Legal rules in the unilateral care model
Now let us consider three different legal arrangements in the unilateral care model.
Under a no liability rule, the injurer is never responsible for any damage caused to the victim, and is never obligated to pay any damages. Then, letting Wj > 0 denote the dollar cost of a unit of care the injurer solves:
The solution is xNL = 0. That is, the injurer takes no care at all, which is inefficient. This is shown in Figure 4.2.2. The no liability rule creates very poor incentives for taking care, and results in an inefficiently low level of care.
Under strict liability, an injurer is obligated to pay all of the victim's damages, irrespective of the amount of care that is taken. Thus, the injurer chooses the level of care that minimises his expected cost of care, which under a strict liability rule is the sum of the cost of care, plus any expected damages to the victim. That is, the injurer solves:
The solution to this problem, x*L, must obey the first-order condition:
This solution is shown in Figure 4.2.3, where total costs rather than marginal costs are shown.
In the unilateral care model, a strict liability rule causes the injurer to internalise the probabilistic externality and take the efficient level of care. Note from the first-order condition for the efficient level of care, and the diagrams above, that this is exactly the same first order condition as we derived for the rule of strict liability.