1. Consider that Kim has a choice among the following
Gamble A: Gamble B:
$60 with probability 0.24 $65 with probability 0.25
$33 with probability 0.24 $30 with probability 0.25
$0 with probability 0.52 $1 with probability 0.50
(a) Rewrite these gambles after applying each of the
steps of the editing phase. Does the result depend
upon the order in which you apply these steps?
(b) Calculate the value of both gambles using the
cumulative prospect theory functions estimated
by Tversky and Kahneman and appearing in
equations 10.6 and 10.7, including their parameter
estimates. Which gamble would the model predict
would be chosen? Does this depend on the order of
the steps applied in editing?
2. Stock market investments are inherently risky. Suppose
that Sasha is heavily invested in a high-tech firm
with a positive earnings outlook. Then reports come
out that the firm’s primary technology is under a legal
challenge from a competitor. If they should successfully
repel the legal challenge, they will make the
spectacular profits that everyone had been expecting,
creating the expected returns on investment. If they
fail, their business model will be irreparably broken
and their stock will be worthless. Legal experts give
the legal challenge a 60 percent chance of being successful.
In the meantime, stock prices have plummeted
in response to the news. Sasha previously had $1
million invested, and it is now worth only $400,000.
What does prospect theory have to say about Sasha’s
likely reaction to the news and devaluation of the
stock? What has happened to the level of risk? What is
Sasha’s likely reference point? Describe the change in
risk aversion. Is Sasha likely to sell out now or hold the
stock? Why? How might this explain behavior in a
stock market crash?
3. You have a collection of valuable artwork worth
$400,000. Suppose that you have preferences represented
by the cumulative prospect theory model
presented in Example 10.3. You are considering an
insurance policy that will pay you the value of
your collection should anything destroy it. Suppose
that the probability of your artwork being damaged
(a) Considering that the current value of your artwork
is your reference point, what is the most you would
be willing to pay for the coverage? Express this as
a percentage of $400,000.
(b) Now, suppose while you are filling out the
paperwork, you are informed that a freak accident
has destroyed half of your collection, leaving you
with only $200,000 worth of rare artwork. If we
consider $400,000 to be the reference point, now
what is the maximum percentage of $200,000 you
would be willing to pay to buy insurance that will
replace $200,000 should the remaining art be
4. Consider the contract problem in Example 10.5. Suppose
that when considering whether to take the contract
or not, the worker tries to maximize the function
U b +maxi h, l Vi, where U b =b0.88, the value b is
the base level of pay in the contract, and Vi is as given
in equations 10.12 through 10.17. Consider that if the
worker takes no contract, she will receive $0.
(a) What is the minimum level of base pay the worker
will accept for a contract with a high base pay and
penalties for poor performance (so b= rh)? What
are the resulting rl, rh?
(b) What is the minimum level of base pay the worker
will accept for a contract with low base pay and
rewards for good performance (so b= rl)? What
are the resulting rl, rh?
(c) Suppose the firm can sell high-quality pizza for $10
and low-quality pizza for $7. Which contract will
the firm offer in order to maximize their profits?