Consider the unilateral precaution model presented in class and in CU.

SC=social cost; w=cost of each unit of precaution; x=amount of precaution I take; p(x)=probability accident happens as a function of precaution; A=constant cost associated with an accident

Let
SC = wx + p (x)A

Cooter and Ulen tell us the cost minimizing function is w= -p'(x)A

Unlike Cooter and Ulen, let's assign a real functional form to the probability function:

p (x) = 1 - √x where permissible values for x satisfy: 0 ≤ x ≤ 1.

Solve the social planner (SP) problem (minimize total social cost of an accident) to find the efficient level of precaution, x*, as a function of w and A.

Solve the victim's problem under a rule of "no liability"; define the victim's optimal level of precaution as xvNL

Solve the victim's problem under a rule of "strict liability" with perfect compensation (D = A); define the victim's optimal level of precaution as xvSL

Repeat parts 2 and 3 for the injurer (i.e., find xiNL and xiSL).

Compare your answers in 2 - 4. to the efficient level of precaution, x*, that you found in part 1.

Which liability rule induces the victim to take positive precaution? Which liability rule induces the injurer to take positive precaution? Under what circumstances should the law prescribe "no liability"? How about "strict liability"?