30 Jun Risk and Insurance Discussion Questions
Risk and Insurance Discussion Questions
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2 months ago
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Question Description
Risk and Insurance
Situation 1
Suppose there is a 5% probability (or risk) that you will get a very severe flu next year. If you get the flu, you will be admitted to the Hospital for at least a week, and in turn you will need to pay $2,000 for a hospital service and medical expenses. Keep in mind that you are risk-averse. While you can’t avoid getting the flu, you can avoid a financial loss due to the flu by buying a health insurance. You were looking for a health insurance with a price equal to your expected financial lose. The price of insurance is called actuarially fair insurance premium.
Question 1. What would the actuarially fair insurance premium (or expected financial lose) be? Make sure to calculate the actuarially fair insurance premium. Show how you calculated the actuarially fair insurance premium.
Situation 2
You could not find any insurance company to offer a health insurance with a price equal actuarially fair premium, due to fact that they are for-profit firm, not not-for-profit organization. Actuarially fair premium is a price that leads to zero-expected-profits of insurance company. Fortunately, you found an insurance company which will hand you an insurance benefit equal to your expected financial lose. But, the insurance company asked you to pay more than actuarially fair premium because there are other costs in order to offer the health insurance to you. The insurance company considered the administrative cost of $30 because they need to mail your monthly bill. Also the insurance company considered the risk bearing cost of $20 because they need to buy an insurance to hedge their own financial risks. For example, if your symptom is extremely serious, the medical bill would be more than $2,000. To hedge the financial risk due to such an unusual situation, the insurance company buy an insurance form another insurance company. Additionally, the insurance company needs a profit of $10.
Question 2. What would the loading cost of the insurance company be? Show how you calculated the loading cost.
Question 3. What would the selling price of the health insurance be? Show how you calculated the selling price.
Situation 3
Suppose you are so risk averse, and therefore so afraid of being uninsured, that you are willing to buy insurance at a higher price than actuarially fair premium $100. When you think of the flu, you worry about not only an expected financial lose but also other related unhappiness. For example, since you will be in the hospital for a week, you cannot attend classes, you cannot see your pets, and you may have no choice but to eat the unappetizing meals provided by the hospital. Therefore, you want to buy a health insurance not only for avoiding an expected financial loss, but also for minimizing other potential displeasure. In short, you are willing to buy a health insurance at a price which is more than actuarially fair premium.
Question 4. If you are willing to pay $175 for the health insurance to insure yourself against the risk of catching the flu next year, what would the risk premium be? Show how you calculated your risk premium.
Question 5. Compare the selling price and your level of willingness to pay for the health insurance. Would you choose to buy the health insurance? If so, what would your welfare gain (consumer’s surplus) be? Show how you calculated the welfare gain.
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