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Alejandro Esteller-Moré esteller@eco.ub.es

Universitat de Barcelona

ABSTRACT: The paper studies the design of a user charge on judicial litigation, which aims both to reduce the congestion of the judicial system, and cover part of the direct costs of the system. In order to do that, we use an economic model, which embodies all the variables that affect both the individual decision to litigate, and the social consequences of it, i.e., congestion costs and higher judicial costs. The paper also makes use of numerical simulations in order to get a clearer idea of the parameters on which the user charge depends. The simulations have attempted to get a picture as close as possible of the present Spanish Judicial System, given the statistical information currently available.

JEL Code: K41, H21, H23

^∗ This paper has benefited both from the funding of the research project CICYT, SEC97-1202 (Ministerio de Educación y Cultura), and from the Research Group on "Fiscal Federalism and Regional Economics", 97SGR-319 (Generalitat de Catalunya), which are gratefully acknowledged.

1. Introduction

Through this short piece of work, we pretend to analyse by means of the economic theory the implementation of an optimal user charge on judicial litigation. Of course, the qualification of the user charge as optimal is conditioned on the aims that are behind the creation of the charge. In our case, that aims come directly from the current reality of the Spanish Judicial System. In particular, with respect to that system some opinions have stated that in the near future there will produce (even) longer delays in the Courts of Justice, unless some measures are adopted. Among these measures, some propose the restoration of the user tax ("tasa judicial"), which was abolished by the Parliament in 1986, due both to efficency (?) and equity causes (Vid. Santos Pastor, 1993, pp. 307-9)¹.

Among those who have announced a likely increase in the congestion costs in the Courts, and to mitigate the problem propose the re-introduction of the "tasa judicial", we find Guillem Vidal, president of the Higher Court of Justice of Catalonia (TSCJ), or Joaquín Bayo, the Senior Judge of Barcelona. Namely, the latter is in favour of the "tasa judicial" "...in order to reduce the number of lawsuits, and so avoid that the society as a whole has to pay judicial actions that are run by big firms, which dispose of more than enough means to fund themselves their whims, but which make use of the justice due to its priceless character" (La Vanguardia, 23^rd, March, 1999). Hence, according to him not only efficiency issues would justify the introduction of the charge (or any other policy), but also equity issues. From the academia, there has also emerged an outstanding analyst of the Spanish system that would find its reintroduction right, though he thought it was quite unlikely to happen, at least in the medium or short run (Santos Pastor, op. cit, p. 139).

This study does not enter into consideration of the degree of validity of the Senior Judge of Barcelona's statements, but simply takes them as given, and then using the tools of the economic theory designs a user charge that attempts to achieve the "great chaos" he foresees in the future does not happen. All the same, the introduction of the user charge is by no means the only solution to the congestion problems of Justice. Thus, we can clearly differentiate two completely different types of policies: first, policies that affect the supply of justice, and secondly, those policies that instead affect the demand of justice. The introduction of the user charge lies within this latter type of policy.

¹ In the Appendix attached at the end of this paper, we describe the main characteristics of such user charge.

For example, a typical supply policy would consist in increasing the number of judges, or the material means at their disposal, so they both would be costly to the public sector. However, not all supply policies have to be costly, since they instead could consist in trying to improve the organisation of the system², or providing better incentives (in money terms, or labour promotion) to the judges to incite them to be more efficient (if possible). With respect to demand policies, these can at the same time be divided into two groups: those that directly condition the demand of justice through regulations, e.g., establishing minimum amounts of claimed liability in order to be able to access the service of the Courts of Justice; and second, those policies that affect indirectly the demand through variations in the price of the access to justice, e.g., establishing a user charge. Obviously, in order the charge be effective, the demand of access to Justice has to be sensitive to variations in the price, or put differently, in order the user charge be effective it must be relatively significant with respect to the expected benefit for the litigant that will emanate from the Judicial process.

As we have noted above, some of the supply policies have the disadvantage with respect to the demand policies that require to be financed from the Public Sector, while the latter do not, and additionally in the case of the user charge even provide extra public revenues³. However, this economic advantage clearly faces political problems of social acceptation, by the future potential plaintiffs (and by those who have clear vested interests in the market, typically the lawyers), as first, it means an increase in the fiscal pressure, and second would be against the fact socially accepted of the priceless and free character of the access to justice. In any case, and especially under those circumstances just cited, that type of supply policies that opt to improve the organisation of the courts of justice or increase the efficiency of the judges would undoubtedly represent the first best solution. Finally, the demand policy of setting minimum levels of claimed liability to access justice does not look nor equitable nor efficient. It does not look efficient to discriminate according the claimed liability, since this way frivolous suits ("litigios de bagatela" in Vidal's words), which are one of the most important causes of delay, would not be penalised. For example, suppose a minimum level of claimed liability of 1.200.000 ptas., then a suit in which a person/firm claims for 1.000.000 ptas., and has an objective probability of wining the case of 20% would not be able to access justice, while a person/firm that claims for 100.000.000 ptas, but with an objective probability of wining of 0.002% would do, though both claims have the same expected benefit. Therefore, frivolous suits would still be run, though their judicial costs and congestion costs are undoubtedly over the expected benefit, and that type of situations are normally inequitable as well, as those who engage in litigation when have so few chances of wining the case do so because the cost of litigation for them is very low, normally big firms, which usually dispose of their own team of lawyers⁴.

² For instance, within this particular type of supply policies, Bayo proposes (La Vanguardia, op. cit.). that the different accusations accumulated against the same person do not disperse, and be conducted to hands of the first judge in order this can apply the condition of recidivist immediately. The first section of the paper cites some other supply policies.

