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Chapter 20: Problem 14

Kory owns a house that is worth \(\$ 300,000 .\) If the house burns down, she loses all \(\$ 300,000\). If the house does not burn down, she loses nothing. Her house burns down with a probability of 0.02 . Kory is risk-averse. a. What would a fair insurance policy cost? b. Suppose an insurance company offers to insure her fully against the loss from the house burning down, at a premium of \(\$ 1,500\). Can you say for sure whether Kory will or will not take the insurance? c. Suppose an insurance company offers to insure her fully against the loss from the house burning down, at a premium of \(\$ 6,000\). Can you say for sure whether Kory will or will not take the insurance? d. Suppose that an insurance company offers to insure her fully against the loss from the house burning down, at a premium of \(\$ 9,000\). Can you say for sure whether Kory will or will not take the insurance?

Short Answer

Expert verified
2. Will Kory take the insurance policy with a premium of $1,500? 3. Will Kory take the insurance policy with a premium of $6,000? 4. Will Kory take the insurance policy with a premium of $9,000?

Step by step solution

01

Calculate the expected loss

To calculate the fair insurance policy cost, we need to find the expected loss. The expected loss is calculated by multiplying the loss value by the probability of the loss occurring. Expected Loss = Value of house * Probability of house burning down Expected Loss = 300,000 * 0.02
02

Fair insurance policy cost

The fair insurance policy cost is equal to the expected loss. Fair Insurance Cost = Expected Loss #b. Suppose an insurance company offers to insure her fully against the loss from the house burning down, at a premium of $1,500. Can you say for sure whether Kory will or will not take the insurance?#
03

Comparing the insurance premium with expected loss

We need to compare the fair insurance policy cost (expected loss) with the given policy premium of $1,500. If the given premium is less than the expected loss, it is considered beneficial for a risk-averse person like Kory.
04

Decision for the $1,500 premium

If the given premium of $1,500 is less than the expected loss, Kory would take the insurance policy, as she is risk-averse. #c. Suppose an insurance company offers to insure her fully against the loss from the house burning down, at a premium of $6,000. Can you say for sure whether Kory will or will not take the insurance?#
05

Comparing the insurance premium with expected loss

We need to compare the fair insurance policy cost (expected loss) with the given policy premium of $6,000. If the given premium is less than the expected loss, it is considered beneficial for Kory.
06

Decision for the $6,000 premium

If the given premium of $6,000 is less than the expected loss, Kory would take the insurance policy, as she is risk-averse. #d. Suppose that an insurance company offers to insure her fully against the loss from the house burning down, at a premium of $9,000. Can you say for sure whether Kory will or will not take the insurance?#
07

Comparing the insurance premium with expected loss

We need to compare the fair insurance policy cost (expected loss) with the given policy premium of $9,000. If the given premium is less than the expected loss, it is considered beneficial for Kory.
08

Decision for the $9,000 premium

If the given premium of $9,000 is less than the expected loss, Kory would take the insurance policy, as she is risk-averse. If not, she would not take the insurance.

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Most popular questions from this chapter

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