Celia chooses how much care, x ∈ [0,1], to take in programming her robot. This effort costs her x^2/2. Nature chooses whether the robot steps on Peter’s pet salamander, leading to emotional harm to Peter of H > 0 (with probability 1 - x). If
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Consider the following steps
- Celia chooses how much care, x ∈ [0,1], to take in programming her robot. This effort costs her x^2/2.
- Nature chooses whether the robot steps on Peter’s pet salamander, leading to emotional harm to Peter of H > 0 (with probability 1 - x). If the robot does step on the salamander then there is a chance of π that Celia will be identified as the culprit.
- If there is no accident (the salamander is not stepped on), then Celia’s payoff is V - x^2/2. Peter and Luke both get zero.
- If there is an accident, but Celia is identified as the culprit, then Celia gets V - x^2/2. Peter gets -H. Luke gets zero.
- If there is an accident, and Celia is identified as the culprit, then Like (the judge) decides a level of compensation D ∈ R+ for Celia to pay Peter. Celia gets V - x^2/2 - D. Peter gets D - H. Luke gets −(βH - D)^2.
f) Now we turn to social otimality rather than equilibrium. Consider the value judgement that the optimal level of care is the one that maximises the expected sum of Celia's and Peter's payoffs. According to this approach, we can ignore Luke's payoffs (as well as any payoff to the salamander or the robot) when considering social optimality. Write down this expected sum.
g) Take a first-order condition with respect to x. Find an expression for the socially optimal level of x, according to the value judgement we made in question (f).
Step by step
Solved in 3 steps
- Consider the following steps Celia chooses how much care, x ∈ [0,1], to take in programming her robot. This effort costs her x^2/2. Nature chooses whether the robot steps on Peter’s pet salamander, leading to emotional harm to Peter of H > 0 (with probability 1 - x). If the robot does step on the salamander then there is a chance of π that Celia will be identified as the culprit. If there is no accident (the salamander is not stepped on), then Celia’s payoff is V - x^2/2. Peter and Luke both get zero. If there is an accident, but Celia is identified as the culprit, then Celia gets V - x^2/2. Peter gets -H. Luke gets zero. If there is an accident, and Celia is identified as the culprit, then Like (the judge) decides a level of compensation D ∈ R+ for Celia to pay Peter. Celia gets V - x^2/2 - D. Peter gets D - H. Luke gets −(βH - D)^2. b) Write down Celia's expected payoff when she chooses x in step 1.Consider the following steps Celia chooses how much care, x ∈ [0,1], to take in programming her robot. This effort costs her x^2/2. Nature chooses whether the robot steps on Peter’s pet salamander, leading to emotional harm to Peter of H > 0 (with probability 1 - x). If the robot does step on the salamander then there is a chance of π that Celia will be identified as the culprit. If there is no accident (the salamander is not stepped on), then Celia’s payoff is V - x^2/2. Peter and Luke both get zero. If there is an accident, but Celia is identified as the culprit, then Celia gets V - x^2/2. Peter gets -H. Luke gets zero. If there is an accident, and Celia is identified as the culprit, then Like (the judge) decides a level of compensation D ∈ R+ for Celia to pay Peter. Celia gets V - x^2/2 - D. Peter gets D - H. Luke gets −(βH - D)^2. A) Draw a game tree to represent this model.#3. Hannah gets 50 utils from visiting her family for Thanksgiving. But there is a 1% chance that she will get the coronavirus from them. If she gets the coronavirus, her utility is -6000 utils. Her total utility would be -5950 (i.e. 50 – 6000). She gets 0 utils from staying healthy (total utility = 50 + 0 = 50). If Hannah doesn't visit her family for Thanksgiving, then she gets -25 utils from eating turkey cold cuts alone in front of the TV. In that case, there is no risk of getting sick. What will Hannah do? a. Visit her family for Thanksgiving b. Not visit her family for Thanksgiving c. Visit her family if she is risk-loving, not visit if she is risk-averse d. Visit her family if she is risk-averse, not visit if she is risk-loving
- Consider the following steps Celia chooses how much care, x ∈ [0,1], to take in programming her robot. This effort costs her x^2/2. Nature chooses whether the robot steps on Peter’s pet salamander, leading to emotional harm to Peter of H > 0 (with probability 1 - x). If the robot does step on the salamander then there is a chance of π that Celia will be identified as the culprit. If there is no accident (the salamander is not stepped on), then Celia’s payoff is V - x^2/2. Peter and Luke both get zero. If there is an accident, but Celia is identified as the culprit, then Celia gets V - x^2/2. Peter gets -H. Luke gets zero. If there is an accident, and Celia is identified as the culprit, then Like (the judge) decides a level of compensation D ∈ R+ for Celia to pay Peter. Celia gets V - x^2/2 - D. Peter gets D - H. Luke gets −(βH - D)^2. h) What would β have to equal, in order for Celia to choose the socially optimal level of x in a Subgame Perfect Equilibrium ?…#3. Hannah gets 50 utils from visiting her family for Thanksgiving. But there is a 1% chance that she will get the coronavirus from them. If she gets the coronavirus, her utility is -6000 utils. Her total utility would be -5950 (i.e. 50 – 6000). She gets 0 utils from staying healthy (total utility = 50 + 0 = 50). If Hannah doesn't visit her family for Thanksgiving, then she gets -25 utils from eating turkey cold cuts alone in front of the TV. In that case, there is no risk of getting sick. What will Hannah do?Cost-Benefit Analysis Suppose you can take one of two summer jobs. In the first job as a flight attendant, with a salary of $5,000, you estimate the probability you will die is 1 in 40,000. Alternatively, you could drive a truck transporting hazardous materials, which pays $12,000 and for which the probability of death is 1 in 10,000. Suppose that you're indifferent between the two jobs except for the pay and the chance of death. If you choose the job as a flight attendant, what does this say about the value you place on your life?
