# Other legal rules in the bilateral care model

So far in our analysis of the bilateral care model, we have considered three rules: no liability, strict liability and a negligence rule that set the due standard of care for the injurer at the efficient level of care, *z =* x*. Let us now consider three other institutional arrangements.

## Strict liability with a defence of contributory negligence

The defence of *contributory negligence* allows the injurer to avoid liability (even if he failed to take any care) *as long as the victim fails to meet some due standard of care.* In other words, the rule is now that the injurer is liable for all damages, but only if the victim met a due standard of care (which the court must choose). Therefore, in contrast to the rule of strict liability that we studied in the previous lecture, there is no longer a guarantee that the victim will recover damages.

We will show that if the court sets the victims due standard at the efficient level x*, then the injurer's best response is to choose *x* = x*. Conversely, since the injurer chooses x*, the victim's best response is to choose x*. Hence, the rule of strict liability with a defence of contributory negligence that is set at x*, induces efficient behaviour.

To see this, suppose that the injurer chooses a level of *x =* x*. Then, if the due standard is set at x*, the victim's costs will be:

The victim's choice problem is therefore similar to the injurer's choice problem under a simple negligence rule in which *z =* x*. We know that the solution to this problem is x*. Thus, the victim's best response to x* under this legal rule is x*.

Now, consider the injurer's choice problem. In general, if the court sets the due standard for the victim at z_{v}, the injurer's costs will be:

Now, suppose that the court sets the due standard for the victim at the efficient level, and suppose that the victim chooses *x _{v} = x* .* Since the victim is taking adequate care, the injurer will be liable for damages. Therefore, the injurer's choice problem is:

The solution to this problem by the injurer is x*, the efficient level of care. Thus, in a non-market setting, x* is a best response to x*, and x* is a best response to x*. This means that (x*, x*) is a Nash equilibrium when the rule is strict liability with a defence of contributory negligence (and assuming that the court has chosen the appropriate due standard). Therefore, in the bilateral care model, a rule of strict liability with a defence of contributory negligence in which is efficient.

How does this rule operate in a market setting? Consider the model developed in section 5.4, where we assume that the marginal costs of care are identical in each industry and are equal to w. Suppose that firms in industry *i* take the efficient level of care, and that industry production is Q_{i}. Then, the profits of firms in industry *v* will be:

Firms in industry *v* can avoid liability by choosing the efficient level of care. Since they no longer face the full marginal social costs of their actions, there will be excessive production of good v. Similarly, since Q_{v} > Q*, firms in industry *i* now face excessively high marginal costs, and will produce too little. Again, the legal rule of strict liability with a defence of contributory negligence does not produce efficient outcomes.