Final answer:
Different utility functions impact the likelihood of buying insurance. Linear and quadratic utility functions make it more likely to buy insurance, while a logarithmic utility function makes it less likely. The expected income and utility can be calculated by multiplying incomes by probabilities and using the utility function.
Step-by-step explanation:
A) Utility Function U = 20Y
If the utility function is U = 20Y, where Y represents income, the individual is likely to buy insurance. This is because with a linear utility function, the individual values income proportionally. Therefore, the individual would want to protect their income by purchasing insurance.
B) Utility Function U = log(Y)
If the utility function is U = log(Y), where Y represents income, the individual is unlikely to buy insurance. This is because the logarithmic utility function implies that the individual values income less proportionally as income increases. Therefore, the individual may not see the benefit in paying for insurance.
C) Utility Function U = 0.5Y²
If the utility function is U = 0.5Y², where Y represents income, the individual is likely to buy insurance. This is because the quadratic utility function implies that the individual values income more than proportionally as income increases. Therefore, the individual would want to protect their income by purchasing insurance.
D) Expected Income and Utility
To calculate the expected income, we multiply the income in each state (healthy and sick) by the respective probabilities and sum the results. In this case, the expected income is (0.80 * $2,000) + (0.20 * $1,000) = $1,800.
To calculate the expected utility, we use the expected income in the utility function. The expected utility is 200 * (1,800^0.5) = 12,727.92.