A negligence rule or due standard of care
Under a negligence rule, the court sets a level of care zt > 0, which is also called a due standard of care. If the injurer takes a level of care xt which exceeds the due standard, then he is not liable for any damage to
Figure 4.2.2 The injurer's care level under a no liability rule
Figure 4.2.3 Injurer care under a strict liability rule
the victim, and his only cost is that which he incurred in taking care. On the other hand, if the injurer fails to meet the due standard (i.e. if xt < z), then he is liable for all of the victim's damages, in addition to the cost of the care he undertook.
Therefore, the injurer's expected cost function under a negligence rule is:
The injurer, once again, chooses the level of care that minimises his expected cost. In the diagram below, the choice of the due standard z-t induces the injurer to take exactly an amount of care that is equal to z, since this is where the injurer's expected cost under this particular negligence rule is the lowest. This outcome need not always occur under this legal rule.
Suppose that the court knew the benefit and cost functions of the two parties, and that it knew the efficient level of care x* which we found earlier. Suppose that the court set the due standard of care zi equal to the efficient level of care x*. Then, substituting this into the injurer's cost function that we derived earlier, we have the injurer's new expected cost function under this particular negligence rule:
The injurer's cost function when the due standard is set at z, = x* is shown in Figure 4.2.4.
As the diagram illustrates, with the due standard set at x*, the injur- er's expected cost function is minimised by choosing x*, the efficient level of care. This gives us a second important result: in the unilateral care model, a negligence rule which sets the due standard at zt = x* is
Figure 4.2.4 The injurer's expected cost function under a negligence rule
efficient. There are other efficient negligence rules as well (for example, suppose that the due standard is set at z-t > x* for sufficiently high Z. This also results in efficient behaviour in the unilateral care model).