³ This is the usually so-called "double dividend" in the literature of environmental economics, when taxes are set up in order to correct negative environmental externalities. Nevertheless, that public resources do not always have to be consider as a "double dividend", especially in the case of the charge, as legally it is defined as a fiscal figure explicitly designed to cover the costs of a public service. Then, depending on the weight of the objectives attached to the charge, to cover the judicial costs or reducing delay in the service, the qualification of the extra public resources as first or double dividend shall be given.

To conclude, we stress again that the role of this paper is nor assessing the degree of congestion of the judicial system in Spain nor discussing potential reasons of that (potential) congestion, which causes the delay in the judicial decisions⁵, nor recommend any particular judicial policy, but as a public economist working out how a user charge should be designed if there were important problems of congestion, and even problems of financing the judicial system, and if this solution were considered optimal and feasible over the rest of policies.

⁴ However, note that setting up minimum levels according to expected benefits like in the example above is technically impossible, since that we have called objective probability cannot be objectively known ex-ante, but after a minimum revision of the case with minimum legal guarantees. In any case, the aim of the example is to show up how the minimum standards should ideally be established, and the perverse consequences of not doing so.

⁵ Vid. Santos Pastor (1989) on the effects of congestion on the judicial system.

The structure of the paper is as follows: in the next section, we discuss some aspects of the Spanish Judicial System that were stressed in a recent White Report on the Spanish Judicial System (1997); in section three, we present the model that describes the behaviour of all the agents involved in the decision to engage in litigation; next, we construct a numerical simulation of the model in order to get a clearer picture of the optimal user charge with respect to changes in key variables that affect the model⁶; finally, we present some conclusions.

2. The White Paper on Justice (1997)

Before studying the shape of an optimal user charge, we will comment certain aspects of the Spanish Judicial System. In order to do so, we will employ the Report that was done in 1997 to assess the present situation of the Administration of Justice in Spain. That Report also provides valuable data about the delays in several bodies of the administration of justice and the opinion of the people with respect to the Courts of Justice.

First, the Report offers interesting statistics about the delays that currently operate in the Spanish Judicial System (p. 255):

Table 1: Global Numbers of initial delays in the Administrative Jurisdiction during the period 1995-1996

⁶ Unfortunately, though the analytical model we think can be applied to the Spanish Judicial System, we have not been able to properly calibrate the numerical model in order it could totally replicate such System. The lack (or sometimes, enough reliability) of all the necessary information is the cause of it. However, the White Report we comment in Section 2 has permitted to us to discern some key parameters of the analytical model in order to carry out the numerical simulations.

Given that numbers, and taking a discount rate equal to 5%, each pta. claimed transformed into 0,8917 ptas. due to delays in 1995, and into 0,8900 in 1996⁷.

Second, through and extensive inquiry the Report finds out to what extent the people makes use of the Justice in order to solve conflicts (vid. pp. 366 and 367 of the Annex of the Report). In particular, when they are asked “What would you do if were in conflict with other person?”, the 60,3 % answered they would try to get a private agreement, the 13,5 % would ask for the intervention of a third person outside the Judicial System, and finally, the 23 % would use the Judicial System. Obviously, the cases that are embodied in that particulat question are civil, while the main congestion produces in the administrative arena (contencioso-administrativo). However, the percentage of the 23% sheds light on to what extent the people makes use of the Judicial System, though it does not on who particularly does it to a greater extent, i.e., big firms versus individual persons.

Third, the Report also stresses the importance of enjoying of a reliable statistical source with respect to the Judicial System (pp. 67-69):

“ A reliable statistics and not only based on quantitative issues, but also qualitative information, is the indispensable starting point (…) for any Judicial policy. Issues like the judicial personnel, the definition of personnel needs,…, the study of litigation, and so the analysis of potential legal and organisation reforms, must have their foundation on a good statistics system” (p. 67).

Unfortunately, this study will still lack such statistical foundation (Vid. footnote 6 of the paper).

Finally, among others, the Report cites the following inconveniences of the present system (pp. 315-318):

⁷ From now on, we will call “discount rate” the rate at which one pta. claimed at the present moment transforms into the future.

a) Imprecision in the share of competencies among the bodies that form the Administration of Justice.

b) Malfunctions in the management between the regional governments and the State bodies.

c) Delays and ineffectiveness.

Hence, the Report simply stresses problems of supply, since even the problem c) is according to the Report due to the multiplicity of requests and authorities within the judicial system. Given this, it is logical that the proposals of the Report focus on supply policies. For instance, they propose (pp. 318-324):

i) Simplification of requests.

ii) Competencies attribution to the regional governments.

iii) Simplification of the organic and functional bodies.

On the whole, the Report serves to us: first, to obtain valuable information to carry out the simulations, and second, makes us explicit the importance of the supply aspects that negatively affect the Judicial System. Hence, according to the Report, it is likely that the user charge by itself does not completely eliminate all the problems of administration of Justice in Spain.

3. The Model

To find out what should the optimal user charge on the decision to litigate be, we will suppose N-identical potential plaintiffs. In order to simplify notation, along all the text we will set N=1. The structure of the sequential decisions of the agent involved in the decision is the following:

1^st. The Social Planner sets up a user charge conditional on the decision of a plaintiff (P) to litigate.

. A P balances the expected costs, which include the charge, and benefits of engaging in litigation against another agent, the defendant, D. We do not allow for the possibility of private settlement between P and D, either because its costs are too high (in comparison to litigation), or simply due to not having been able to reach an agreement. If expected costs are lower than expected benefits, she engages in litigation, otherwise she does not, and the game ends at this stage.

