5.3 Welfare Analysis
5.3.3 Information Costs
The preceding analysis does not consider administrative costs, in particular, information costs to the court, the litigants and their lawyers. Consideration of information costs offers guidance regarding which one of the triples of gain-, cost- and harm-allocation rules should be implemented in a given class of cases.131 This subsection offers an
131Consideration of administrative costs other than information costs also may shed light on which triple(s)
of allocation rules should be implemented in a given class of cases. For instance, Kaplow and Shavell (1996), Dari-Mattiacci (2005), and Shavell (2007a) (at pp. 79-83, 115-18, 131-32) have explored how error costs in respect of the determination of tort liability or the assessment of compensatory damages affect incentives to take precautions. To focus on analyzing information costs, this subsection ignores the other administrative costs; hence the present arguments rise no higher than suggesting that differences in information costsaffect,
intuitive analysis to reveal that, even though many triples of allocation rules satisfy the Externalities-Optimization Principle, they typically do not generate the same information costs. The objective is to ascertain the different kinds of information that may be required to implement various triples of allocation rules; how such information is obtained is beyond the present scope. To this end, assume that any required information is available at a cost, which cost may be prohibitively high. However, if such cost is incurred, then the required information is obtained with certainty.
To consider the interesting cases first, assume the socially optimal activity level is positive (x∗ > 0). This subsection will conclude with dropping that assumption.
Let a functionL(δ, γ, λ)describe the actor’sliabilityunder an arbitrary triple of gain-,
cost- and harm-allocation rules(δ, γ, λ):
L(δ, γ, λ)=δG(x) −γC(x)+λH(x), (68)
where the actor’s choice xdepends on(δ, γ, λ)via her first order condition (60).
Equation (68) reveals what a judge (or a social planner) would need to know if she were to set the actor’s liability L(δ, γ, λ)in order to generate socially optimal incentives.
Choosing a triple of allocation rules in accordance with the Externalities-Optimization Principle is sufficient and necessary for social optimality (see Proposition 11) whenx∗ >0.
For instance, equation (68) reveals that, to implement the externalities-internalization triple
(δ, γ, λ)=(0,0,1), the judge would setL(0,0,1)=H(x). Hence, she would need to know
enough about the valueH(x); thus the information costs of ascertainingH(x)arise.
The judge would need different information if she were to implement an optimal gain-allocation rule without shifting any of the victim’s harm to the actor and any of the actor’s cost to the victim. Formally, the judge chooses a triple of allocation rules
(δ, γ, λ)=(δ∗,0,0)such thatδ∗satisfies condition (66) in Corollary 28, which is a special
case of the Externalities-Optimization Principle. Equation (68) reveals the judge would set the actor’s liability to L(δ∗,0,0)= δ∗
G(x). The actor’s utility-maximizing choice x
depends onδ∗, which is an intermediate value (see Corollary 28) that potentially depends
on how functionsG,H orC change at the margin when her action changes; howC,C or Hchanges at the margin may be relevant because it may affect xthrough the actor’s first
rather than conclusively determine, which triple(s) of allocation rules should be applied to a given class of cases. Alternatively, consideration of information costs would be paramount if one were to interpret the present arguments as premised on an assumption that, when applied to the relevant class of cases, one triple of allocation rules(δ1, γ1, λ1)generates greater information costs than another triple(δ2, γ2, λ2)does if and
Allocation rules The actor’s liability Information required (0,0,1) H(x) H(x) (δ∗,0,0) δ∗G(x) G(x), givenδ∗ ∈ (0,1) maybe G0(x),C0(x), H0(x) (δ∗∗, γ∗∗, λ∗∗) δ∗∗G(x) −γ∗∗C(x) H(x),C(x),G(x), givenδ∗∗, γ∗∗, λ∗∗ ∈ (0,1) +λ∗∗ H(x) maybeG0(x),C0(x), H0(x)
Table 1: The information costs of implementing three different triples of gain-, cost- and harm-allocation rules that satisfy the Externalities-Optimization Principle.
order condition (60). In other words, the judge would need to know enough aboutG(x),
and she might need to know enough aboutG0(x),C0(x)orH0(x). Thus the information
costs of ascertaining these values arise.
Moreover, different information costs may arise if the judge were to choose a triple of intermediate allocation rules, (δ∗∗, γ∗∗, λ∗∗)withδ∗∗, γ∗∗, λ∗∗ ∈ (0,1), in accordance with
the Externalities-Optimization Principle. In this case, the judge would need to know the values G(x), C(x) and H(x), and she might need to know how functions G, H or C
change at the margin.132 Thus implementing (δ∗∗, γ∗∗, λ∗∗)gives rise to the information
costs of ascertaining these values.
As Table 1 summarizes, the externalities-internalization triple (0,0,1) typically im-
poses smaller information costs than the triple of intermediate allocation rules,(δ∗∗, γ∗∗, λ∗∗);
both triples generate the information costs of ascertaining the valueH(x), but(δ∗∗, γ∗∗, λ∗∗)
also generates the information costs of ascertaining G(x) and C(x), and potentially
G0(x), H0(x),C0(x). For similar reasons, the triple(δ∗∗, γ∗∗, λ∗∗)may generate greater
information costs than the triple(δ∗,0,0)does. Moreover, whether information costs are
greater under(0,0,1)or(δ∗,0,0)depends on whether it is more costly to ascertain
H(x);
orG(x)and, potentially,G0(x),C0(x)orH0(x).133 Thus the main advantage of choosing
the externalites-internalizing triple(0,0,1)over the other externalities-optimizing triples
is the avoidance of the information costs of ascertaining marginal changes in the gain, harm or cost functions.
To conclude the present discussion of information costs, consider the possibility that it is socially optimal to take zero action (x∗= 0). Proposition 12 reveals that the court would
not need to induce social optimality by optimizing net externalities,if it already knew the
132To see that implementing (δ∗∗, γ∗∗, λ∗∗) may not require knowledge of G0(x), C0(x) and H0(x),
suppose the judge effectuates socially-optimal restitution of net gain in accordance with Corollary 27. Condition (65) in Corollary 27 doesnotdepend on these derivatives, and any triple of allocation rules that
satisfies this condition only generates the information costs of ascertainingG(x),C(x)andH(x).
133Notice that ascertaining the level of functionHevaluated at x— that is,H(x)— is not the same
socially optimal action is zero. With that knowledge, the court to deter a positive action could apply to the actor any triple of onerous allocation rules that typically generates small information costs. For example, the court could apply δ = 1, γ = 0, and an arbitrary λ. However, unless the case is obvious or complete internalization of externalities is
attainable (λ=1), the court would need to consider marginal changes in the gain, cost and
harm functions in order to determine whether social optimality requires zero or positive action in the first place (see equation (58) and condition 61). In other words, unless the case is obvious or complete internalization is attainable, the court to ascertain what social optimality requires would have already generated information costs that are similar to those arising from implementing optimal intermediate liabilities. Thus the preceding analysis of information costs continues to apply to cases where it is not obvious whether social optimality requires zero or positive action.