Suppose that the insurance company would set the premium by imposing a zero profit restriction. That is, the premium would be set to be (1+L)EB, where L is the loading factor and EB is the expected benefit. Let us assume that L = 10%.

a. Let us first consider a homogenous population of 10,000 people, each has a probability of 0.2 to incur a medical bill of $10,000, and a probability of 0.8 to be healthy. If the insurance company decides to offer health insurance plans with a uniform premium to this population, what would be the premium?

b. Let us now assume that there are 1,000 less healthy newcomers introduced into this population. They have a probability of 0.5 to incur a medical bill of $40,000 and a probability of 0.5 to be disease free. If the insurance company cannot distinguish the newcomers from the rest, it has to offer health insurance plans with a uniform premium to everyone. What would be the new premium in dollar amount? Calculate the percentage change in premiums for the existing policy holders.

c. Now, in an effort to lower the premium, the government needs to put relatively healthy young people in the mix. Suppose that they can persuade 3,000 young people to buy health insurance. These young people would only have 10% chance incurring a medical bill of $2,000. What would be the new premium if the insurance company would sell policies with a uniform premium to all three groups?

d. How many young people (instead of 3,000 assumed in part c) need the government to persuade to buy health insurance would the uniform premium fall back to the original level calculated in part a)?

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WORKINGS a 10000 people x 02 probability of incurring a medical bill of 10000 x 101 2000 10000 peopl... View the full answer