. If according to (2) P decides to engage in litigation, she asks for representation to an advocate (A), who then decides whether to accept or not the case (as we will later show, this will not become a binding assumption in our model).

. If A does accept the case, next she has to decide the level of effort that will exert on the case on behalf of P.

Our main objective is to find out the optimal user charge that has to be imposed on the decision to litigate, given the externalities litigation generates, which we will later on properly describe, and a certain amount of income to be collected to cover judicial expenses. As usual, we have to operate backwards to solve such kind of sequential problems, and so each agent will take as given the decision of those who precede her. Therefore, we start solving the fourth stage.

3.1. Once A has accepted the case, decides what level of effort to exert.

The solution to this first problem will be trivial. The notation we will use is the following: is the probability the has of wining the case, so , which value is set according to A's beliefs, which are private information; ) K(E is the rate of transformation of that probability, which varies according to the level of effort, E , exerted by A, is the liability P claims for; α is the percentage of such liability A earns iff P wins the case; Z is the fixed amount of money A charges to P by her legal services, independently of the final result of the trial; finally, are the costs of the advocate by having represented P, which depend positively on her effort. The variables depending on E we assume have the following properties⁸:

\[\partial K / \partial E \equiv K ^ {\prime} (E) \geq 0; \quad K ^ {\prime \prime} (E) \leq 0; \quad K (0) = 1; \quad K (\infty) = K _ {m a x} \equiv \overline {{K}}; a n d K ^ {\prime} (E) = 0 \Rightarrow E \rightarrow \infty\]

\[C _ {A} ^ {\prime} (E) \geq 0; C _ {A} ^ {\prime \prime} (E) \geq 0; C _ {A} (0) = C _ {A} ^ {\min} \equiv \underline {{C}} _ {A} (\text { i.e., fixed costs }); \text { and } C ^ {\prime} (E) = 0 \Rightarrow E \rightarrow 0\]

We assume A will choose the level of effort from the following maximisation problem:

\[\begin{array}{l l} M a x & K (E). \vec {p} _ {j}. [ (\alpha . X _ {j}) + \tilde {Z} - C _ {A} (E) ] + [ 1 - (K (E). \vec {p} _ {j}) ]. [ \tilde {Z} - C _ {A} (E) ] \\ E & \end{array}\]

from the First Order Condition (FOC) with respect to E, we implicitly obtain the optimal level of effort,

\[E: \quad K ^ {\prime} (E ^ {*}). \vec {p} _ {j}. (\alpha . X _ {j}) = C _ {A} ^ {\prime} (E ^ {*}),\tag{[1]}\]

that is, at the optimum, A equalises the marginal benefit from exerting an additional unit of effort (left-hand side of the FOC) to its marginal cost (right-hand side). Hence, we have obtained the function of A's effort, which expresses as . Operating simple comparative static over that FOC, we can sign out the following derivatives:

\[\frac {d E}{d \vec {p} _ {j}} = (\alpha . X _ {j}). \left\{\frac {(K ^ {\prime}) ^ {2}}{K ^ {\prime} . C _ {A} ^ {\prime \prime} - K ^ {\prime \prime} . C _ {A} ^ {\prime}} \right\} \geq 0; \quad \frac {d E}{d (\alpha . X _ {j})} = (\vec {p} _ {j}). \left\{\frac {(K ^ {\prime}) ^ {2}}{K ^ {\prime} . C _ {A} ^ {\prime \prime} - K ^ {\prime \prime} . C _ {A} ^ {\prime}} \right\} \geq 0\]

as . The level of effort of A increases with the amount of the variable retribution, and the subjective probability of wining the case. The graph below shows the advocate’s effort at equilibrium and the direction of variations from that

⁸ For functions of a single variable, partial differentiation is indicated by a prime; for functions of several variables, total differentiation is indicated by subscripts.

equilibrium.

Note the following particular cases ("corner solutions"):

1) If , or , or both, the FOC transforms into , and (recall she has already accepted to represent legal interests).

2) If , then , so , and consequently

3.2. The Advocate decides whether to represent or not the Plaintiff.

In order to make such decision, A ponders the following inequality, given an optimal level of effort she will exert, :

\[K (E ^ {*}). \vec {p} _ {j}. (\alpha . X _ {j}) \geq W _ {0} - \bar {Z} + C _ {A} (E ^ {*})\tag{[2]}\]

is the "reservation rent" A can earn non-accepting the case. Depending on the structure of the market of advocates, these rents will be greater than, or 0 (in this latter case, the market for A's is perfectly competitive, and so does not leave to them rents). From expression [2], we find out the "critical level of probability"⁹, , beyond which A will accept the case, and viceversa,

\[\tilde {p} _ {j} = \frac {W _ {0} - \bar {Z} + C _ {A} (E ^ {*})}{\alpha . X _ {j}}, \quad \text { so } \tilde {p} _ {j} = \tilde {p} (W _ {0}, \bar {Z}, X _ {j}, \alpha)\tag{[3]}\]

From now on, we will assume that such "critical level" is non-binding, i.e., is big enough with respect to . Therefore, in the case P decides to litigate (which depends on the binding constraint we will next analyse), A will always accept the case.

3.3. The Plaintiff decides whether to litigate or not.

P's problem will be very similar to the previous one. Hence, P will find it optimal to litigate iff the following condition holds:

\[K (E ^ {*}). p _ {j}. [ \delta . (1 - \alpha). X _ {j} - \tilde {Z} - T ] - [ 1 - (K (E ^ {*}). p _ {j}) ]. [ \tilde {Z} + T ] \geq 0\tag{[4]}\]

i.e., she will litigate always in the case the expected benefits are greater than expected costs, taking as given A's effort (see section 2.1), and A's "critical level of probability" (see 2.2). δ is the inter-temporal rate of discount of the expected benefits P is claiming for, is P's subjective probability (normally, different from ), and T is a user charge conditional on accessing the Courts of Justice.

