Question

2. There is a 3% chance that Betsy becomes ill and this illness will cost her $15,000. AAA Insurance offers Betsy a policy that will cover these costs in the event that she gets sick. This policy costs $1000 (or 6.67% of the policy coverage).

   1. (4 points) Assuming there is a 0.5% administrative fee per policy, what are the expected profits of AAA Insurance?

   2. (4 points) Would you expect AAA insurance to be able to offer this policy in a competitive market? Explain.

   3. (4 points) Again, assuming the health insurance market is perfectly competitive, what is the equilibrium price of insurance (as a percent of coverage)?

Answer 1

a) assuming a large enough number of policy buyers, the expected profits of AAA insurance (per policy) can be calculated as:

Insurance premium (or cost of policy for the buyer) - Administrative cost - Expected payout for cover illness

= 1000 - 0.5% x 1000 - 15000 x 3%

= 1000 - 5 - 450

= $545 per policy or 54.5% of premium (545 / 1000)

b) In a competitive market, new insurance companies would enter and will offer similar policies with a lower price to grab market share (of such a lucrative product). This will result in the price of such policies to go down till it settles at around the real cost, i.e., about $455, and AAA insurance would also need to offer this policy at the same reduced price

c) The equilibrium price of this policy, as mentioned in point b, is about $455 (expected payout in case of illness plus administrative cost)

As a % of coverage it would be: 455 / 15000 = approx. 3%