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

Assignment: Risk and Insurance

Assignment: Risk and Insurance

Assignment: Risk and Insurance

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 premiumbe? 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.

Situation 4

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.

Situation 5

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?

You must proofread your paper. But do not strictly rely on your computer’s spell-checker and grammar-checker; failure to do so indicates a lack of effort on your part and you can expect your grade to suffer accordingly. Papers with numerous misspelled words and grammatical mistakes will be penalized. Read over your paper – in silence and then aloud – before handing it in and make corrections as necessary. Often it is advantageous to have a friend proofread your paper for obvious errors. Handwritten corrections are preferable to uncorrected mistakes.

Use a standard 10 to 12 point (10 to 12 characters per inch) typeface. Smaller or compressed type and papers with small margins or single-spacing are hard to read. It is better to let your essay run over the recommended number of pages than to try to compress it into fewer pages.

Likewise, large type, large margins, large indentations, triple-spacing, increased leading (space between lines), increased kerning (space between letters), and any other such attempts at “padding” to increase the length of a paper are unacceptable, wasteful of trees, and will not fool your professor.

The paper must be neatly formatted, double-spaced with a one-inch margin on the top, bottom, and sides of each page. When submitting hard copy, be sure to use white paper and print out using dark ink. If it is hard to read your essay, it will also be hard to follow your argument.

ADDITIONAL INSTRUCTIONS FOR THE CLASS

Discussion Questions (DQ)

Initial responses to the DQ should address all components of the questions asked, include a minimum of one scholarly source, and be at least 250 words.
Successful responses are substantive (i.e., add something new to the discussion, engage others in the discussion, well-developed idea) and include at least one scholarly source.
One or two sentence responses, simple statements of agreement or “good post,” and responses that are off-topic will not count as substantive. Substantive responses should be at least 150 words.
I encourage you to incorporate the readings from the week (as applicable) into your responses.
Weekly Participation

Your initial responses to the mandatory DQ do not count toward participation and are graded separately.
In addition to the DQ responses, you must post at least one reply to peers (or me) on three separate days, for a total of three replies.
Participation posts do not require a scholarly source/citation (unless you cite someone else’s work).
Part of your weekly participation includes viewing the weekly announcement and attesting to watching it in the comments. These announcements are made to ensure you understand everything that is due during the week.
APA Format and Writing Quality

Familiarize yourself with APA format and practice using it correctly. It is used for most writing assignments for your degree. Visit the Writing Center in the Student Success Center, under the Resources tab in LoudCloud for APA paper templates, citation examples, tips, etc. Points will be deducted for poor use of APA format or absence of APA format (if required).
Cite all sources of information! When in doubt, cite the source. Paraphrasing also requires a citation.
I highly recommend using the APA Publication Manual, 6th edition.
Use of Direct Quotes

I discourage overutilization of direct quotes in DQs and assignments at the Masters’ level and deduct points accordingly.
As Masters’ level students, it is important that you be able to critically analyze and interpret information from journal articles and other resources. Simply restating someone else’s words does not demonstrate an understanding of the content or critical analysis of the content.
It is best to paraphrase content and cite your source.
LopesWrite Policy

For assignments that need to be submitted to LopesWrite, please be sure you have received your report and Similarity Index (SI) percentage BEFORE you do a “final submit” to me.
Once you have received your report, please review it. This report will show you grammatical, punctuation, and spelling errors that can easily be fixed. Take the extra few minutes to review instead of getting counted off for these mistakes.
Review your similarities. Did you forget to cite something? Did you not paraphrase well enough? Is your paper made up of someone else’s thoughts more than your own?
Visit the Writing Center in the Student Success Center, under the Resources tab in LoudCloud for tips on improving your paper and SI score.
Late Policy

The university’s policy on late assignments is 10% penalty PER DAY LATE. This also applies to late DQ replies.
Please communicate with me if you anticipate having to submit an assignment late. I am happy to be flexible, with advance notice. We may be able to work out an extension based on extenuating circumstances.
If you do not communicate with me before submitting an assignment late, the GCU late policy will be in effect.
I do not accept assignments that are two or more weeks late unless we have worked out an extension.
As per policy, no assignments are accepted after the last day of class. Any assignment submitted after midnight on the last day of class will not be accepted for grading.
Communication

Communication is so very important. There are multiple ways to communicate with me:
Questions to Instructor Forum: This is a great place to ask course content or assignment questions. If you have a question, there is a good chance one of your peers does as well. This is a public forum for the class.
Individual Forum: This is a private forum to ask me questions or send me messages. This will be checked at least once every 24 hours.