Jude owns a house worth $250,000 in an area that is prone to tornadoes. Suppose there is a 5 percent chance during the next year that Jude's house will incur $50,000 of damage from a tornado and a 1 percent chance that his home will be completely destroyed by a tornado. Suppose an insurance company offers him a policy that fully reimburses him in the event that his home is damaged by a tornado. The insurance company charges a $10,000 premium for this policy. Which of the following statements is true?The expected value of Jude's home when he buys insurance is higher than the expected value if he does not buy insurance.If Jude is risk neutral, he will prefer to not buy insurance.Economists would say it is irrational to purchase the insurance.
A)II only
B)I and III only
C)I only
D)II and III only

Question

Quizplus · Accepted Answer

The expected value of Jude's home without insurance is calculated by considering the probabilities of damage and total loss. With a 5% chance of $50,000 damage, the expected loss is $2,500 (0.05 * $50,000). With a 1% chance of total loss ($250,000), the expected loss is $2,500 (0.01 * $250,000). Adding these, the total expected loss is $5,000. Paying a $10,000 premium for insurance results in a certain loss higher than the expected loss without insurance, making it less appealing for a risk-neutral person. Therefore, statement II is correct. Statement I is incorrect because the insurance premium is higher than the expected loss, reducing the expected value of the home if insurance is bought. Statement III is incorrect because purchasing insurance can be rational for risk-averse individuals, despite the premium exceeding the expected loss.

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