,b does not vary with J. This assumption seems to be consistent with actual practice (see MacKinnon, supra note 7; and Stuart M. Speiser, Attorneys' Fees (1973)). While technically the lawyer's fraction is a matter of negotiation between the client and the lawyer, in practice there appears to be little negotiation. Instead, some general rules or norms (such as 25 percent if the case is settled out of court and 33 percent if it goes to trial) govern the majority of contracts. These norms are similar to those governing real estate commissions
6 CONTINGENT FEES 385 equilibrium contingent fee, which implies P = Cp/lE(), (2) 1  [ = [E(J)  Cv]/E(J). (3) Equation (2) insures that lawyers will accept any suit filed by accident victims since in doing so they will cover their costs on average. In practice, of course, lawyers will not accept any suit that a plaintiff wishes to bring. In fact, law firms typically conduct review sessions to discuss new cases and ultimately reject a large percentage for lack of merit. Nonetheless, we retain the above simplification for two reasons. First, much of the discussion at these sessions concerns whether the injurer was negligent, and most rejections are cases where he was not. In our analysis of the negligence rule below, cases in which the injurer was not negligent are never brought (under either fee system) since we assume that there is no uncertainty over the injurer's care level. Rather, the uncertainty in our model is solely over J, the victim's damages, which are likely to be more difficult to assess accurately at early stages of the screening process and about which the victim is more likely to have private information. Thus, a large portion of cases for which J  Cp < 0 will presumably make the cut under a contingent fee. Second, with the possible exception of proposition 4 (see Section IV), the fact that some unprofitable cases are weeded out does not affect our results since these same cases would not be filed under a system of hourly fees either. Thus, we can simply eliminate such cases from consideration and assume that the remaining accidents with which we are concerned are those for which such a determination is not possible. Provided there remains some uncertainty over J on the part of lawyers for these cases, our results hold. Thus, for expositional convenience we continue to assume throughout that, given (2), lawyers will accept all suits filed by plaintiffs under a contingent fee. We assume that plaintiffs incur no costs themselves (for example, time costs) apart from their lawyer's fee. (As shown in the Appendix, most of the results of our analysis continue to hold if this assumption is relaxed.) In the absence of other costs, plaintiffs will file suits under a contingentfee arrangement provided the fraction of the award that they retain, 1 ,B, is greater than zero. From (3), this holds if and only if and are generally based on recommendations of courts and state and local bar associations. Although New York instituted a slidingscale approach, this appears to be the exception rather than the rule. For the implications of this assumption, see note 14 infra.
7 386 THE JOURNAL OF LEGAL STUDIES E(J)  Cp > O. (4) Thus, an equilibrium contingentfee arrangement (with 1 given by [2]) will exist if and only if condition (4) holds. This arrangement involves a pooling or averaging of returns from contingentfee cases. To see this, rewrite (4) as F(Cp)[E(J J < Cp)  Cp] + [1  F(Cp)][E(J J > Cp)  Cp] > 0. The interpretation of this condition is straightforward. The first term is the expected loss from unprofitable suits multiplied by their frequency in the population, and the second term is the expected surplus from profitable suits multiplied by their frequency. Equation (4') therefore says that, in order for equilibrium contingent fees to exist, the latter must more than compensate for the former. That is, unprofitable suits must be pooled with profitable suits, with the latter in effect subsidizing the former. Thus, some of the expected surplus from highj plaintiffs must be implicitly transfered to lowj plaintiffs in order to cover the lawyer's expected losses on such clients.12 The pooling of suits that is required to induce lawyers to accept contingentfee cases is not possible, however, if either (1) lawyers can observe J and set p accordingly or (2) victims can choose between contingent and hourly fee lawyers. Considering these in turn, suppose that lawyers observe J and set 1 according to P(J).13 Then for each J, the lawyer would accept the case if and only if P(J)J  Cp  O. Thus, lawyers cover their costs on each suit, and no pooling is involved.t4 This 12 The pooling nature of the equilibrium seems consistent with the notion that in practice contingent fees work on the basis of averages. For example, MacKinnon, supra note 7, at 82, notes that "when the mass of cases is taken as a whole, the idea of using overcharges to some clients to offset undercharges to others does not seem an unfair way to support a system of providing competent legal services to clients who need them." 13 Note that, in order for the pooling equilibrium to be eliminated, there must be a onetoone correspondence between client types (O) and rates (13). If there are more client types than possible rates, pooling would continue to occur. 