Question

Suppose a risk-lover has an initial wealth of $6,000 and a utility function U(M) = M^2 . He faces a 70 percent chance of losing $5000, and a 30 percent chance of losing $3000.

What is the most a consumer would pay for insurance against these losses? Is the premium bigger than or smaller than the expected loss?

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...

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....

Suppose Rita has log utility in wealth, ?(?) = ln(?), and has an
initial wealth of $40,000. There is a 25% chance that she will be
healthy this year and her wealth won’t be affected by illness.
However, there is a 50% chance that she will have a minor illness
at some point and a 25% chance that she will experience a major
illness. In the case of a minor illness, she will lose $5,000 of
her wealth, but a...

Suppose Alana has personal wealth of $10,000 and there is a
probability of 0.2 of losing her car worth $6,400 in an
accident. Her utility (of wealth) function is given
by u(w) = w0.5,
where w is wealth.
(a) What is Alana's expected wealth, expected utility, and
utility of expected wealth? If she can insure "fully", and if this
insurance is fair, how much would it cost her?
(b) What is the maximum amount Alana would be prepared to pay
for full insurance?...

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...

Suppose you are endowed with with a utility function over wealth
given by: u(w) = 7w + 100. Further, suppose you are offered a
gamble that pays $10 with probability 30% and $100 with probability
70%. (A) What is the expected value of this gamble? (B) Would you
rather have the gamble, or a guaranteed $70? (C) Now suppose your
utility function is u(w) = 100w − 18. How does your answer in (B)
change? (D) Suppose the utility function...

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?

Suppose that everyone is risk averse and has the same utility
function and an annual income of $50, 000 but people face different
risks to health. Person A has a 20% chance of experiencing a health
shock that requires $400 in expenses while Person B has a 0.2%
chance of experiencing a health shock that requires $40, 000.
(a) Calculate Person As expected loss.
(b) Calculate Person Bs expected loss.
(c) Graphically illustrate that Person B would be willing to...

Suppose a consumer has the utility function u(x, y) = x + y.
a) In a well-labeled diagram, illustrate the indifference curve
which yields a utility level of 1.
(b) If the consumer has income M and faces the prices px and py
for x and y, respectively, derive the demand functions for the two
goods.
(c) What types of preferences are associated with such a utility
function?

A small business owner has a log utility function,?(?) = ln(?).
She faces a 10% chance of having a fire that will reduce her net
worth to $1.00, a 10% chance that a fire will reduce her net worth
to $50,000, and an 80% chance that her business will retain its
value of $100,000.
a. What is the business owner’s expected wealth?
b. What is the utility of expected wealth in this scenario?
c. What is the expected utility of...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 17 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago