Suppose that individual A’s utility function, which only depends on wealth (W), is defined asU(W) = W0.5 ,where W stands for her/his wealth.
Based on this utility function, answer the following questions:
a) Suppose her/his initial wealth is $10,000, and there is a 20% chance that she may get sick. In the event of illness, the cost of medical care is $1,000. Given this information, calculate her/his expected utility.
b) In order to cover potential cost due to future cost of care, individual can buy full insurance. If health insurance is available for her/his with a premium of $100, will she buy insurance? Explain and show your work.
c) What is the maximum amount of insurance premium that she is willing to pay? Explain and show your work.