Suppose, after undergoing genetic testing, you discover that you have a health condition that could result in the emergence of a disability which would make it impossible for you to continue to work. The probability of this happening is 50%. Currently your expected lifetime earnings are $5,000,000, but if the disability hits, your expected lifetime earnings will consist primarily of income earned from government support programs -- and will not add up to more than $1 million.
a. Suppose that you are risk averse and your tastes are state-independent. Illustrate your expected utility in a graph with lifetime consumption on the horizontal and utility on the vertical axis.
b. Illustrate how much you would be willing to pay for full insurance.
c. Illustrate what you showed in (b) in a
different graph that has consumption in the "good" state on the horizontal and consumption in the "bad" state on the vertical.
d. What would a full menu of actuarily fair insurance contracts look like in your graph from part (c)? Where would you optimize in that graph?
e. Now suppose that you believe consumption will be more meaningful if the health condition does not materialize. What changes in your graph from part (d)?
What will be an ideal response?
b. The most you would be willing to pay for full insurance is an amount that results in a consumption level that gives the same utility as the expected utility B without insurance. This amount is indicated by the darkened horizontal line segment in the graph above.
c. This is illustrated in the graph below.
d. The actuarily fair insurance contracts lie on a line through A with slope -1 (as shown below). You would optimize at C with full insurance.
e. The only thing that changes is the "MRS" of the indifference curves -- it becomes steeper, implying you will no longer fully insure when offered a full menu of actuarily fair insurance contracts.
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What will be an ideal response?