We can then state P's probability level, , beyond which it is optimal for her to litigate,

⁹ See, e.g., Polinsky and Rubinfeld (1998).

\[\check {p} _ {j} = \frac {\tilde {Z} + T}{\bar {\delta} . X _ {j} . (1 - \alpha) . K (E ^ {*})} \leq 1\tag{[5]}\]

so , as we already know is non-binding, or in other words, it is always the case that . Note that is taken as given by so the discount rate is a parameter, , though we will next see this is not the case, but depends on

Again, operating comparative static over the implicit function given by [5], we find out the following reactions of

\[\frac {d \check {p} _ {j}}{d T} = \frac {1}{X _ {j} . (1 - \alpha) . \bar {\delta} . \left\{K ^ {*} + \check {p} _ {j} . K _ {E ^ {*}} ^ {\prime} . E _ {p _ {j}} \right\}} \geq 0\tag{[6]}\]

An increase in the user charge unambiguously strengthens the conditions to find it optimal to litigate; exactly the same analytical formula applies for marginal variations in Variations in the expected net award, , that derives from litigation produces a decrease in

\[\frac {d \check {p} _ {j}}{d [ (1 - \alpha) . X _ {j} ]} = - \frac {\check {p} _ {j}}{(1 - \alpha) . X _ {j}}. \left\{\frac {K ^ {*} + (1 - \alpha) . X _ {j} . K _ {E} . E _ {(1 - \alpha) . X _ {j}} ^ {*}}{K ^ {*} + \check {p} _ {j} . K _ {E} . E _ {p _ {j}} ^ {*}} \right\} \leq 0\tag{[7]}\]

as can be checked from [1], , so ceteris paribus, induces more litigation.

The discount rate can be lessened in function of the level of litigation, so from this fact derive the "congestion costs" of the judicial system. P takes such value as given when taking her private decisions, from which follows a negative externality on the rest of plaintiffs, which depends on the level of litigation in the following way,

\[\delta = \delta [ \Omega (\check {p} _ {j}) ], s. t. \delta_ {\Omega} \leq 0\tag{[8]}\]

where , being the distribution function of potential plaintiffs over is the density function, and as we have previously said the total population of potential plaintiffs has been normalised to the unity. We assume that when the distribution of potential plaintiffs above the "critical level of probability" increases, i.e., there is more demand for litigation, there will be more congestion, and so the discount rate will be lower. Thus, . Another externality derived from the decision to litigate comes from the fact that the plaintiffs when forming such decision do not take into account the increase provoked in the marginal judicial costs either. That is, this latter type of cost depends on the total amount of plaintiffs, , such that , where C are the judicial costs.

3.4. The Social Planner sets up a user charge on litigation.

In function of all previous optimal behaviours, the Social Planner (SP) designs a user charge, in such a way that pretends to achieve a minimum amount of revenue collection, and most important, it is designed to incite P to internalise the negative effects on congestion and judicial costs her decision to engage on judicial litigation provokes.

To model such objective, we will assume the SP minimises the summation of those two types of costs, given the demand of litigation, expression [5], and an external revenue requirement, . Therefore, the SP's problem is the following:

¹⁰ That seems to us a reasonable objective function, given a positive social benefit of the judicial system itself, which we take as a parameter. In words, Pastor (1993, p. 42) attach a very similar objective to judicial policy, which would consist "... in the maximisation of the access to Justice, given an amount of resources, or in the minimisation of the social costs of the process (those derived from the judicial errors and direct costs), given a level of judicial tutelage". In a different way, Shavell (1982) defines the "socially appropriate" incentive to bring suit such that private parties take into account the legal expenses of the process, but also the potential benefit that her action derives in the reduction of the likelihood the potential defendants cause damages to the potential plaintiffs.

\[\begin{array}{c c c} \text {Min} & C (\check {p}) - \delta (\check {p}) \equiv \text {Max} & \delta (\check {p}) - C (\check {p}) \\ T & & T \\ & s. t. & T. \int_ {p _ {j}} ^ {1} f (p _ {j}). d p _ {j} \geq R \quad (\beta) \end{array}\]

which FOC expresses as follows:

\[T: \delta_ {\Omega} \Omega_ {p _ {j}}. p _ {T} ^ {j} - C _ {\Omega}. \Omega_ {p _ {j}}. p _ {T} ^ {j} + \beta . \{T. \Omega_ {p _ {j}}. p _ {T} ^ {j} + \Omega \} = 0\]

where has already been characterised in [6]. We define the "marginal social costs of litigation" , as the increase in litigation costs (congestion costs and judicial costs per se) in terms of social planner's revenue, , when the number of plaintiffs increases ¹¹, so from the FOC can show the implicit optimal user charge as:

\[T ^ {*} = \pi + \frac {\theta (\check {p} _ {j}) ^ {- 1}}{\check {p} _ {T} ^ {j}} = \pi + \frac {X _ {j} . (1 - \alpha) . \bar {\delta} . (K ^ {*} + \check {p} _ {j} . K _ {E ^ {*}} . E _ {p _ {j}} ^ {*})}{\theta (\check {p} _ {j})} \geq 0\tag{[9]}\]

once we have inserted expression [7], and is the conditional probability that the amount of plaintiffs decreases when the "critical level of probability", , marginally increases, given that up to that point there are plaintiffs. This is the so-called "hazard rate". Therefore, we can clearly check how the charge is additively composed by two parts: the first one contains the negative effects on congestion and judicial costs derived from litigation, and the second one, complies with the revenue requirement¹². In the following section, on the basis of the theoretical model, we carry out a series of numerical simulations in order to describe the Spanish Judicial System as close as

