# hw11

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```					UNIVERSITY OF WISCONSIN
Economics 101 – Spring 2007
Professor Wallace
Problem Set 11
Due on May 4th at noon in your TA’s mailbox (opposite 7226 SS)
homework will not be accepted. Remember that you can help each other but each student has to
hand a hand-written solution of the problem set.

1. John decides to bet on the outcome of a rolled die. If the die shows an even number then John
will win \$10. If the die shows an odd number, John wins nothing. The expected value of John’s
gamble is
A) \$0
B) \$5
C) \$10
D) There isn’t enough information to tell

2. Bill faces an uncertain outcome. The expected wealth he receives from this outcome is \$100. Bill
reckons that his expected utility from this uncertainty he faces is 20, while the utility he would
obtain from receiving \$100 for certain is 25. What can we say about Bill’s risk attitudes?
A) Bill is risk averse
B) Bill is risk neutral
C) Bill is risk preferring
D) There isn’t enough information to say anything about Bill’s risk attitudes.

3. A risk-averse individual is offered a choice between a gamble that pays \$1000 with a probability
of 25% and \$100 with a probability of 75%, or a payment of \$325. Which would he chooses? What
if the payment was \$320? (When you answer this question, you have to show your work. )

4. Draw a utility function that exhibits risk-loving behavior for small gambles and risk-averse
behavior for larger gambles.

5. Ray Barone needs our advice. He is thinking about purchasing a lottery ticket that gives \$100
with probability 0.5 and zero otherwise. The ticket costs \$40. His utility function is
u c)  c .
(
A) Plot his utility function in the graph. Is Frank risk averse?
B) What is the expected value of the lottery? (give the number and mark it on the graph).
C) What is the expected utility from this lottery? (give a number and mark it on the graph).
D) What is the certainty equivalent of the lottery? Is it greater or smaller than the expected value
of the lottery? Give economic interpretation of this number.
E) Should Raymond purchase the lottery ticket?
F) Give answers to questions b-e, assuming his utility function given by u(c) = c

6. Ryoji, Hiren and Jeff each have 4 dollars to spend in a bar. Their utility functions are

1
U  bR , UH  bH , and UJ  bJ , respectively, where b denotes the consumption of bottles of
2
R

beer in the bar. The price of a bottle of beer is \$1. Unfortunately the bar is in a dangerous part of
town and there is a 50% chance that they will get mugged on their way to the bar. If that happens
they loose all their money.
A) Find the expected consumption of beer for each one of them.
B) Find the expected utility for each one of them.
C) Assume now that they can buy "protection" from the neighborhood bad guy at \$1 each (If they
buy protection they do not get mugged). Who will buy the "Protection package"?
D) What is the maximum amount of money that each one is willing to pay for protection?

7. The figure below shows Shannon’s utility of wealth curve.

Shannon is offered a job as a salesperson in which there is a 50% chance that she will make \$4,000
a month and a 50% chance that she will make nothing.

(a) What is Shannon’s expected income from taking this job?

(b) What is Shannon’s expected utility from taking this job?

(c) How much would another firm have to offer Shannon with certainty to persuade her not to
take this risky sales job?

Assume now that Shannon is building a small weekend shack on a steep, unstable hillside. She
spends all her wealth which is \$4,000 now on this project. There is 75% chance that the house will
be washed down the hill and be worthless.
How much is Shannon willing to pay for an insurance policy that pays her \$4,000 if the house is
washed away?

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8. Lori who is risk averse has two pieces of jewelry, each worth \$1,000. She wants to send them to
her sister in Thailand. She is concerned about the safety of shipping them. She believes that the
probability that the jewelry won’t arrive is 1/2. Is her expected utility higher if she sends the articles
together or in two separate shipments?

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