- A driver's wealth $100,000 includes a car of $20,000. To install a car alarm costs the driver $1,750. The probability that the car is stolen is 0.2 when the car does not have an alarm and 0.1 when the car does have an alarm. Assume the driver's von Neumann-Morgenstern utility function is U(W) = ln(W). Suppose the driver is deciding between the following three options: (a) purchase no car insurance, do not install car alarm; (b) purchase fair insurance to replace the car, do not install car alarm; and (c) purchase no car insurance, install car alarm. Of these three options, the driver prefers: A. option (a). B. option (b). C. option (c). D. options (a) and (b). E. options (a) and (c). F. options (b) and (c). G. all options equally. H. none of these options.Chicken Little is risk-neutral, but is concerned about the sky falling. She believes that there is a 20% chance of this happening. If it does, her egg collection (valued at $320,000) will be crushed. A backyard bunker salesman offers to sell her a disaster shelter, installed, for only $70,000. Given Chicken Little's beliefs, should she buy the shelter?Assume that there are two parties, I and V. I engages in an activity that tends to injure V. V and I both can take care to reduce the expected harm from accidents. Specifically, suppose that if I takes no care (i.e., spends $0 on accident precautions), expected injury to V is $250. If I spends $40 on accident precautions, however, the expected injury to V is reduced to $175. Further suppose that V has a choice between taking no care or spending $50 in care to avoid accidents. If V spends $50 in care, V’s expected harm falls by $20 regardless of the level of care that I takes. Assume that courts adopt the socially‐optimal level of injurer care as the negligence standard. That is, if I takes less than the socially‐optimal level of care, she will be found negligent and must pay for all damages to V. If I takes at least the socially optimal level of care, she will not have to compensate V for his damages. 1. Under a negligence standard, what is I’s dominant strategy? a) I does not have a…
- Assume that there are two parties, I and V. I engages in an activity that tends to injure V. V and I both can take care to reduce the expected harm from accidents. Specifically, suppose that if I takes no care (i.e., spends $0 on accident precautions), expected injury to V is $25. If I spends $5 on accident precautions, however, the expected injury to V is reduced to $18. Further suppose that V has a choice between taking no care or spending $4 in care to avoid accidents. If V spends $4 in care, V’s expected harm falls by $2 regardless of the level of care that I takes. Assume that courts adopt the socially-optimal level of injurer care as the negligence standard. That is, if I takes less than the socially-optimal level of care, she will be found negligent and must pay for all damages to V. If I takes at least the socially optimal level of care, she will not have to compensate V for his damages. What is the Nash equilibrium of this game under a rule of no liability? Question…Consider a worker whose utility is equal to the amount of dollars she has (U = $) and who can earn $100 a day as a bank teller. However, she takes a job as a worker in a firm that produces shirts. She and her coworkers are monitored at random by their employer to see if they are exerting a target level of effort of e* = 15 units. Assume that the probability of any worker being monitored is p. Also assume that e* is the same level of effort the worker would have to exert as a bank teller. If she is monitored and her employer finds that she is exerting at least 15 units of effort, she is paid > $100. If she is caught putting in less than 15 units of effort, she is fired on the spot but given severance pay of w < w. Say that she suffers a disutility of effort of $2, in monetary terms, for every unit of effort she exerts, so that the dollar cost of exerting the target level of effort of e* is - 2e*. (If she chooses to exert a lower level of effort than e*, we can assume that she will not…You are considering two options for your next family vacation. You can visit Disney World or Chicago. Your utility from Disney World is 100 if the weather is clear, and 0 if it rains. Chicago is worth a utility of 70 if the weather is clear and a utility of 40 if the weather is rainy. Also assume that the chance of rain at Disney World is going to be 50% and the chance of rain in Chicago is 40%. As a utility maximizer, should you plan to go to Disney World or Chicago? (Explain using relevant equations)