Stephanie's utility function is given by U = W^1/2where W is the value of her house. She is considering whether to buy tornado insurance for her house. Her house is currently valued at
$105,625. She knows that her house will be destroyed by a tornado with probability .10 this spring. If it is hit, the rubble will be worth $15,625. What is the maximum amount that she is willing to pay for insurance if the insurance company pays $46875 and refunds her insurance premium in case of a tornado?

Question

Quizplus · Accepted Answer

Stephanie's utility without insurance is a weighted average of the utility if her house is destroyed and if it isn't, based on the probability of a tornado. Without insurance, her expected utility is 0.9U($105,625) + 0.1U($15,625). With insurance, and paying a premium X, her utility becomes 0.9U($105,625 - X) + 0.1U($105,625 + $46,875 - X) because the insurance pays out $46,875 and refunds the premium X if the tornado hits. The maximum she would pay for insurance is the value of X that makes her indifferent between having insurance and not having it. Calculating the exact amount requires solving for X in the utility equations, but the correct choice is based on understanding the insurance's impact on her expected utility.

Stephanie's Utility Function Is Given by U = W1/2 where

Stephanie's Utility Function Is Given by U = W^1/2where