The reasonable person standard: a new perspective on the incentive effects of a tailored negligence standard

Abstract

This paper compares the effects of a uniform reasonable person standard to a due care standard that is tailored to individual capabilities. This is done in a framework in which potential injurers can invest in developing greater capability. I show that the uniform reasonable person standard may induce better or worse investment incentives, depending on whether greater capability is represented by reduced precaution costs or reduced accident costs. In so doing, I show that recent results showing that the reasonable person standard creates better investment incentives are not general, but depend on the model of injurer capacity used. I go on to show the availability of “over-tailoring” of the negligence standard as a novel form of subsidy for investment in care technology. In some circumstances, holding an injurer to a lower standard of care than would be optimal in a perfectly static world can result in a trade-off between dynamic and static efficiency that is superior to that generated by either a uniform or tailored standard of care.

Appendix

The following numerical example provides an illustration of the possibility of over-tailoring. Consider a world with only two skill levels, unskilled (α _U ) and skilled (α _S ). For unskilled and skilled injurers, respectively, let us assume that accident costs and precaution costs are as follows:

Unskilled

$$H_{U} \left( x \right) = Ae^{ - Bx}$$

(16)

$$C_{U} \left( x \right) = e^{Cx} - 1$$

(17)

Skilled

$$H_{S} \left( x \right) = SAe^{ - Bx} ,{\text{ where }}\left( {S < \, 1} \right)$$

(18)

$$C_{S} \left( x \right) = e^{Cx} - 1$$

(19)

These formulas are arbitrary, except that they have been designed to satisfy the assumptions of the Inverse Model. That is, both skilled and unskilled injurers experience the same costs of precaution, but skilled injurers generate lower expected accident costs (by a factor of S) at a given level of precaution. In addition, both types of injurers experience diminishing returns from additional precaution, and positive non-decreasing costs of taking additional precaution. The constants, at this point, are arbitrary, but A, B, and C can be thought of as representing, respectively, the expected losses if the injurer exercises no precaution, the rate at which expected accident costs decline with additional precaution, and the rate at which precaution costs increase with additional precaution.

Given these assumptions, and assuming no investment in developing skill is required to become unskilled, the social costs generated by unskilled and skilled injurers, respectively, are:

$$SC_{U} = Ae^{ - Bx} + e^{Cx} - 1$$

(20)

$$SC_{S} = SAe^{ - Bx} + e^{Cx} - 1 + g(\alpha_{S} , \theta )$$

(21)

Confronted with these social costs, a policy maker attempting to tailor the standard of care so as minimize social costs, but unable to observe g, would impose a tailored standard of care

$$x_{TU} = \frac{{\ln \left( \frac{AB}{C} \right)}}{B + C}$$

(22)

on unskilled injurers, and a tailored standard of care

$$x_{TS} = \frac{{\ln \left( \frac{ABS}{C} \right)}}{B + C}$$

(23)

on skilled injurers.

Re-arranging the equations, we find that total social costs are lower for a skilled injurer (and thus skill is desirable) when:

$$g(\alpha_{S} , \theta ) < A\left( {e^{{ - Bx_{TU} }} - Se^{{ - Bx_{S} }} } \right) + \left( {e^{{Cx_{TU} }} - e^{{Cx_{S} }} } \right)$$

(24)

where x _S is the care exercised by the skilled injurer, which may be different from x _TS .

The key question, then, is whether this inequality is ever satisfied where (1) x _S  < x _TS ; (2) the injurer would not choose to become skilled if held to a standard of x _TS ; and (3) the injurer would choose to become skilled if held to the lower standard x _S ? If so, it would be possible to set an over-tailored standard x _OT for skilled injurers that, while sub-optimal in a purely static world, leads to lower overall social costs in a world where injurers can invest in skill.

