01 Jul Risk and Insurance Discussion Questions
Risk and Insurance
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.
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.
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.
After buying the health insurance at the selling price, you worry less about the flu (this is called the problem of “moral hazard”). For example, before buying the insurance, you used to wash your hand 8 times per day, but after buying the insurance, you wash your hand just 4 times per day. This may lead to an increased chance of 10% of getting flu.
Question 6. What would the increased actuarially fair insurance premium be? Show how you calculated actuarially fair insurance premium.
Before purchasing insurance, you behaved carefully against the flu. Based on your previous behavior, the insurance company calculated actuarially fair insurance, sold the insurance to you, and was willing to cover your expected financial lose. After purchasing the insurance, you became careless. In turn, the insurance company cannot know (they could guess but can’t verify) your changed behavior against the flu (this is called the problem of “asymmetric information”). Thus, the insurance company have no choice but to cover your increased expected financial lose.
Question 7. Compare the actuarially fair premium before you acquired insurance (Question 1) to the actuarially fair premium after receiving insurance (Question 6). What would the cost of moral hazard (the difference between these two actuarially fair premiums) be in this case? Show how you calculated the cost of moral hazard.
Question 8. Suppose your copayment rate is zero, and the insurance company copayment rate is 100%. How much do you assume the cost of moral hazard? Also, how much does the insurance company assume the cost of moral hazard? Show how you calculate both costs of moral hazard. Under this insurance, do you have an incentive to be more careful against the flu?
Question 9. Suppose your copayment rate is 30% and the insurance company copayment rate is 70%. How much do you assume the cost of moral hazard? Also, how much does the insurance company assume the cost of moral hazard? Show how you calculate both costs of moral hazard. Under this insurance, do you have an incentive to be more careful against the flu?
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