4. Consider a simplified model of preventive care. Suppose that there is only on

Question

4. Consider a simplified model of preventive care. Suppose that there is only one disease, flu, which can be eliminated by taking a flu shot, with a cost of $100. The probability of getting flu is 0.3. Without insurance, the cost of treating the flu is $500. If one buys insurance with a 10% co-pay rate, the treatment cost is $650. The consumer is risk averse with a risk-aversion parameter of-0.002. Part A. Without insurance: a. Calculate the expected cost. b. Calculate the variance and associated risk premium. c. What is the net benefit of taking the flu shot? Will you take the shot?

Explanation / Answer

Note:- As per guideline I have answered more than four subparts (six).

Part A. Without insurance: a) The expected cost will be $550 per instance. (500+10% co-payment) b) The risk can be calculated basis the probability method. The probability of getting sick is 99.7:0.3. If you don’t get ill, you may loose 100 but if you claim, you will get a benefit of 400. c) The net benefit of taking flu shot is 650-100=550. Taking the shot is worth avoiding the risk of high payment. Part B. With insurance (assuming you bear the full cost of the flu shot): a) With insurance, the expected cost of treatment is 100 only. b) The risk is of only 100. If you don’t climate, you will lose it else you can get the advantage of the insurance. c) The net benefit of taking flu shot is 650-100=550. Taking the shot is worth avoiding the risk of high payment.

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