Question

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

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

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

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?#

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.

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?#

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.

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?#

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.

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.

Key concepts

Risk Aversion

Risk aversion is a key concept in understanding how individuals make decisions in uncertain situations. People who are risk-averse prefer to avoid uncertainty and potential losses, even if it means forgoing greater potential gains. This is because the pain of losing does not equate equally to the pleasure of gaining for them.

For example, in Kory's situation, her risk aversion means she values security over taking the risk that her house may or may not burn down. Although the chance of fire is only 2%, the potential loss of $300,000 is significant. Thus, she might prefer to pay an insurance premium to eliminate that risk, even if the premium is higher than the expected loss.

By paying a premium for insurance, Kory reduces the chances of experiencing a devastating financial loss, giving her peace of mind. Her decision to buy insurance hinges on comparing the premium to her expected loss, while taking into account her aversion to risk.

Expected Loss

Expected loss is a fundamental calculation in insurance economics. It represents the average loss one might expect to experience over time. Calculating expected loss helps determine what a fair insurance policy might cost.

To compute Kory's expected loss, we use the formula:
Expected Loss = Value of the Loss x Probability of the Loss

In this case, Kory's expected loss if her house burns down is:
\[\text{Expected Loss} = 300,000 \times 0.02 = \$6,000\]

By calculating this, Kory or the insurance company can determine what the average cost of potential loss is over time. Ideally, insurance premiums would be set around this value for the insurance to remain fair. However, determining a fair premium also involves weighing the person's risk aversion.

Premium Calculation

Premium calculation is crucial in evaluating whether an insurance policy offers a good deal for the buyer. It involves deciding how much the insured should pay to cover potential risks.

To determine a reasonable premium, insurers often start with the expected loss calculation, which we've already identified as $6,000 for Kory's scenario.

• A premium of $1,500 is significantly lower than the expected loss, suggesting a favorable deal for Kory, if not underpriced for the insurer.
• A $6,000 premium matches the expected loss, making it a neutral option that might still attract Kory due to her risk aversion.
• A $9,000 premium exceeds the expected loss, but for a risk-averse person, paying this sum might still be worth the peace of mind.

It's important to note that insurance premiums include considerations like administrative costs, profit margins, and the individual's risk profile, which may adjust the premium away from the expected loss value.