14 This has important implications for the comparison of incentives to sue under the two fee systems. In particular, if lawyers observe J and set rates according to 3(J), then the probability of a suit is the same under a contingent fee as under an hourly fee. This can be seen as follows. If p = 3(J), then for each J the lawyer would accept the case if and only if 3(J)J  Cp 2 O. By the assumption of perfect competition, this becomes,b(j)j  Cp = O. Thus, the lawyer will accept the case if and only if 11(J) = (J  Cp)/J. Potential clients will want to file suit under the contingent fee if and only if 113(J) 2 0. Combining these conditions, it is clear that a suit will actually be filed if and only if J  Cp > 0. As will be seen below (see eq. [5]), this is precisely the condition for a suit to be filed under the hourly fee. Thus, with perfectly discriminating contingent fees, the pooling equilibrium would break down, and there would no longer be an increased conditional probability that a suit will be filed under the contingent fee. However, as argued in note 11 supra, in practice 1 does not appear to vary much by case. (4')
8 CONTINGENT FEES 387 is, of course, the obvious result if lawyers can weed out unprofitable cases by observing J. To see why the pooling equilibrium breaks down if victims can choose between contingent and hourly fee lawyers, consider an accident victim with expected damages equal to J. Under a strict liability rule, her expected net return is J  Cp under an hourly fee and (1 ,B)J under a contingent fee. She will thus prefer an hourly fee if J  Cp > (1  OJ or, equivalently, if J 2 Cp/13. (Accident victims with J < Cp/[3 prefer a contingent fee.) Thus, if given an opportunity to opt out of the pool, the highj clients will find it beneficial to do so. However, this will lower the average J in the pool, resulting in an expected return for contingentfee lawyers of 13E(J\J < Cp/,B)  Cp < o.15 Thus, contingentfee lawyers never cover their costs and hence exit the market. As a result, no contingentfee arrangements would be available in equilibrium.16 While the requirement that victims not be able to choose between fee types is clearly a simplification, there are several reasons why, in practice, most clients might not view the hourly fee arrangement as a viable choice. First, many potential clients will not have the financial resources necessary to secure the services of an hourly fee lawyer, regardless of the strength of their case. Thus, the only access they have to the legal system is through contingent fees. Second, even clients with sufficient resources may prefer a contingentfee arrangement because of risk aversion. While we have not included risk aversion in our model, it seems reasonable that it would be a basis on which clients might rule out consideration of an hourly fee lawyer. Finally, in practice, virtually all personal injury cases are accepted on a contingentfee basis. Thus, the client may view the contingentfee arrangement as the only viable possibility. In summary, if condition (4) is satisfied, lawyers cannot observe J, and plaintiffs cannot choose between fee arrangements, then under strict liability an equilibrium fee given by (2) will exist. Henceforth, we assume that these conditions hold, which implies that any suit brought by a plaintiff will be accepted by a contingentfee lawyer. 15 As an illustration, suppose J is distributed uniformly on [0, J]. Then 3E(J\J < Cp/[3)  Cp = p(cp/2p)  Cp = Cp/2 < o. 16 This is an example of an adverse selection problem, and the result obtained here is consistent with previous work on adverse selection (for example, Rothschild & Stiglitz, supra note 8). Note, however, that this argument has implicitly assumed that lawyers offering both types of fees are identical in all other respects. In particular, it assumed that the quality of service provided by lawyers is the same under the two fees. This is unlikely to be true, however. As noted above, an important function of the contingent fee, according to many authors, is the incentive it provides lawyers to work in the best interest of their clients. We have ignored this effect in this article.
