8. Consider the following social problem.5 A pedestrian is hit by a car and lies injured on the road. There are n people in the vicinity of the accident. The injured pedestrian requires immediate medical attention, which will be forthcoming if at least one of the 7.! people calls for help. Simultaneously and independently, each of the n bystanders decides whether or not to call for help (by dialing 911 on a cell phone or pay phone). Each bystander ob- tains 1) units of utility if someone (anyone) calls for help. Those who call for help pay a personal cost of c. That is, if person 13 calls for help, then he ob- tains the payoff 'v c; if person i does not call but at least one other person calls, then person i gets '0; nally, if none of the n people calls for help, then person iobtains zero. Assume 'U > c. 4. Reconsider the pedestrian-injury example of Exercise 8 in Chapter 11. Sup- pose you are a prominent legal expert. The government has asked for your Exercises 1 69 advice on a proposed law specifying punishment of bystanders who fail to call for help. If the law is enforced, then with some probability a \"do noth- ing\" bystander will be forced to pay a ne. (a) In words, explain how this law changes the game played between the bystanders. If you can, sketch and solve a version of the model incorpo- rating the ne and the probability that a bystander is prosecuted. (b) Compare the following two rules: (1) a bystander can be prosecuted if he or she fails to call, regardless of whether another person calls; and (2) a bystander can be prosecuted for not calling only if no one else calls (in which case the pedestrian's injury is not treated, resulting in lifelong health problems). (c) What kind of bystander law would you recommend? Explain your crite- rion (efciency?)