Reference no: EM132380446
Assignment -
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.
You have the following information on ten individuals, A-J:
|
Individual
|
Wealth
|
Pr(Sick)
|
Cost of being sick
|
|
A
|
$210,000
|
0.25
|
$5,000
|
|
B
|
$160,000
|
0.25
|
$25,000
|
|
C
|
$90,000
|
0.20
|
$10,000
|
|
D
|
$120,000
|
0.05
|
$10,000
|
|
E
|
$230,000
|
0.05
|
$5,000
|
|
F
|
$250,000
|
0.05
|
$25,000
|
|
G
|
$50,000
|
0.25
|
$20,000
|
|
H
|
$200,000
|
0.20
|
$25,000
|
|
I
|
$100,000
|
0.10
|
$15,000
|
|
J
|
$190,000
|
0.05
|
$15,000
|
Each individual has the same utility function as given in the text as equation 8.2. Please note that the 'cost of being sick' is not their wealth if they are sick. It is how much their wealth is reduced if they are sick. This is different from the example in the text, where you are given wealth if they are sick. Wealth if sick = initial wealth - cost of being sick.
Part 1: Fully informed insurance company
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.
Part 2: Uninformed insurance company
11. If the insurance company (1) doesn't know the risk of each individual, but does know the expected cost of the group's sickness, and (2) sets a single premium that is actuarially fair for the group as a whole, what would be the premium, assuming all ten individuals purchase insurance?
12. Give 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 you've identified in question 12 didn't buy insurance and the insurance company set a new premium for the group that did buy insurance, 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?