9 388 THE JOURNAL OF LEGAL STUDIES B. The Effect of Fee Arrangements on Incentives to Sue In this subsection we consider the impact of the two types of fees on the incentive for accident victims to file suit, given that an accident has occurred. Later, we examine the impact of the fee type on the number of accidents. Hourly Fees. Consider first the hourly fee. In this case, given competitive lawyers, a plaintiff simply pays her lawyer an amount equal to the latter's cost, Cp, and retains her award, equal to J in expected terms. The plaintiff's net expected return from filing suit is thus J  Cp. Hence, she will file suit if and only if J  Cp > 0. (5) Consequently, the proportion of all accident victims who file suit (and hence become plaintiffs) under an hourly fee is given by the probability that J > Cp, that is, by 1  F(Cp). Contingent Fees. For the contingent fee, given 0 < 13 < 1, a plaintiff will file suit under a contingent fee if and only if (1 ,B)J > 0 or, equivalently, J > 0. (6) Thus, in contrast to the hourly fee, all accident victims file suit, resulting in more lawsuits under a contingent fee given the number of accidents. The results in this section are summarized as follows: PROPOSITION 1. Given the number of accidents that have occurred, more suits are filed by accident victims under contingent fees than under hourly fees. In other words, the probability of a suit conditional on an accident having occurred is higher under contingent fees than under hourly fees. In this sense, the claim that contingent fees lead to excessive litigation, defined as the filing of suits for which J  Cp < 0 or, equivalently, suits that would not be filed under an hourly fee, is true. However, as shown below, it is not necessarily true when the effect of the fee arrangement on the number of accidents is considered. C. Effect of Fee Arrangements on the Number of Accidents In this subsection, we broaden our discussion to ask what impact the fee type has on the number of accidents that actually occur. To motivate the analysis, consider how this impact might be felt. Suppose that individuals engaged in risky activities (referred to henceforth simply as injurers) perceive an increase in the likelihood that accident victims will file suit. This increases the expected liability of injurers, all else being equal, thus
10 CONTINGENT FEES 389 providing them an incentive to take more care in preventing accidents. As a result, the expected number of accidents declines.17 To capture this effect formally, we extend the above model as follows. Let p(x) equal the probability of an accident occurring, where x is the injurer's level of care, and p' < O, p" > 0. (We normalize the cost of x to be one dollar per unit.) For simplicity, we assume that the magnitude of damages conditional on an accident is independent of x.18 We employ this amended model to examine the incentives for injurers to take care under the two types of fees. Hourly Fees. Consider first the injurer's incentives under an hourly fee. In this case, injurers know that, if an accident occurs, victims will only file suit if J > Cp. Injurers (like lawyers) do not know a victim's type, but they know that the probability of a random victim filing suit is 1  F(Cp). Consequently, the expected liability of an injurer (defendant), conditional on a suit, is E(J{J > Cp) = { JdF(J) [1  F(Cp)]. (7) The total expected costs of the injurer prior to the occurrence of an accident is therefore x + p(x)[1  F(Cp)][E(J/J > C,) + Cd], (8) where the second term is the probability of an accident times the probability of a suit given an accident, times the expected costs of a suit (including the lawyer's fee) conditional on one being filed. The injurer chooses x to minimize (8), yielding the firstorder condition 1 + p'(x)[l  F(Cp)][E(J J > Cp) + Cd] = 0. (9) Denote the solution to (9) by xh. 17 The intuition is identical to that in A. Mitchell Polinsky & Daniel L. Rubinfeld, The Welfare Implications of Costly Litigation for the Level of Liability, 17 J. Legal Stud. 151 (1988), who show that with costly litigation, greater care by injurers can be achieved by awarding plaintiffs damages in excess of their actual losses. Png, supra note 4, derives a similar result, both with respect to the size of the plaintiffs award and the magnitude of her litigation costs. In ex ante terms, these effects are the same as increasing the probability of a suit conditional on an accident. Such an argument regarding contingent fees is informally made by Miller, supra note 1, at This is in contrast to Polinsky & Rubinfeld, supra note 17, in which damages are a function of care, but corresponds to Steven Shavell, Suit, Settlement, and Trial: A Theoretical Analysis under Alternative Methods for the Allocation of Legal Costs, 11 J. Legal Stud. 55 (1982); and Png, supra note 4. It is easy to show that this simplification does not qualitatively affect our results. (However, see note 24 infra.)
