Question

Suppose that your utility function is U = √ I where I is the amount of income you make per month. Suppose that you typically make $8,100 per month, but there is a 5 percent chance that, in the next month, you will get sick and lose $3,200 in income.

(a) What is your expected utility if you do not have health insurance to protect against this adverse event? [1 mark]

(b) Suppose you can buy insurance that will fully cover your losses if you get sick. What would be the actuarially fair premium? [1 mark]

(c) What is your expected utility if you buy the insurance policy at an actuarially fair premium? [1 mark]

(d) What is the most that you would be willing to pay for this policy? [1 mark]

Answer #1

Suppose that Elizabeth has a utility function U= (or U=W^(1/3) )
where W is her wealth and U is the utility that she gains from
wealth. Her initial wealth is $1000 and she faces a 25% probability
of illness. If the illness happens, it would cost her $875 to cure
it.
What is Elizabeth’s marginal utility when she is well? And when
she is sick? Is she risk-averse or risk-loving?
What is her expected wealth with no insurance?
What is...

Suppose that an economist has a utility function U =
(Income)0.25. Her income is $65K a year, but there is a
10 percent chance of becoming ill and making only $57K.
(a) What is her expected utility if she does not have
insurance?
(b) What is the actuarially fair insurance premium?
(c) How much is she willing to pay for insurance?

1. Suppose Bob has income of $18,000. There is a 20% chance that
Bob will get sick and have to spend $10,000 of his income on a
treatment. Suppose Bob’s income-utility relationship is given by:
Where I is Bob’s income.
U(I) = square root I
Complete the table below to find Bob’s total certain utility for
various levels of wealth, along his marginal utility associated
with increases in his wealth.
Wealth
Certain Utility
Marginal Utility = change in utility...

if the consumer’s U(c) = square root c, the probability of an
adverse event is 0.25, and as the adverse event happens the
consumer’s consumption is 9; when the adverse event does not occur
the consumption is 24,
the consumer’s utility from the expected consumption is?
why is the consumer's utility from the expected consumption and
the result of consumer’s expected utility different?
design an insurance product with a fair premium and indicate
how it impacts the consumer's outcomes for...

Questions 14-16 are parts of this question
June’s utility of income is U(I) = I^0.5 (which is the square
root of I). Her income is $5000 and she faces a 40% chance of
losing $3000.
What is the actuarially fair premium (AFP) to cover this risk?
(3)
What is June’s maximum willingness to pay for insurance against
this risk? (5)
Suppose June is now pooled with (charged the same premium as)
Jim, who faces a 60% chance of losing $3000....

1. Suppose that John has an income of $50,000 when
healthy. If he falls sick, he has to pay $10,000 to cover his
medical bills. There is a 40% probability that John will become
sick.
a. Calculate John’s expected income E (I).
b. Suppose that John’s utility function is: U(I) = ln
(I). Calculate John’s expected utility of income E
(U(I)).
c. Calculate the utility of John’s expected income U (E
(I)). Compare this value to your answer in (b)....

Given that your current wealth is $10,000 invested in a cupcake
shop at Coldwell’s student cafeteria, and assuming that there is a
20% chance of an earthquake destroying the business and reducing
your investment to $2,453.
a. What is the expected wealth?
b. What would be an actuarially fair market premium?
c. If the certain utility of the expected wealth you calculated
in point a) above, is higher than the expected utility, would you
buy the insurance given the premium...

Suppose Hannah is strictly risk averse with a utility function u
over monetary amounts (y):
u(y)=y^(1/2)
Hannah is facing a risky situation: Either nothing happens to
her wealth of $576 with probability 3/4 or she losses everything
(so ends up with $0) with probability 1/4.
Question 1
What is the expected payoff that Hannah is facing? Provide the
numerical value.
Numeric Answer:
Question 2
What is Hannah's expected utility in this gamble? Provide the
numerical value.
Numeric Answer:
Question 3...

Consider an individual whose utility function over wealth is
U(W), where U is increasing smoothly in W (U’ > 0) and convex
(U’’ > 0).
a. Draw a utility function in U-W space that fits this
description.
b. Explain the connection between U’’ and risk aversion
c. True or false: this individual prefers no insurance to an
actuarially fair, full contract. Briefly explain your answer

Continuous demand for insuarance: What fraction of a person’s
potential losses will they choose to insure if they are free to
choose any level of insurance? Consider the following model. Sam
has an income of W, and with probability p experiences a loss of L
≤ W. An insurance company offers a range of insurance policies. A
policy that pays Sam I in the event of a loss can be purchased for
a premium of a×I. Sam must choose an...

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