N =1. N=1

N.Ω

¹¹ Note the total number of plaintiffs is N.Ω , where in our case, in order to simplify notation, we have set

¹² Note how the shape of the optimal user charge in [9] follows the so-called Sandmo Additivity Property, Sandmo (1975). That is, the taxation of a good or service that produces negative externalities is additively composed by two parts, on the one hand, that which internalises the social damage caused by its consumption, and on the other hand, that which attempts to obtain public revenues at the least marginal cost.

possible.

4. A numerical example: Comparative static

4.1. Methodology

The numerical simulations will serve us to get a clearer idea of the how the optimal user charge, implicitly defined by [9], depends on certain variables of the model, so developing a comparative static study. To do so, we will first assume some functional forms that will relate all the variables we have previously defined. First, we assume follows an exponential distribution,

\[F \left(\check {p} _ {j}\right) = Q. \left(1 - e ^ {- p _ {j}}\right); \quad a n d \quad f \left(\check {p} _ {j}\right) = Q. e ^ {- p _ {j}}\tag{[10]}\]

where is a constant to be calibrated from the numerical example, which reflects other factors different from that can influence the decision to litigate, e.g, degree of optimism, opportunity costs of litigation, both in time terms and money terms, or any other that might affect the tendency of the population (or the individual, since recall N=1) to litigate.

According to [10], graphically represented above, even when , as long as some potential litigants will engage in litigation, while if , all the litigants will do, independently of the value of .

With respect to congestion costs, we model them in the following way:

\[\delta = \hat {\delta}. (1 - \Omega^ {2}); s. t. \partial \delta / \partial \Omega = - 2. \Omega . \hat {\delta} \leq 0, a n d (\partial (\partial \delta / \partial \Omega) / \partial \Omega) = - 2. \hat {\delta} \leq 0\tag{[11]}\]

so we assume congestion costs are increasing in the number of plaintiffs. is the base or minimum discount rate (there is an unavoidable delay due to the normal administrative process, given the structural characteristics of the judicial system), such that if , the discount rate approaches the normal one, and in the limit when (all the potential plaintiffs become real litigants) the discount rate reaches its minimum, so

The judicial costs we assume evolve according to the following formula,

\[C = F C + c. \Omega^ {2}; s. t. \partial C / \partial \Omega = 2. c. \Omega \geq 0, a n d (\partial (\partial \delta / \partial \Omega) / \partial \Omega) = 2. c \geq 0\tag{[12]}\]

FC are the judicial fixed costs, while c is the variable cost. Total costs are increasing in the amount of plaintiffs. Hence, if , there would only be fixed costs (e.g., the buildings of the courts), while if ， (recall we have normalised the number of potential plaintiffs to one). We can again range the judicial costs within a closed interval,

Finally, the private costs of the advocate, , are represented in the following way:

\[C _ {A} = F C _ {A} + c _ {A}. (E ^ {2} - 1); \text { s.t. } \partial C _ {A} / \partial E = 2. c _ {A}. E \geq 0, \text { and } (\partial (\partial C _ {A} / \partial E) / \partial E) = 2. c _ {A} \geq 0\tag{[13]}\]

Thus, , and if , null level of effort, there are not variable costs for A;

. The function that relates the efforts of A with the positive results for P of wining the trial represents as:

\[K = \log E, s. t. \partial K / \partial E = 1 / E \geq 0, a n d (\partial (\partial K / \partial E) / \partial E) = - 1 / E ^ {2} \leq 0\tag{[14]}\]

so we assume that A has to exert a minimum level of effort, , in order P has chances of wining, independently of her original probability of doing it.

4.2. Numerical Results

In the Tables attached to the end of the paper (after the appendix), we present the value of the optimal user charge, according to variations in the amount of claimed liability (X). Nevertheless, we will do so within different contexts: first, depending on the way the advocate charges her services to the plaintiff; second, depending on the value of the unitary judicial costs through third, for different values of what we have called base discount rate and finally, for different values of the unitary costs of the advocate . Given the lack of statistical information of the Spanish Judicial System (vid. footnote 6), we have calibrated a system that only partially reflects the Spanish one, with the hope that in the future it will be possible to do reflect it completely. Therefore, given the following artificial values:

\[\tilde {Z} = 1 0 0. 0 0 0 \text {ptas}; c = 4. 0 0 0 \text {ptas}; F C = 0; c _ {A} = 2. 0 0 0; \alpha = 0, 0 5; X = 1. 0 0 0. 0 0 0 \text {ptas};\]

we have set , and (according to the data presented in Section 1 of the paper), in such a way that using expression [11] we have:

\[\delta = \hat {\delta} (1 - \Omega^ {2}) = 0, 9 5. (1 - 0, 2 3 ^ {2}) = 0. 8 9 9 7 4 5\]

i.e., such value approximates very closely to the value given by the Table 1 (with a "discount rate" of 5%): each pta. claimed approximately transforms into 0.9 ptas. Given all that parameters, in the calibration we have obtained . That means that

\[\begin{array}{l l} i f & p _ {j} = 0, \quad t h e n \Omega \equiv 1 - F (p _ {j}) = 1 \\ i f & p _ {j} \geq 0. 1 6, \quad t h e n \Omega \equiv 1 - F (p _ {j}) = 0 \end{array}\]

Finally, the shadow price of public resources (the Lagrangean multiplier of the Social Planner's problem) has been set to one, . Later on, in the numerical simulations, such parameter also keeps that value, and can be shown that the results are not very sensitive to variations of

A) Optimal user charge for different methods of payment to the advocates.

