Questions

1. Consider that Kim has a choice among the following

prospects

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

is 0.03.

(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

destroyed?

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?