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?