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 = 20%. a. Let us first consider a homogenous population of 10,000 people, each has a probability of 0.3 to incur a medical bill of $10,000, and a probability of 0.7 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 newcomers to this population. However, the newcomers are less healthy. They have a probability of 0.5 to incur a medical bill of $20,000 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. Based on this simple calculation, what can we say about the impact of pre-existing condition provision included in the ACA?