Refer to pages 168-169 in Bernell. This assignment has you calculate actuarially fair premiums for 10 individuals and the maximum premium they are willing to pay.
Then, assuming that the insurance company can only charge an actuarially fair premium for the group of 10 as a whole, you must determine the premium and which of the 10 individuals would opt to not be insured.
You are encouraged to set this assignment up in Excel. You can use the example in the text to check if you have your formulas set up correctly.
This is an individual assignment. That means you cannot work in groups, share answers, or otherwise collaborate on working these problems. The intent is to ensure that you can do some basic economic calculations, not whether you can get answers by working in a group.

Part 1: Fully informed insurance company
You have the following information on ten individuals, A-J:
                                                               Cost of
Individual       Wealth       Pr(Sick)    being sick
A                   $150,000       0.05          $20,000
B                   $70,000          0.10          $15,000
C                   $80,000          0.15          $25,000
D                   $100,000       0.20          $10,000
E                   $250,000       0.25          $30,000
F                   $50,000          0.30          $5,000
G                   $25,000          0.35          $10,000
H                   $130,000       0.40          20,000
I                   $40,000          0.45          $15,000
J                   $120,000       0.50          $15,000
Each individual has the same utility function as given in the text: U = Wo.s.

For each individual, calculate:
a. The actuarially fair premium.
b. The loading factor if the insurance company charged a premium that would give the individual the same level of expected utility without insurance.
The above will be entered in Moodle as the answers to 1a, 1b, 2a, 10b.
Part 2: Uninformed insurance company
11. If the insurance company (a) doesn't know the risk of each individual, but does know the expected cost of the group's sickness, and (b) sets a single premium that is actuarially fair for the group as a whole, what would be the premium?
12. Given your answer to 11, which individuals would opt to NOT buy insurance? To answer this, you need to compare the certain utility (with the premium) and compare that to the expected utility without insurance.
13. If the individuals identified in 12 didn't buy insurance and the insurance company set a new premium for the smaller group, what would that new premium be?
14. Questions 12 and 13 illustrate the problem of adverse selection and why a market for insurance may fail. If this continues, with individuals dropping their insurance as premiums are increased, which single individual would be left buying insurance?

Refer to pages 168-169 in Bernell. This assignment has you calculat...