providin The president of a firm in a highly competitive industry believes that
ID: 3735012 • Letter: P
Question
providin The president of a firm in a highly competitive industry believes that an employee of the company is confidential information to the competition. She is 90 percent certain that this informer is the treasu the firm, whose contacts have been extremely valuable in obtaining financing for the company. If she e him and he is the informer, the company gains $100000. If he is fired but is not the informer, the co loses his expertise and still has an informer on the staff, for a net loss to the company of $500000 president does not fire the treasurer, the company loses $300000 whether or not he is the informer in either case the informer is still with the company ny is providing urer of 18.22 If the informer, since Before deciding the fate of the treasurer, the president could order lie detector tests. To avoid possible lawsuits, such tests would have to be administered to all company employees, at a total cost of $30000 Another problem is that lie detector tests are not definitive. If a person is lying, the test will reveal it 90 percent of the time: but if a person is not lying, the test will indicate it only 70 percent of the time. What actions should the president take?Explanation / Answer
r the largest loss and largest gain he can imagine. He answers with the values $200,000 and $300,000, so she assigns utility values U(200,000) = 0 and U(300,000) = 1 as anchors for the utility function. Now she presents John with the choice between two options: Option 1: Obtain a payoff of z (really a loss if z is negative). Option 2: Obtain a loss of $200,000 or a payoff of $300,000, depending on the flip of a fair coin. Susan reminds John that the EMV of option 2 is $50,000 (halfway between $200,000 and $300,000). He realizes this, but because he is quite risk averse, he would far rather have $50,000 for certain than take the gamble in option 2. Therefore, the indifference value of z must be less than $50,000. Susan then poses several values of z to John. Would he rather have $10,000 for sure or take option 2? He says he’d rather take the $10,000. Would he rather pay $5000 for sure or take the gamble in option 2? (This is like an insurance premium.) He says he’d rather take option 2. By this time, we know the indifference value of z must be less than $10,000 and greater than $5000. With a few more questions of this type, John finally decides on z = $5000 as his indifference value. He is indifferent between obtaining $5000 for sure and taking the gamble in option 2. We can substitute these values into equation
U(5000) = 0.5U(200,000) + 0.5U(300,000) = 0.5(0) + 0.5(1) = 0.5
Note that John is giving up $45,000 in EMV because of his risk aversion. The EMV of the gamble in option 2 is $50,000, and he is willing to accept a sure $5000 in its place. The process would then continue. For example, since she now knows U(5000) and U(300,000), Susan could ask John to choose between these options: Option 1: Obtain a payoff of z. Option 2: Obtain a payoff of $5000 or a payoff of $300,000, depending on the flip of a fair coin. If John decides that his indifference value is now z = $130,000, then with equation (10.3) we know that U(130,000) = 0.5U(5000) + 0.5U(300,000) = 0.5(0.5) + 0.5(1) = 0.75 Note that John is now giving up $22,500 in EMV because the EMV of the gamble in option 2 is $152,500. By continuing in this manner, Susan can help John assess enough utility values to approximate a continuous utility curve.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.