Your utility function is u(c) = √c where c is consumption. Your income is W = $40, 000. With probability p = 0.05 you get sick and have medical expenses of δ = $30, 000. (a) What is your expected utility without insurance?
Question
Your utility function is u(c) = √c where c is consumption. Your income is W = 30, 000. (a) What is your expected utility without insurance?
Solution
To calculate the expected utility without insurance, we need to consider both scenarios: getting sick and not getting sick.
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If you get sick, your consumption (c) will be your income (W) minus your medical expenses (δ). So, c = 30,000 = 10,000 = 100.
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If you don't get sick, your consumption (c) will be your income (W), so c = 40,000 = 200.
The expected utility is the sum of the utilities in each scenario, weighted by the probability of each scenario. The probability of getting sick is p = 0.05 and the probability of not getting sick is 1 - p = 0.95.
So, the expected utility without insurance is:
E[u(c)] = pu(c if sick) + (1-p)u(c if not sick) = 0.05100 + 0.95200 = 5 + 190 = 195.
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