11 390 THE JOURNAL OF LEGAL STUDIES Contingent Fees. Consider now the incentives of injurers when plaintiffs hire lawyers under a contingent fee. As shown above, all accident victims file suit and all suits are accepted by lawyers if,b is set according to (2). As a result, the expected costs of injurers in this case are x + p(x)[e(j) + Cd]. (10) Minimizing this expression yields the firstorder condition 1 + p'(x)[e(j) + Cd] = O, (11) whose solution will be denoted xc. Comparison of Care Levels. In order to compare the care levels chosen under the two fees, we define the function i G(a) = [1  F(a)][E(J\J > a) + Cd] = J JdF(J) + [1  F(a)]Cd, (12) *a which is simply the expected cost to the injurer of a lawsuit, conditional on an accident having occurred, written as a function of the victim's cost of filing suit, a. It reflects both the probability of a suit being filed conditional on an accident occurring and the expected award to the plaintiff conditional on a suit being filed. Both of these depend on the incentive to file suit, as determined by a. In the case of an hourly fee, a = Cp. Alternatively, for the case of a contingent fee where the victim faces no upfront cost of filing suit, a = 0 and (12) reduces to G(O) = E(J) + Cd. (13) Taking the derivative of G(.) with respect to a yields G'(a) = f(a)(ot + Cd) < 0. (14) The negative sign in (14) results from the combination of two effects that work in opposite directions. An increase in a will decrease the probability of a suit being filed once an accident has occurred, which tends to decrease G. However, it will also increase the expected award given that a suit is filed (thereby increasing G) since suits are more likely to be filed by plaintiffs with high J's. The result in (14) indicates that the first of these effects will always outweigh the second effect. Given the definition of G, x' solves 1 + p (x)g(cp) = 0, while Xsolves 1 + p'(x)g(o) = 0. In addition, by (14), G(0) > G(Cp); that is, injurers face a higher expected cost of litigation given an accident under a contingent fee as compared to an hourly fee. The reason, as argued above, is simply that the hourly fee deters the lower tail of accident victims from filing suit while the contingent fee does not; with zero private costs and a positive expected return, all accident victims want to file suit under a
12 CONTINGENT FEES 391 contingent fee and, with the caveats discussed in Section IIA, all such suits are accepted by lawyers. As a result, the optimal level of care taken by injurers under a contingent fee exceeds that taken under an hourly fee, given the assumptions on p(x), that is, x* > x^.19 It follows immediately that the probability of an accident, and hence the number of accidents, is lower under a contingent fee than under an hourly fee. Thus, we state the following. PROPOSITION 2. Under a strict liability rule, a contingent fee induces more accident victims to file suit than an hourly fee does, which in turn elicits greater care by injurers and, consequently, fewer accidents. On net, therefore, the overall number of lawsuits may be higher or lower under a contingent fee compared to an hourly fee.20 III. THE IMPACT OF CONTINGENT FEES UNDER A NEGLIGENCE RULE In this section we extend the argument to the case of a negligence rule and show that, as with strict liability, the impact of the contingent fee on the number of suits filed is ambiguous once the incentives for injurer care are considered. A. The Effect of Fee Arrangements on the Incentive to Sue Under the negligence rule, the injurer is liable for the victim's damages if the injurer failed to satisfy the due standard of care, provided the victim files suit. Let x be the standard of care. Given this standard, the above analysis of the incentives for accident victims to file suit must be amended to include the requirement that x < x for a suit to be profitable. The reason, of course, is that if x  x, the injurer will not be held liable for the victim's damages, thus making the expected payoff from the suit zero.21 Thus, regardless of the type of fee, a victim will never file suit, nor will a lawyer ever accept the case, if the injurer satisfied the standard of care since we assume lawyers can observe the injurer's care level. 19 This can be seen by totally differentiating (9) to get dx/dcp = p'(x)g'(cp)/p"(x)g(cp) < 0, given p'(x) < 0 and p"(x) > Note that this conclusion is presumably reinforced if contingent fees provide an incentive for lawyers to work harder for their clients than hourly fees since this would further increase the injurer's expected costs of litigation conditional on an accident. Interestingly, Kritzer et al., supra note 1, found that the number of hours a lawyer devotes to a case under a contingent fee exceeds that under an hourly fee only for high J cases, while the reverse is true for low J cases, although they do find evidence that the quality of time is uniformly higher under a contingent fee. 21 We assume that the court does not make errors in determining whether the standard of care has been satisfied. For the implications of introducing such errors, see A. Mitchell Polinsky & Steven Shavell, Legal Error, Litigation, and the Incentive to Obey the Law, 5 J. L. Econ., & Org. 99 (1989).
