Your utility function is U = , where C is the amount of consumption that you have in any given period. Your income is $6

[answerhappygod]

Your utility function is U = , where C is the amount of
consumption that you have in any given period. Your income is
$62,500 per year, and there is a 2% chance that you will be
involved in a catastrophic accident that will cost you $40,000 next
year. Note that you spend all of your income in any state of the
world so that income and consumption are the same in any given
state of the world (i.e., accident/ no accident).
a) What is your Utility if there is no accident?
b) What is your (statistically) Expected Utility?
c) What is your statistically expected or
average income over different states of the
world?
d) Calculate an actuarially fair insurance premium. This is the
amount you would pay every year to cover the average cost of the
accident based on its probability over the years; it is the
difference between the no-accident income and your actual expected
or average income from part c). This is the premium that insurance
companies would collect and pay out entirely to those unfortunate
enough to have an accident, with no profit or other funds left to
the insurance company. In other words it is just a redistribution
from the fortunate to the unfortunate.
e) What is the most that you would be willing to pay for
insurance, given your utility function? Do this in two steps: i)
calculate the income (or consumption) received with
certainty which has the same utility as you would have
in a world in which you are uninsured and face the possibility of
an accident -- that is, your expected utility from part b).
ii) Calculate the difference between this and your
no-accident income this is the most you would be willing to pay to
remove all risk because you would at least keep the same level of
utility or satisfaction after paying it as you have in the actual
risk-filled world.
The answer to e) is more than that in d) which shows
insurance companies can obtain premiums in
excess of what they pay out to the insured because of the
risk-aversion of the insured individuals.