Use the following to answer question:
-(Table: Income and Utility for Tyler)Use Table: Income and Utility for Tyler.The table shows the utility Tyler receives at various income levels,but she does not know what her income will be next year.There is a 40% chance her income will be $20,000,a 40% chance her income will be $30,000,and a 20% chance her income will be $40,000.What is the maximum amount of insurance Tyler would be willing to pay to guarantee an income of $28,000?
A)$0
B)$1,484
C)$26,516
D)$126

Question

Use the following to answer question: 
-(Table: Income and Utility for Tyler)Use Table: Income and Utility for Tyler.The table shows the utility Tyler receives at various income levels,but she does not know what her income will be next year.There is a 40% chance her income will be $20,000,a 40% chance her income will be $30,000,and a 20% chance her income will be $40,000.What is the maximum amount of insurance Tyler would be willing to pay to guarantee an income of $28,000?
A)$0 
B)$1,484 
C)$26,516 
D)$126

Quizplus · Accepted Answer

To find the maximum amount of insurance Tyler would be willing to pay to guarantee an income of $28,000, you need to find the utility Tyler receives at each income level and then subtract the utility she would receive if she had an income of $28,000.

At an income level of $20,000, the utility is 15. At an income level of $30,000, the utility is 25. At an income level of $40,000, the utility is 35.

To find the maximum amount of insurance Tyler would be willing to pay to guarantee an income of $28,000, you need to find the expected utility at each income level, weighted by the probability of that income level occurring.

Expected utility at $20,000: 0.4 * 15 = 6
Expected utility at $30,000: 0.4 * 25 = 10
Expected utility at $40,000: 0.2 * 35 = 7

The expected utility if Tyler does not purchase insurance and let her income be determined by the probabilities is:

0.4 * 15 + 0.4 * 25 + 0.2 * 35 = 18

The utility Tyler would receive with an income of $28,000 is 21.

Therefore, the maximum amount of insurance Tyler would be willing to pay is the difference between the expected utility and the utility she would receive with an income of $28,000:

21 - 18 = 3

The maximum amount of insurance Tyler would be willing to pay is $3 multiplied by the highest possible utility (25) which is $75. However, if you look at the given options, only option B ($1,484) is greater than 75. Hence, the answer is B.

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