Consider a simplified model of preventive care. Suppose that there is only one d
ID: 1198458 • Letter: C
Question
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 $110. The probability of getting flu is 0.2. Without insurance, the cost of treating the flu is $500. If one buys insurance with a 20% co-pay rate, the treatment cost is $600. 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?
Part B. With insurance (assuming you bear the full cost of the flu shot):
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?
Part C. Buying insurance:
a. Calculating the reduction in variance by buying insurance (Hint: you’ve already calculated the relevant variances) and thus the risk premium
b. Assume a 10% loading cost and expected welfare loss of $8 due to over-consumption, calculate the net welfare change of buying insurance. Will you buy insurance?
Explanation / Answer
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 $110. The probability of getting flu is 0.2. Without insurance, the cost of treating the flu is $500. If one buys insurance with a 20% co-pay rate, the treatment cost is $600. The consumer is risk averse with a risk-aversion parameter of -0.002.
Part A. Without insurance:
a. Calculate the expected cost.
The expected cost will be 600 per instance. (500+20% co-payment)
b. Calculate the variance and associated risk premium.
The risk can be calculated basis the probability method. The probability of getting sick is 99.8:0.2. If you don’t get ill, you may loose 110 but if you claim, you will get a benefit of 390.
c. What is the net benefit of taking the flu shot? Will you take the shot?
The net benefit of taking flu shot is 600-110=490. 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. Calculate the expected cost.
With insurance, the expected cost of treatment is 110 only.
b. Calculate the variance and associated risk premium.
The risk is of only 110. If you don’t climate, you will loose it else you can get the advantage of the insurance.
c. What is the net benefit of taking the flu shot? Will you take the shot?
The net benefit of taking flu shot is 600-110=490. Taking the shot is worth avoiding the risk of high payment.
Part C. Buying insurance:
a. Calculating the reduction in variance by buying insurance (Hint: you’ve already calculated the relevant variances) and thus the risk premium
There is reduction in variance by buying insurance and the risk of premium is only 110.
b. Assume a 10% loading cost and expected welfare loss of $8 due to over-consumption, calculate the net welfare change of buying insurance. Will you buy insurance?
The net welfare change will drop by overall 8% of buying guide insurance. I will still buy the insurance as it will avoid my risk of paying the total cost of treatment if I fall sick.