# The second-best due standard of care under a negligence rule

The negligence rule explored in the previous section can be improved upon, however. There is a second-best due standard of care that is not equal to x*, but which can increase welfare. Suppose that the due standard of care is increased to *x _{i} *

*>*x*. Define

*x*to be the point where

_{t}*w*(x*). This point is shown in Figure 4.3.3.

_{i}x_{i}= w_{i}x* + HAs long as the due standard is set at *x _{t} *

*<*

*x,*each firm will decide to meet the due standard

*x*to avoid liability. Thus, each firm's marginal cost rises. This creates losses, and firms exit the industry. Let

_{i}*n*(

*x*) be the number of firms in a long-run competitive equilibrium when the due standard of care is

_{{}*xi.*In the long-run competitive equilibrium, each firm continues to produce the same quantity

*q*(for the same reasons as discussed above), and we have:

Differentiating both sides with respect to *xi* yields:

Both sides are positive, and *P'**<0* , so we have *n'(*) < 0, and the number of firms in any long-run competitive equilibrium declines as *xi *rises. Now total welfare is:

and the change in welfare as the due standard changes is:

Let us examine expression (4.11) term by term. Consider the first term, —n( *xi* )qw_{i}. As the due standard of care is increased, there is a welfare cost to consumers because the market price of the good rises.

*Figure 4.3.3* The second-best negligence rule

As the due standard of care is changed and firms take more care, the marginal change in the market price is simply equal the marginal cost of care, which is:

Since the total market quantity is *Q = n* (x )q, the change in consumer welfare is:

which is the first term in the expression (4.11).

Now consider the second term. It is the derivative of *qn(Xi )H*(*X*) with respect to X_{i}. But *qn( Xi )H* (*X _{{}*) is simply the total external harm that production in this industry causes.

In other words, the change in welfare as the due standard of care rises is equal to the reduction in harm caused by production, less the change in consumer surplus from higher prices. The optimal second-best due standard will be above x* as long as *W'(X _{i}*) > 0 for some

*X*

_{i}.Notice also that if the due standard is set so that *X _{i} > X_{i},* each firm will choose

*not*to meet the high due standard of care, and will instead choose to be negligent and to minimise costs will choose the efficient level of care,

*x*x*. If this happens, firms will be found to be negligent and will have to pay damages of

_{{}=*H*(x*). But they will also behave efficiently with respect to care. Moreover, this increases marginal and average costs to the level they would be if firms faced a rule of strict liability. In other words, as the due standard is increased, a negligence rule begins to 'look like' a strict liability rule. Therefore, welfare is maximised. Thus, it is possible for negligence rules to achieve full efficiency, as long as the due standard of care is set sufficiently high.