An injurer held to a standard of care x _OT will find it in her interest to become skilled when the costs of becoming skilled are less than the reduction in precaution costs she will experience as a result of being held to a lower standard of care:

$$g(\alpha_{S} , \theta ) < e^{{Cx_{TU} }} - e^{{Cx_{OT} }}$$

(25)

Solving this equation for x _OT , we obtain:

$$x_{OT} < \frac{{\ln (e^{{Cx_{TU} }} - g(\alpha_{S} , \theta ))}}{C}$$

(26)

In extremis, the injurer held to a standard of care x _OT will find it just barely in her interest to become skilled when

$$g(\alpha_{S} , \theta ) = e^{{Cx_{TU} }} - e^{{Cx_{OT} }}$$

(27)

Combining this with Eq. 24 and solving for x _OT gives

$$x_{OT} > \frac{\ln S}{B} + x_{TU}$$

(28)

Taken together, these equations establish the following conditions for over-tailoring

$$\left\{ {\begin{array}{*{20}c} {\frac{\ln S}{B} + x_{TU} < x_{OT} < \frac{{\ln (e^{{Cx_{TU} }} - g(\alpha_{S} , \theta ))}}{C}} \\ {x_{OT} < x_{TS} } \\ \end{array} } \right.$$

(29)

Whenever these conditions are satisfied, it would be possible to achieve reduced total social costs by lowering the applicable standard of care for skilled injurers below x _TS to x _OT in order to induce injurers to become skilled (see Fig. 2).

Fig. 2

This graph shows how, under the Inverse Model, an over-tailored standard of care can result in lower overall social costs. Here, the cost of becoming skilled is high enough that even tailoring the standard of care provides insufficient incentive for the injurer to become skilled. In the graph, this is shown by the fact that the costs faced by a skilled injurer held to a tailored standard, IC _S (tailored)—represented by the dotted green horizontal line—are higher than (above) the costs faced by an unskilled injurer, IC _U —represented by the solid black horizontal line. If, however, the skilled injurer is held to a standard of care between x _min (over) and x _max (over)—which are even lower than (to the left of) x _S *—the injurer will have sufficient incentive to become skilled, while still generating fewer total social costs than if he were to remain unskilled (Color figure online)

It may be useful to provide a numerical example, if it is not immediately apparent that these conditions may all be satisfied simultaneously. If, for example, we set our constants to A = $100, B = 0.1, C = 0.1, $g\left( {\alpha_{S} , \theta } \right)$ = $7, and S = 0.2 (meaning that skilled injurers cause one-fifth as many accident losses at any given level of care), we obtain the following tailored standards

$$x_{TU} = 2 3.0 3$$

$$x_{TS} = 1 4. 9 8$$

Faced with these standards, however, we can see that injurers would be better off remaining unskilled. The costs experienced by an unskilled injurer are approximately $9, while the costs experienced by a skilled injurer, including the cost of becoming skilled, are approximately $10.50 even under a tailored standard (they would be even higher, approximately $12.90, under a uniform standard). As a result of all injurers remaining unskilled, total social costs—given by Eq. 20—are approximately $19.

Equation 29, however, yields the following range of values for an “over-tailored” standard of care for skilled injurers.

$$6. 9 3< x_{OT} < 10. 9 9$$

Imposing a standard of care below x _OT  = 10.99 on skilled injurers would result in skilled injurers experiencing total costs below $9—an improvement over unskilled costs, thus giving injurers an incentive to become skilled. At the same time, skilled injurers subject to a standard x _OT  > 6.93 would still generate fewer social costs than unskilled injurers. Skilled injurers subject to a standard x _S  = 10.99, for example, would generate total social costs of only approximately $15.70, which is an improvement over the total social costs of approximately $19 generated by unskilled injurers. As the standard of care x _OT is slid down still further to 6.93, more of the benefits of skill are transferred to the skilled injurer, yielding skilled costs of only approximately $8, and social costs of approximately $17.90—higher, but still an improvement over the approximately $19 in social costs generated by unskilled injurers.