13 392 THE JOURNAL OF LEGAL STUDIES B. The Effect of Fee Arrangements on the Number of Accidents Hourly Fee. Given the preceding discussion, accident victims who hire lawyers on an hourly fee basis will file suit under a negligence rule if and only if J > Cp and x < x. The injurer thus chooses x to minimize x ifx 2 X, and (15) x + p(x)g(cp) if x < x, where the second line is identical to the injurer's costs under strict liability as given by (8) above. Clearly, the injurer will never choose x > x. Thus, depending on how x is set, he will either choose x, in which case there will be no lawsuits, or he will choose x~ < x, the level of care that minimizes the second line, in which case lawsuits will be filed by all victims for whom J > Cp. The injurer will choose x~ < x, making him negligent, if the minimized value of the second line is less than x, which is possible if x is set very high. Contingent Fee. In the case of the contingent fee, the condition for an accident victim to file suit is now simply that x < x. The resulting problem for injurers is thus to minimize x ifxx7, and (16) x + p(x)g(o) if x<x, where the second line again corresponds to the injurer's costs under strict liability as given by (1). By the same reasoning as before, the injurer will either choose x, in which case there will be no lawsuits, or x*, the level of care that minimizes the second line of (16), in which case all victims will file suit. Comparison of Care Levels. In comparing the solutions for the two types of fees under a negligence rule, three cases must be considered. Case 1. The first case is where x is sufficiently low that injurers choose x under both fees. This will occur if either (a) both x' and x* exceed x or (b) both x~ and x* are less than x and the minimized values of the second lines of (15) and (16) are greater than x. One such x is 2l in Figure 1. Case 2. At the other extreme is the case where x is set high enough that injurers choose care less than x under both types of fees. This will be true if the minimized value of the second lines of (15) and (16) are less than x. (A necessary condition for this, of course, is that both x' and xc are less than x.) In this case, all of the results from the strict liability case apply. An example of this case is given by x2 in Figure 1. Case 3. The final case is one in which injurers satisfy the standard of
14 CONTINGENT FEES 393 Dollars x + p(x)g(0) \ /^ x + p(x)g(cp) xl x,* Xc* xi xl Care (x) FIGURE 1 care under one type of fee but not under the other. However, because G(0) > G(Cp)that is, because the injurer's expected cost of litigation conditional on an accident is higher with a contigent fee than with an hourly feethe second line of (16) must exceed the second line of (15) for all x. Consequently, the only possible outcome for this case is where injurersatisfy the standard of care under a contingent fee but not under an hourly fee. In such a case, x[ must be less than x~ (as in case 2), while x* may be above or below x (as in case 1). An example of this case is given by X3 in Figure 1. Taken together, these cases imply the following. PROPOSITION 3. Under a negligence rule, one of the following occurs. (a) Injurersatisfy the standard of care under both contingent and hourly fees. In this case they have identical impacts on the number of suits filed (zero suits are filed) and the level of care chosen by injurers. (b) Injurers violate the standard of care under both fees. In this case, the results obtained under strict liability continue to hold, that is, the contingent fee results in more lawsuits given an accident has occurred, but also greater care by injurers. Thus, overall a contingent fee can either increase or decrease the total number of suits filed. (c) Injurersatisfy the standard of care under a contingent fee but violate it under an hourly fee. In this case, fewer (zero) lawsuits are filed under a contingent fee, and injurers take more care.
