You live in an area where there is a possibility of a massive earthquake, so consider purchasing earthquake insurance for your home at an annual cost of $180. The probability of an earthquake damaging your home in the course of a year is 0.001. If this occurs, you estimate that the cost of the damage (fully covered by insurance) will be $160,000. Your total assets (including the house) are worth $250,000. a) Apply the maximum expected value decision rule to determine the alternative (to buy insurance or not) that maximizes the value of your assets after one year. b) You developed a utility function that measures the value of your assets in x dollars (x ≥ 0). This utility function is U(x) = √x. Compare the utility of reducing the total of your assets for the next year by a value equal to the value of the insurance, with the expected utility next year of not purchasing tremor insurance. Should you purchase the insurance?
You live in an area where there is a possibility of a massive earthquake, so consider purchasing earthquake insurance for your home at an annual cost of $180. The probability of an earthquake damaging your home in the course of a year is 0.001. If this occurs, you estimate that the cost of the damage (fully covered by insurance) will be $160,000. Your total assets (including the house) are worth $250,000.
a) Apply the maximum expected value decision rule to determine the alternative (to buy insurance or not) that maximizes the value of your assets after one year.
b) You developed a utility function that measures the value of your assets in x dollars (x ≥ 0). This utility function is U(x) = √x. Compare the utility of reducing the total of your assets for the next year by a value equal to the value of the insurance, with the expected utility next year of not purchasing tremor insurance. Should you purchase the insurance?
The probability that an earthquake in a year (q) = 0.001
Probability of not having an earthquake (p)=0.999
Loss due to earthquake (L) = $160,000
Insurance premium per year (P)= $180
Total value of home W0 = $250,000
We will calculate the expected wealth in both cases ( case (i) insurance purchased; case (ii) insurance not purchased,) to solve the first part of this question.
To solve the second part, we have to calculate the expected utility if insurance is purchased and if insurance is not purchased.
Note: The cost of damage is fully covered by insurance
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