In order to accommodate the fixed fee, , to the amount of liability, X, ex-ante the simulations, we have calculated the former as a parameter always equal to 10% of X, independently of the result of the trial. In Tables 3.1, 3.2 and 3.3, we present the value of the user charge with the particularity that each of them reflects a different method of payment to the advocates. In the first case (1.1), it would the “normal , the advocate charges a fixed amount and a percentage of X in case of wining the case ; in the second case (1.2), he charges only a fixed amount, so (analytically, that supposes according to the assumptions set up in section 3.1 that and , Z is a 10% higher than its normal value; and finally, in the third case (1.3), and . The next graph compares the value of the average user charge rate, , in each of the three payment systems quoted above.

That one quoted as “normal case” is the one which implies for all values of claimed liability both the greatest average user charge and greatest marginal user charge (case 1.1), being the average tax rate increasing in the claimed liability, while the other two cases, case 1.3 and case 1.2, the average user charge remains practically constant at 5,5% and 2%, respectively.

Graph 1: Average user charge rate for different methods of advocates charges

In comparison with case 1.1, the presence of a greater value of in case 1.2 "mitigates" the need of T, since both variables have the same effects on the demand of litigation (see expression [5]). In case 1.2, given that α = 0 , K=1, we have that

\[\check {p} _ {j} = \frac {Z + T}{\bar {\delta} X}; \quad T = \pi + \frac {\delta X}{\theta (\check {p} _ {j})}\]

so the “critical probability level” and the average tax rate remains practically constant along all the range of values of X. Moreover, in conjunction with what has just been stated above, the high value of provokes the low value of T, sinceθ is increasing in as we will later show.

In case 1.1, the percentage of litigants is always greater, and so are the negative externalities. Anyhow, the correct comparison to do is within each case, i.e., between the situation with and without charges given a system of payment. Thus, in both situations we can check from the Tables how the introduction of the user charge provokes an important decrease in the variable judicial costs, and at the same time an increase in the inter-temporal discount rate.

Finally, the method of payment that reflects the case 1.3 brings about high percentages of litigation, since then, for example, without user charge, P would always engage in litigation (see expression [5], for , and so A would do in accordance with our assumptions of section 3.2 that rule her behaviour. This is so since according to the method of payment "cuota litis" all the risks of litigation fall on , but as derives from our model, she will accept the case, so the great level of litigation. In spite of this fact, which points out in the direction of increasing the value of T, we can check how the second part of expression [9] points out right in the opposite direction, i.e., to a decrease in T. This latter fact is due to the lower value of the net claimed liability, , and to the lower value of the discount rate. This decrease in the net claimed liability and in with respect to case 1.1 makes the optimal user charge to be lower, despite the higher percentages of litigation for all values of X.

On the other hand, we can finally check how the shape of the average user charge is decreasing in This is partly due to the increasing "hazard rate", which recall appears in the denominator of the second part of expression [9]:

\[\frac {\partial \theta (\check {p} _ {j})}{\partial \check {p} _ {j}} = \frac {Q e ^ {- \check {p} _ {j}} (Q - 1)}{(1 - Q - Q e ^ {- \check {p} _ {j}}) ^ {2}} \geq 0; \quad \frac {\partial}{\partial \check {p} _ {j}} \left(\frac {\partial \theta (\check {p} _ {j})}{\partial \check {p} _ {j}}\right) = \frac {(Q - 1) Q e ^ {- \check {p} _ {j}} [ 1 - F (\check {p} _ {j}) ]}{[ Q - 1 + f (\check {p} _ {j}) ] ^ {3}} \geq 0\]

where the second partial derivative effectively holds for Q=6,76029. This provokes that the higher the "critical probability level", the higher the "hazard rate", and so ceteris paribus, the lower the optimal user charge. This is so since at a high "critical probability level", the marginal loss of plaintiffs due to an increase in the user charge is great, given all the litigants-contributors that have already been lost up to that point, so the "marginal cost of taxation" is higher then. This property specially applies to case 1.1, while for case 1.2 remains practically constant for all values of X, and in case 1.3 we have seen such effect compensates for the low value of claimed liability and lower discount rates for all X.

B) Optimal user charge for different values of normal discount rate, .

In this second simulation (see Tables 3.1, 4.1, 4.2, 4.3 and 4.4), the values of , are 0,95 (case 1.1), 0,8 (case 2.1), 0,6 (case 2.2), 0,3 (case 2.3) and 1 (case 2.4). The rest of values are identical to those used in the calibration. A higher “normal or base discount rate”, , can mean two very different things: either a structural inefficiency of the Judicial System, or a greater accuracy of the judicial process result, i.e. there produce less mistakes in the judicial decision. However, in our model, since the accuracy of the result is not contemplated (otherwise, it should have been included in the objective function to be maximised by the Social Planner), so we assume zero judicial errors, a higher “normal or base discount rate” has to be interpreted as higher inefficiency of the judicial process, ceteris paribus.

The effects of a variation in the base discount rate are very similar to those that would produce in front of variation in the claimed liability. However, in the former case they are not so acute, since variations in do only affect the critical level of probability of , but not A's effort, which remains constant for any value of (see expression [1]).

