Question

Question 24 page 397 Chapter 16.(Principles of Microeconomics) book

Imagine that you can divide 50 year old men into two groups: those who have a family history of cancer and those who do not.   For the purposes of this example, say that 20% of a group of 1,000 men have a family history of cancer, and these men have one chance of 50 of dying in the next year, while the other 80% of men have one chance in 200 of dying in the next year. The insurance company is selling a policy that will pay $100,000 to the estate of anyone who dies in the next year.

If the insurance company were selling life insurance separately to each group, what would be the actuarially fair premium for each group?

If an insurance company were offering life insurance to the entire group, but could not find out about family cancer histories, what would be the actuarially fair premium for the group as a whole?

What will happen to the insurance company if it tries to charge the actuarially farm premium to the group as a whole rather than to each group separately? Include in your answer a full explanation as to who purchase the insurance and who does not.

Answer 1

1) group 1 = men have a family history of cancer

group 2 = men who do not have a family history of cance

Group 1 Calculations

Number of men in Group 1 = 20% of 1000 = 200

Potential number of men dying in next year = (1/50)*200 = 4

Damage payable = 4*100,000 = 400,000, which will be charged to 200 men.

Therefore, insurance premium per person in group 1 = 400,000/200 = $2000

Group 2 Calculations:

Number of men in Group 1 = 80% of 1000 = 800

Potential number of men dying in next year = (1/200)*800 = 4

Damage payable = 4*100,000 = 400,000, which will be charged to 800 men.

Therefore, insurance premium per person in group 1 = 400,000/800 = $500

B) Assuming that the total Potential number of men dying in next year = 4+4 = 8 men.

Damage payable = 8*100,000 = 800,000, which will be charged to 1000 men.

Therefore, insurance premium per person in group 1 = 800,000/1000 = $800

C) If the insurance company tries to charge same premium to the group as a whole, the men from Group 2 are expected to not take the insurance from this insurance company and rather take it from another company which offers a fair premium based on their categorization, as the cost is much higher to them.

The men from Group 1 are expected to take the insurance coverage and pay a lower premium than the fair premium applicable, resulting in lower premium collection for the insurance company.

The expected losses of the insurance company will thus be higher as more and more people with higher risk characterstics will take the insurance coverage and the number of people from lower risk characteristic will decrease.