15 394 THE JOURNAL OF LEGAL STUDIES Note that option c implies that, under a negligence rule, it is possible for contingent fees actually to lead to less litigation than hourly fees even holding the number of accidents fixed because of the greater probability that the injurer complied with the due standard of care. This is in direct contrast to the results under strict liability and the claims that have been made in the literature. IV. COMPARISON WITH SOCIAL EFFICIENCY Thus far our analysis has considered only what the effects of a contingent fee would be relative to an hourly fee. In particular, we have not tried to evaluate whether the impact on incentives to sue or the injurer's care level is good or bad from society's perspective. In this section, we explicitly compare the injurer's care under the two types of fees to social efficiency. In models with costless litigation, the socially efficient care level is defined to be the level that minimizes the sum of the costs of care and expected damages, that is, the level of x that minimizes x + p(x)e(j). (17) This is the "firstbest" level of care, that is, the level that a social planner would like to impose.22 However,, if care must be induced through the legal system and litigation is costly, the firstbest outcome may not be achievable. A "secondbest" alternative would then be to choose x to minimize the sum of the costs of care, expected damages, and expected legal fees, that is, the level of x that minimizes x + p(x)[e(j) + q(cp + Cd)], (18) where q is the probability that a suit is filed given an accident has occurred.23 Clearly, in this secondbest case, total expected social costs depend on both the level of care (x) and the probability of a suit (q). Strict Liability. Under strict liability, the injurer's choice problem can be summarized as: min{x + p(x) q[e(jij > a) + Cd]}, (19) where a = Cp under an hourly fee and a = 0 under a contingent fee. Furthermore, the probability of a suit conditional on an accident is given by q = 1  F(a). (20) 22 See Polinsky & Rubinfeld, supra note This is the definition of efficiency used by Shavell, supra note 3, at , for the case of q = 1. Note that (17) is a special case of (18) where q = 0.
16 CONTINGENT FEES 395 Thus, q = 1 under a contingent fee (since F(0) = 0) and q = [1  F(Cp)] < 1 under an hourly fee. From (19) and (17), it is clear that under strict liability the firstbest level of care is not attainable under either fee since, in the absence of lawsuits, injurers will never take care under strict liability.24 Thus, the analysis of the two fees falls within the realm of the second best choice, defined by (18). However, comparing (19) and (20) to (18) implies that, given q, neither the hourly fee nor the contingent fee yield efficient care by this standard either. In the case of the contingent fee where q = 1, the inefficiency stems solely from the fact that the defendant is not required to pay the plaintiff's legal fees, thus making the private cost of suit to the defendant less than the social cost. Consequently, injurers take too little care, a result that has been established in previous work.25'26 In the case of an hourly fee (where q < 1), again injurers do not face the full social costs of litigation. However, there is a second source of inefficiency not present under the contingent fee. Because the probability of a suit conditional on an accident is less than one under an hourly fee, the defendant does not face the full expected damages, E(J), but rather [1  F(Cp)]E(J\J > Cp) < E(J). This second effect reinforces the injurer's incentive to take less care. Note, however, that even though injurers take greater care under the contingent fee than under the hourly fee, we cannot necessarily claim that the contingent fee is more efficient since expected social costs under the contingent fee ([18] evaluated at x* and q = 1) are not necessarily less than expected social costs under an hourly fee ([18] evaluated at x~ and q = 1  F(Cp)). Although the contingent fee results in more care and thus fewer accidents, the number of suits conditional on an accident is greater. Thus, the sum of expected prevention costs, damages, and legal fees may be greater or less under the contingent fee Polinsky & Rubinfeld, supra note 17, show that the firstbest outcome (with zero lawsuits) can be attained under strict liability if the award that would have to be paid to plaintiffs is suitably adjusted. This is possible in their model because (1) the magnitude of damages depends on the injurer's level of care (in contrast to our model) and (2) they consider only what amounts to an hourly fee. Thus, plaintiffs can be deterred from filing suit if the care level of injurers is sufficiently high since plaintiffs' expected payoffs thereby fall below their costs of filing suit. 25 See, for example, Shavell, supra note 18; Png, supra note 4; and John C. Hause, Indemnity, Settlement, and Litigation, or I'll Be Suing You, 18 J. Legal Stud. 157 (1989). 26 If defendants were required to pay all legal fees (Cp + Cd) as under the British system, then (18) and (19) would have the same solution, given q = 1 and a = Note that this result is consistent with the general theory of the second best. When multiple sources of inefficiency exist, eliminating one source does not necessarily improve efficiency.
