only need answer to question 7. question 6 is for reference.

6. Consider an automobile-pedestrian accident situation. Suppose that: (i) the probability of an accident is p(x) = 26, where x is the driver's speed (in miles per hour) and where the driver's maximum speed is 95 miles per hour (due to the technological limitations of his car); (ii) the damages (in dollars) to the pedestrian in the event of an accident are D(x) = 2x2; and (iii) the gross benefit (in dollars) to the driver of driving at speed x is B(x) = 100x. (a) What is the driver's efficient speed? (b) What speed will the driver choose under a rule of no liability? (c) What speed will the driver choose under a rule of strict liability? (d) What speed will the driver choose under a negligence rule with the due care standard set equal to the efficient speed? (e) Compare and contrast strict liability and negligence from the standpoints of efficiency, compensation, and administrative cost. 7. Consider again the automobile-pedestrian accident situation in problem 6. Suppose now that the pedestrian can reduce the probability of an accident by 36 percent if she stops and looks both ways before crossing the street, but that the delay would cost her the equivalent of $500. (a) Show that it is efficient for the pedestrian to stop and look both ways before crossing the street. (b) What now is the driver's efficient speed? Is this higher or lower than your answer to problem 6(a)? Why? (c) Under which liability rules will the driver and the pedestrian both take efficient care