Litigation with a Variable Cost of Trial

Amy Farmer; Paul Pecorino

doi:10.1515/rle-2015-0004

Article

Litigation with a Variable Cost of Trial

Amy Farmer and Paul Pecorino

Published/Copyright: May 21, 2015

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From the journal Review of Law & Economics Volume 12 Issue 2

Abstract

We develop a model of pretrial bargaining under asymmetric information where both the plaintiff and the defendant’s cost of proceeding to trial is an increasing function of the judgment at trial. This contrasts with the standard assumption that costs at trial are a constant. As a result of this assumption, fee shifting can affect the incidence of trial in a model in which it would otherwise have no effect. Fee shifting will increase the incidence of trial if the plaintiff expects to shift the variable costs of trial to the defendant on net and will lower the incidence of trial if the defendant expects to shift these costs to the plaintiff. The model also implies that a reallocation of the variable costs of trial from the defendant to the plaintiff will lower the incidence of trial.

Keywords: pretrial bargaining; asymmetric information; trail costs

Appendix

Consider a generalized model where the cost of a trial varies positively with the judgment, but is not restricted to vary linearly. The more general cost functions become

[23]CD=θD0+wDg(J),

[24]CP=θP0+wPg(J),

where g′(J) > 0 and g″(J) ≤ 0 and w_D, w_P > 0. When g″(J) = 0, we have the linear case analyzed in Section 2. The w coefficients will be varied as part of our comparative statics exercise. Making use of eqs [23] and [24], we write the expected payoff at trial for a type J plaintiff as follows:

[25]EPTrial(J)=pJ−g(J)[(1−pz0)wP+(1−p)z0wD]−((1−pz0)θP0+(1−p)z0θD0)

If g(J) =J and we replace the w_i with θi1, then eq. [25] will reduce to eq. [3]. As before, the borderline type J* is solved from OD=EPTrial(J∗). All plaintiffs of type J ≤ J* will accept the offer O_D and all plaintiffs J > J* will reject the offer and proceed to trial.

The expected cost for the defendant at trial against a plaintiff of type J is

[26]EDTrial(J)=pJ+g(J)(pz0wP+[1−(1−p)z0]wD)+pz0θP0+[1−(1−p)z0]θD0

where substitutions for C_D and C_P have been made from eqs [23] and [24]. The defendant’s problem is to choose the offer O_D in order to maximize the following:

[27] −(ODF(J*)+(1−F(J*))[pz0θP0+(1−z0(1−p)θD0)]+∫J*J¯[pJ+g(J)(pz0wP+[1−(1−p)z0]wD)]f(J)dJ).

Note that J* is a function of the offer O_D via eq. [25]. The first- and second-order conditions from the maximization of eq. [27] may be expressed as

[28]f(J*)(g(J*)[wP+wD]+θP0+θD0)=F(J*)(p−wPg'(J*)+z0g'(J*)[pwP−(1−p)wD])

[29]f(J*)(p−g'(J*)[2wP+wD]+z0g'(J*)[pwP−(1−p)wD])−f'(J*)(g(J*)[wP+wD]+θP0+θD0)−F(J*)g''(J*)(1−pz0)wP+(1−p)z0wD)≡Δ'>0

The equilibrium cutoff type J* is obtained from eq. [28], while eq. [29] may be used to sign the comparative statics. Compared with eq. [6], in eq. [28], g(J∗)wP+wD replaces J∗[θP1+θD1] on the left-hand side, while p−wPg′(J∗)+ z0g′(J∗)[pwP − (1−p)wD] replaces p−θP1+z0[pθP1−(1−p)θD1] on the right-hand side. If we assume that g(J) is linear, eqs [28] and [29] will reduce to eqs [6] and [7].

Consider the effect of an increase in the use of fee shifting:

[30]dJ∗dz0=F(J∗)g′(J∗)[1−p]wD−pwPΔ′

The sign of [30] depends upon the sign of [1−p]wD−pwP. If this term is positive, the defendant is shifting fees onto the plaintiff in expected value terms, and increased use of fee shifting lowers the incidence of trial. If [1−p]wD−pwP<0 then the plaintiff is shifting fees onto the defendant in expected value terms, and increased use of fee shifting results in a higher incidence of trial. Thus, the analog to Result 1 holds.

If we set z₀= 0, we obtain the following comparative statics, which are the analogs to eqs [12a–d]:

[31]dJ∗dθD0=dJ∗dθP0=f(J∗)Δ′>0

[32]dJ∗dwD=f(J∗)g(J∗)Δ′>0

[33]dJ∗dwP=f(J∗)g(J∗)+F(J∗)g′(J∗)Δ′>0

[34]dJ*dwP|dwD=−dwP=F(J*)g′(J*)Δ>0

In eq. [34], it is shown that if w_P is increased while w_D is decreased by the same amount, the borderline type will increase and fewer cases will proceed to trial. This is the analog to Result 2.

Acknowledgment

We would like to thank two anonymous referees and participants at the 2013 American Law and Economics Association Meeting for providing helpful comment on the paper.

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Published Online: 2015-5-21

Published in Print: 2016-7-1

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https://doi.org/10.1515/rle-2015-0004

Keywords for this article

pretrial bargaining; asymmetric information; trail costs