17 396 THE JOURNAL OF LEGAL STUDIES Negligence. Under a negligence rule, it is theoretically possible to forestall all suits through the appropriate choice of the due standard of care, in which case q = 0 and the socially efficient level of care is the firstbest level defined by (17). We assume (as is common in studies of negligence) that the due standard of care, x, is set equal to the firstbest level, denoted x*. Consider first the injurer's choice under an hourly fee. The second line of (15) differs from (17) by the presence both of Cd and 1  F(Cp) in the former. Clearly, the presence of Cd increases the injurer's expected costs (if negligent) relative to social costs. However, the fact that a suit will be brought only with probability q = 1  F(Cp) < 1 reduces private costs relative to social costs. The net effect is ambiguous. Thus, x' may be either larger or smaller than x. If it is larger, then the solution to (15) is x, and the firstbest level of care is achieved. If, however, x~ is less than x and the minimized value of the second line is also less than x (cases 2 and 3 above), then the solution to (15) is x~ < x, and firstbest care is not achieved. An example where this is true is shown in Figure 2. Alternatively, in the case of a contingent fee, it can be shown that the firstbest outcome will always be achieved. Comparing (17) with the second line of (16), it is clear that the social costs differ from private costs only by the presence of Cd in the injurer's problem. Thus, the injurer's expected costs if negligent are greater than the social costs in (17), implying that x* > x. Hence, according to cases 1 and 3 above, the solution to (16) is x = x*. This is also illustrated in Figure 2. Note that, in this case, the firstbest outcome is attained despite the distribution of legal fees since no suits ever occur in equilibrium. We summarize these results in the following proposition. PROPOSITION 4. Under a negligence rule, if the due standard of care is set equal to the firstbest level, then the firstbest level of care is always attainable under a contingent fee (even if defendants expect to pay only their own legal fees); however, the firstbest level of care may or may not be attainable under an hourly fee. In other words, if x = x* (where hence there is no role for lawyers. However, their potential presence is necessary in order for the threat of lawsuits to exist. Clearly, if no such threat existed, injurers would have no incentive to take care A similar qualification obviously applies as well to firstbest outcomes in the model of Polinsky & Rubinfeld, supra note 17. See Janusz A. Ordover, Costly Litigation in the Model of Single Activity Accidents, 7 J. Legal Stud. 243 (1978), for a model that explicitly addresses this issue.
18 CONTINGENT FEES 397 Dollars v \ / x + p(x)g(o) "^ \ / x + p(x)e(j) V^ >, x + p(x)g(cp) ' // s ~ ~ _ ~ rx ~ ~~~~ Xh* X Xc* Care (x) FIGURE 2 V. CONCLUSION Contingent fees are the predominant (if not the sole) form of compensation for plaintiffs' lawyers in personal injury suits. Yet they are looked on with suspicion by many observersenough suspicion, in fact, to warrant regulation by many states.29 One of the principal charges seems to be that they encourage excessive litigation. In this article we have evaluated this claim using a simple model of accidents that incorporates the effect that fee arrangements would have on injurers' choice of care (and thus on the number of accidents). The results can be summarized as follows. We first showed conditions under which an equilibrium contingentfee arrangement could exist. Given the diversity of plaintiff types, this rex* minimizes [17]), then the solution to (16) is xc*, while the solution to (15) is less than or equal to x*. A final word of qualification is necessary here. As defined above, the firstbest efficient outcome is one in which no lawsuits are actually filed; quired a pooling of high and lowpayoff plaintiffs. In addition, we showed that such a pooling was only possible if lawyers cannot observe a plaintiff's type ex ante, and plaintiffs cannot choose between hourly and 29 Danzon, supra note 1, at 213.
