The unilateral care model
Suppose that only one party - the injurer - is undertaking some potentially harmful activity and that the level of care in order to prevent harm to others can be described by a positive number xi > 0. Assume that the party who may be harmed (the victim) cannot take their own precautions to avoid damage. This is known as the unilateral care model, because only one party can affect the probability of an accident occurring and the harm that can occur.
The probability of harm that is associated with the injurer's level of care xt is:
It is natural to assume that the higher the level of care taken, the lower will be the chance that the injurer will harm the victim. Therefore, we will assume that:
It is also natural to assume, as with most economic technologies, that there are diminishing marginal returns to care: as more care is taken the marginal reduction in care is positive but gets smaller and smaller. Therefore, we will assume that:
The probability of harm function is therefore downward sloping and convex. Should an accident occur, we will assume that the victim suffers damages or harm with monetary value h > 0. We will assume that both parties are risk neutral. Thus, the expected damage to a victim, given a level of care equal to xi is taken by the injurer, is:
In our economic analysis of accident law, we will call p (xt) h the expected damage or expected harm function. It could also be the case that the level of damages itself depends on the level of care taken by the injurer, so we could write
Then, the expected damage function would be:
If we let:
with H' (xi) ее dH(Xil < 0 and H" (xi) e= dH(x) > 0, then this encom- dxi dxp
passes both cases in (4.1) and (4.2).