Assume the average annual expected health care costs per person are distributed as follows: Number 25...

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Assume the average annual expected health care costs per person are distributed as follows: Number 25 20 20 15 10 7 1 1 1 100 Ave ann.. Cost 0 200 750 4,000 10,000 20,000 50,000 100,000 500,000 Case #1: Individual Health Insurance. Assume the following regarding a proposed health insurance company, Health USA: a. Health USA will be subsidized by the US Treasury, and so will assume 0% load for the net of expenses, profit, and interest. This means Health USA just wants to break even. b. This time, your experience as a pricing actuary has grown, and you're now going to set the premium anticipating likely adverse selection. c. Members don't know exactly what their health care cost will actually be for the following year, but they have some sense. Assume that members will join Health USA as long as the premium is NO MORE than 3x their expected cost. d. Health USA is barred by Congress from underwriting; it must accept all applicants regardless of health ("guaranteed issue") and it must charge all applicants the same rate e. There is no health care inflation, so the above expected costs apply indefinitely. 1. Since each prospective insured pays 100% of the premium, at what level should you set the premium to enable Health USA to breakeven, while getting the maximum number of people to sign up? (Hint: look at average cost if only last group stays, if only last 2 groups stay, if only last 3 groups stay, etc., until you find an average cost such that IF you set premium at that level, the "3x" condition is satisfied and the company has premiums = claim costs.) You must show your work. Assume the average annual expected health care costs per person are distributed as follows: Number 25 20 20 15 10 7 1 1 1 100 Ave ann.. Cost 0 200 750 4,000 10,000 20,000 50,000 100,000 500,000 Case #1: Individual Health Insurance. Assume the following regarding a proposed health insurance company, Health USA: a. Health USA will be subsidized by the US Treasury, and so will assume 0% load for the net of expenses, profit, and interest. This means Health USA just wants to break even. b. This time, your experience as a pricing actuary has grown, and you're now going to set the premium anticipating likely adverse selection. c. Members don't know exactly what their health care cost will actually be for the following year, but they have some sense. Assume that members will join Health USA as long as the premium is NO MORE than 3x their expected cost. d. Health USA is barred by Congress from underwriting; it must accept all applicants regardless of health ("guaranteed issue") and it must charge all applicants the same rate e. There is no health care inflation, so the above expected costs apply indefinitely. 1. Since each prospective insured pays 100% of the premium, at what level should you set the premium to enable Health USA to breakeven, while getting the maximum number of people to sign up? (Hint: look at average cost if only last group stays, if only last 2 groups stay, if only last 3 groups stay, etc., until you find an average cost such that IF you set premium at that level, the "3x" condition is satisfied and the company has premiums = claim costs.) You must show your work.

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