We can observe from the implicit expression [9] how a greater , both supposes an increase in the value of , and also an increase in the part of T that aims to collect revenues for all values of X. The reason is simple: first, a greater decreases (see expression [5]), which ceteris paribus provokes more congestion and judicial costs, so the need of a greater (through ; and second, for an increasing "hazard rate" in , we check how a greater value of also supposes a greater T in the second part of expression [9] at an increasing rate, since can be checked how the “marginal tax rate”, , is increasing, though the average tax rate is decreasing.

δˆ = δ

¹³ Recall that the plaintiff considers the discount rate as a parameter when forming the "critical probability level", so .

Then, graphically the optimal user charge evolves according to the variation of X for the different values ofδˆ in the following way:

Graph 2: Average user charge rate for different "normal" discount rates Note that in the graph . Paradoxically, our optimal user charge provokes that the more inefficient the administration of justice is, the lower the average user charge rate is for each value of X.

C) Optimal user charge for different values of unitary judicial costs, c.

In this case, we allow to vary the unitary judicial costs which enter the expression of total judicial costs in [12], and then obtain an optimal user charge in each case for the different values of X. These values of c are: 4.000 ptas (case 1.1), 8.000 ptas (case 3.1), 15.000 ptas.(case 3.2), 35.000 ptas (case 3.3). The results are shown in Tables 3.1, 5.1, 5.2 and 5.3, respectively.

As expected, if we compare all four cases from the Tables, can check how the optimal user charge is increasing in the value of the unitary judicial costs in order to internalise the externality that arises in the judicial costs. However, graphically, we can observe how in relative values with respect to X the user charge does not vary much in each one of the situations. This is provoked by the relatively small value of c in comparison with the values of X.

Graph 3: Average user charge rate for different unitary judicial costs D) Optimal user charge for different values of unitary advocate's costs,

The values of we have used for the comparative static analysis have been: 2.000 ptas. (case 1.1), 4.000 ptas. (case 4.1), 10.000 ptas. (case 4.2) and 15.000 ptas. (case 4.3), and the results are shown in Tables 3.1, 6.1, 6.2 and 6.3, respectively.

A higher value of unfailingly provokes a decrease in A's effort, as can be easily checked from total differentiation of expression [1]. Hence, this fact causes an increase in the critical level of probability, , and so less demand of litigation, and less congestion and direct judicial costs, keeping all the rest of parameters of the model constant. This forces the reduction of the optimal user charge together for all values of X.

This last comparative analysis, together with that one analysed in the series of cases 3, has simply served us to bear in mind that when setting up the user charge if we want to achieve certain objectives will have to be taken into account the context in which litigation develops.

Graph 4: Average user charge rate for different unitary advocates' costs

5. Conclusions

We end the paper with some comments, which only partially pretend to justify the introduction of the user charge, since the comments of the Introduction still apply. The "tasa judicial" was abolished in 1986, precisely when the "Value Added Tax" (VAT) was introduced in the Spanish Fiscal System. Some of those who are against the user charge, correctly argue that the VAT, which is paid by the plaintiff for the advocates' services, has occupied the space left by the user charge. According to our model, that is true, since it would add in the numerator of expression [5], through the increase of the advocates' fees. However, the tax base of the VAT are the advocate’s fees while the tax base (as we have considered it) of the user charge rate is the claimed liability. Therefore, the effective average tax rate of the VAT will always be below the simulated values of the user charge. Moreover, in most of the simulated cases, the “optimal” average user charge rate is increasing in the monetary amount of the claimed liability, while in the VAT the average tax rate is constant.

The responsibility of setting up such user charge is in hands of the regional governments (Comunidades Autónomas), which on behalf of the central government administer such public function within their territory . Given their secular lack of own financial instruments, we think the introduction of the user charge (which revenue collection in 1985 was about 6.000 millions of ptas.) would be positive from the perspective of their fiscal responsibility. However, this kind of matters have to be carefully dealt at the political level, that is, citizens shall not see the restoration of the user charge as a mere increase in the fiscal pressure, but a means to correct the potential inefficiencies and inequities of the judicial system¹⁵.

The political economy of introducing such a user charge would suppose the implementation of a tax schedule in function of the claimed liability. That is the objective parameter on which the user charge should be based on. However, if the Social Planner has information about a certain group of potential plaintiffs that has a lower inherent "critical probability level", e.g. big firms, she could decide either to apply the user charge only to that group or simply set up two different tax schedules. That is a decision of the Social Planner on the basis of her private information and social judgements.

The Table below reflects the dividends the “user charge” would offer in different settings (according to diverse cases properly described in section 4.2)¹⁶: first, the user charge lessens the externalities of litigation that produce both in the discount rate and in the unitary judicial costs; and, second, it allows the public administration to collect additional revenues. Thus, the user charge makes possible to achieve two dividends, the main one, the internalisation of the externalities that emanate from judicial litigation, and the second one, to collect additional revenues. However, we also stress a third dividend, which we have already cited in the paragraph above: the possibility of using the fiscal responsibility by the regional governments. This is a qualitative dividend, but also very important, given the claims for more revenues of the regional governments. Of course, not all the regional governments would need to establish such user charge, but would depend on their particular litigation demand, judicial costs structure and social objective function to maximise: that means fiscal responsibility.

¹⁴ Vid. López (1994), especially pp. 160-164, about the competencies the Spanish regional governments have on the administration of justice.

¹⁵ The social attitude towards increases in fiscal pressure and towards the functioning of the Spanish Judicial System is well reflected in the following statement of Alvira and García (1999), which derives from publicopinion polls: "The Administration of Justice works badly, and most of the society does not think that it needs more funding..." (p. 28). Additionally, among all the public services provided by the State "Justice" is the service with the worst qualification, and with a decreasing valuation since 1994 (vid. Table 1, p. 27).

