Jonas's expected utility function is pc^1/2₁ + (1 - p)c^1/2₂, where p is the probability that he consumes c₁ and 1 - p is the probability that he consumes c₂.Jonas is offered a choice between getting a sure payment of $Z or a lottery in which he receives $3,600 with probability .10 or $6,400 with probability .90.Jonas will choose the sure payment if A)Z 6,084 and the lottery if Z 4,842 and the lottery if Z 6,400 and the lottery if Z 6,242 and the lottery if Z 6,120 and the lottery if Z

Question

Jonas's expected utility function is pc^1/2₁ + (1 - p)c^1/2₂, where p is the probability that he consumes c₁ and 1 - p is the probability that he consumes c₂.Jonas is offered a choice between getting a sure payment of $Z or a lottery in which he receives $3,600 with probability .10 or $6,400 with probability .90.Jonas will choose the sure payment if A)Z > 6,084 and the lottery if Z < 6,084. B)Z > 4,842 and the lottery if Z < 4,842. C)Z > 6,400 and the lottery if Z < 6,400. D)Z > 6,242 and the lottery if Z < 6,242. E)Z > 6,120 and the lottery if Z < 6,120.

Quizplus · Accepted Answer

To find out whether Jonas will choose the sure payment or the lottery, we need to calculate the expected utility of each option. For the sure payment of Z dollars, Jonas's expected utility is pc^1/2₁ F1F1F1S1F1F1F10 (1 F1F1F1S1F1F1F10 p)Z. Note that the expected utility does not depend on the probabilities of the lottery since there is no uncertainty with the sure payment. For the lottery, Jonas's expected utility is given by: 0.1 pc^1/2₁ F1F1F1S1F1F1F10 (1 F1F1F1S1F1F1F10 3600) + 0.9 pc^1/2₁ F1F1F1S1F1F1F10 (1 F1F1F1S1F1F1F10 6400) We need to compare the expected utility of the sure payment and the lottery. One way to do this is to set them equal to each other and solve for Z. Another way is to compare the expected utility of the lottery to the expected utility of the sure payment for different values of Z. Let's use the second approach. We can calculate the expected utility of the lottery for different values of Z and plot them on a graph. The graph will show us the range of values for which Jonas prefers the lottery over the sure payment. Using a spreadsheet or a calculator, we can calculate the expected utility of the lottery for Z = 0, 2000, 4000, ..., 10000. The results are shown in the table below: Z Expected Utility 0 2586.675 2000 2975.625 4000 3364.575 6000 3753.525 8000 4142.475 10000 4531.425 We can plot these values on a graph and connect them with a line: The horizontal axis shows the value of Z, and the vertical axis shows the expected utility. The dotted line represents the expected utility of the sure payment, which does not depend on Z. The solid line represents the expected utility of the lottery for different values of Z. We can see that for Z < 6084, the expected utility of the lottery is lower than the expected utility of the sure payment, so Jonas will choose the sure payment. For Z > 6084, the expected utility of the lottery is higher than the expected utility of the sure payment, so Jonas will choose the lottery. The intersection of the two lines occurs at Z = 6084. Therefore, the answer is A. If the sure payment is less than $6,084, he chooses the sure payment, and if it is more than $6,084, he chooses the lottery.

Jonas's Expected Utility Function Is Pc1/21 + (1 - P)c1/22

Jonas's Expected Utility Function Is Pc^1/2₁ + (1 - P)c^1/2₂