19 398 THE JOURNAL OF LEGAL STUDIES contingentfee lawyers, conditions that we argued are likely to hold in practice. Given the existence of equilibrium contingent fees, we then showed that under a rule of strict liability, the contingent fee would lead to more suits (as generally thought) if we hold the number of accidents constant. However, the increased incentive for accident victims to sue under a contingent fee (as compared to an hourly fee) induces potential injurers to take greater care in preventing accidents. When this effect is considered, the overall impact of contingent fees on the volume of litigation is ambiguous. While the number of suits conditional on accidents rises, the number of accidents falls. Thus, under strict liability, the unconditional number of suits under the contingent fee could be larger or smaller than under the hourly fee. Under a negligence rule, depending on the standard of care, it is possible that even the number of suits conditional on an accident having occurred will be smaller with a contingent fee because of the increased likelihood that the injurer has complied with the due standard. Again, this results from the effect of the fee on the injurer's care. Thus, under either strict liability or negligence, once injurer incentives are considered, there appears to be little theoretical justification for the common claim that contingent fees lead to excessive litigation. Finally, under strict liability, neither contingent nor hourly fees yield the firstbest outcome, defined to be the minimum sum of prevention costs plus expected damages with no suits actually being filed (and thus no legal costs incurred). In addition, although the hourly fee involves a second source of inefficiency not present under contingent fees, it is not possible to rank the two fee systems on the basis of efficiency. However, under a negligence rule, contingent fees always yield the firstbest outcome if the standard of care is set at the firstbest level. This outcome is also possible under hourly fees, but it is not assured. In view of these results, contingent fees appear to have several beneficial effects on social welfare, despite the charges of critics. Indeed, our results showed that the consequence of contingent fees most attacked by criticsnamely, the increased incentive for accident victims to initiate litigationalso generates social benefits. The critics of contingent fees, it seems, have largely overlooked these longrun effects. APPENDIX THE ROLE OF FILING COSTS In this appendix, we consider the implications of relaxing the assumption that the only costs a plaintiff incurs are those paid to her lawyer. In particular, suppose that plaintiffs, in addition to incurring a lawyer's fee,
20 CONTINGENT FEES 399 must pay a further cost of filing suit. This may take the form of an explicit fee or simply time costs.30 Will the presence of such a cost affect the incentives to file suit under the two types of fees? In particular, is it possible that such a cost will result in more suits being filed under an hourly fee than under a contingent fee (holding the number of accidents fixed)? To answer this question, let w equal the plaintiff's cost of filing suit. Then she will now do so under an hourly fee if and only if J>Cp and under a contingent fee if and only if or + w (1  P)J> w J > w/(11), 0 < 1 < 1. The condition for more suits to be filed under a contingent fee is thus or, rearranging, Cp + w > w/(113),b < Cp/(Cp + w). (A1) Since,B = Cp/E(J) in equilibrium (see [2]), this condition becomes E(J) > Cp + w, (A2) which says that the expected damages suffered by the average accident victim is greater than the social costs of bringing the suit. Whether this condition holds, of course, is an empirical question, but it seems likely that it would. If it does, all the results in this article go through with the exception of proposition 4. The reason is that with a filing fee it is no longer true that all accident victims will file suit under a contingent fee if the injurer is negligent. Hence, attainment of the firstbest outcome under a contingent fee, while still possible, is no longer assured. 30 See Rosenberg & Shavell, supra note 9; and Danzon, supra note 1.
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