¹⁶ The quantitative results of the introduction of the "user charge" should be taken carefully, since we have

Table 2: Main results in the demand of judicial litigation, variable judicial costs and discount rate due to the introduction of the “user charge” ( at X=6.000.000 ptas)

already said that the currently available information for Spain is limited.

6. References

1. ALVIRA, F., GARCÍA, J. (1999): "Creencias y actitudes de los contribuyentes", Cuadernos de información económica, No. 146, pp. 26-37.
2. CONSEJO GENERAL DEL PODER JUDICIAL (1997): Libro blanco de la Justicia (2 volumes, one of Annexes), Madrid.
3. LÓPEZ , J.F. (1994): Justicia y Estado Autonómico. Orden competencial y Administración de Justicia en el Estado compuesto de la Constitución Española de 1978, Ed. Civitas.
4. PASTOR, S. (1989): "Fundamentos de economía de la justicia y política judicial (I)", Economía Pública, Vol. 5, No. 4, pp. 131-69.
5. - (1993): Ah de la Justicia!. Política Judicial y Economía, Centro de Publicaciones del Ministerio de Justicia, Ed. Civitas.
6. POLINSKY, A.M., RUBINFLED, D. (1998): "Does the English Rule discourage lowprobability-of-prevailing plaintiffs?", Journal of Legal Studies, Vol. 27, pp. 519-35.
7. SANDMO, A. (1975): "Optimal Taxation in the presence of externalities", Swedish Journal of Economics, 77, pp. 86-98.
8. SHAVELL, S. (1982): "The social versus the private incentive to bring suit in a costly legal system", Journal of Legal Studies, Vol. 11, pp. 333-39.

APPENDIX:

Description of the Spanish “user charge” on judicial litigation before 1986

In fact, legally what existed before 1986 was not a user charge on judicial litigation, but an indirect tax on it (Vid. Texto Refundido de la Ley del Impuesto sobre Trasnmisiones Patrimoniales y Actos Jurídicos y Documentados, Act 3050/1980, 30^th December, Arts. No. 40 to 47). Therefore, it was a tax, so the revenue collected from it was not affected to the provision of Justice. Despite this legal fact, with respect to the economic effects on judicial litigation there is no difference between both tax figures, it is still a higher cost for the litigant. Next, we describe the main elements that shaped the tax.

Among others, the facts that caused the tax due were (arts. 51.1, 51.2):

a) Jurisdictional resolutions and arbitration awards, the writings of those related with them, and also those formalities and judicial proceedings that are carried out, and testimonies.

b) The writings addressed to the public administrations, and certificates, licences, permissions and authorisations that emanate from them.

In case a), the person or persons legally obliged to pay the tax are those interested by the resolutions or arbitration award. In case b), the person that addresses the writings, or the person to whom such writings are addressed (art. 52).

The tax base (art. 53) was normally the monetary amount of claimed liability. In penal cases, the tax base will be calculated as the summation of the fines and pecuniary sanctions to be imposed.

Finally, the tax due was calculated from the tax schedule that we present below (note we have transformed the monetary amounts that appear in the original tax schedule into 1999 prices). Then, the tax due depended both on the amount of claimed liability, and on the number of sheets of the resolution that emanates from the Judge. The tax price per sheet was increasing in the amount of claimed liability. In those cases that the claimed liability was not pecuniary each sheet implied a tax price of 82 ptas.

Table: Spanish Tax Schedule on Judicial litigation before 1986 (Act 3050/1980, Art. 54.2)

Graph : Average tax rate on judicial litigation (No. of sheets: 10)

The fact the tax price per sheet was increasing in absolute values with respect to the claimed liability did not impede the tax was regressive with respect to the amount of claimed liability (i.e., the average tax rate is decreasing), as the graph right above shows (in the graph, the average tax rate has been calculated setting the number of sheets equal to 10 independently of the monetary valuation of the claimed liability). Moreover, the average tax rates are well below to any set of simulated average tax rates according to our model. However, we stress again the aim of a tax is not the same of a user charge, so this could explain the divergence between our simulated values and those that emanate from the effective tax rates given by the tax schedule applicable before 1986¹⁷. That is, as we have said in the beginning of the paper “the qualification of the user charge (or the tax figure) as optimal is conditioned on the aims that are behind the creation of the charge” (or the tax figure), and then if the aims are not equal, the tax figures cannot be compared in terms of optimality.

¹⁷ Additionally, one could argue that the necessary number of sheets for a judicial writing depends positively on the amount of claimed liability.

Table 3_. 1 : Optimal user charges for different values of claimed liability where advocates ^' fees embody both a proportional and a fixed amount

Table 3_.2 : Optimal user charges for different values of claimed liability where advocates ^'fees are a fixed quantity

Table 4_.2 : Optimal user charges for different values of claimed liability and base discount rate = 0_, 6

Table 5_. 1 : Optimal user charges for different values of claimed liability and unitary judicial costs = 8_. 000 ptas

Table 5_.2 : Optimal user charges for different values of claimed liability and unitary judicial costs = 1 5_. 000 ptas

Table 5_.3 : Optimal user charges for different values of claimed liability and unitary judicial costs=35 000 ptas

Table 6. 1 : Optimal user charges for different values of claimed liability and unitary advocates ' costs =4. 000 ptas

Table 6_.2 : Optimal user charges for different values of claimed liability and unitary advocates ^' fees = 1 0_. 000 ptas

Table 6_.3 : Optimal user charges for different values of claimed liability and unitary advocates ^' fees = 1 5_. 000 ptas