1. (20 points] Steve is driving his truck and can choose a level of care to exert, which is denoted by m, which must be nonnegativei His cost of exerting a is given by wr. That is, Steve's marginal cost of exerting care is w. The probability pm) that he causes harm of A to someone else is given by lr + 1}. So p"(r} = lf[.r + 1]2. Suppose A = 405 and u: = 5. What is the socially optimal level of care '? With what probability is Steve in an accident? 2. (20 points :1 Kurt operates a bar at which Herb is a regular . There are steps going into the barI and these are in bad. repair and have some loose steps. Herb's balance is not the best and he often does not look where he is walking . One day Herb slips and falls , which injures the back of his head , causing harm of 9130 to him . Suppose they litigate ,and Herb claims that Kurt was negligent because his steps were in bad repair. Kurt counters that Herb was negligent by not being careful going down the steps the steps. The court nds that the optimal level of care for both Herb and Kurt was T0 each . Additionally, it finds that the actual level of care Herb used was 50, and the actual level of care Kurt exerted was 50. (a) If the court uses simple negligence , what is its ruling T {b} If the court uses comparative negligence , what is its ruling T (c) [f the court uses negligence with a defense of contributory negligence , what is its ruling '? {cl} If the court uses strict liability with a defense of contributory negli gence , what is its ruling '? 3. (20' points) 3. Kala is operating an ATV on the beach. The level of care he chooses influences whether there is an accident in which his ATV harms a sunbather. Kala's cost of exerting care of :c is given by wr. That is, Kala has a constant marginal cost of exerting care which is w. The probability of an accident is given by p(r}, which is decreasing in I, and the harm imposed on a sunbather in the event of an accident is given by A