Deck 6: Bracketing Decisions

Question 1

Hedonic editing and framing concern how individuals evaluate events, whereas choice bracketing concerns how certain decisions are actually made.

Answer 1

True

Question 2

Rational choice theory already assumes that individuals bracket decisions in certain ways.

Answer 2

False

Question 3

Under expected utility theory, if poor individuals receive the same utility from an additional dollar as a wealth individual, then preferences are best described with a non-linear utility function.

Answer 3

False

Question 4

The difference between narrow bracketing and broad bracketing is the number of decisions that are bracketed together.

Question 5

There is an objective way to measure whether a set of decisions has been narrowly bracketed or broadly bracketed.

Question 6

Narrow bracketing leads individuals to sub-optimal choices when there is a characteristic that is only present in a group of objects, but not present in each individual object.

Question 7

Narrow bracketing can lead to addiction because I consider the benefits of my addictive behavior today separately from the costs it will impose on me tomorrow.

Question 8

Social heuristics refer to the cues our society gives us on how to bracket our decisions. One such example is the Food Pyramid, which tells us how much of each food group to eat every day.

Question 9

Narrow bracketing of decisions and melioration is the only way to explain addictive behavior.

Question 10

A decision-maker always arrives at different choices if he segments his decisions.

Question 11

An individual's certainty equivalent is the amount of money the individual must receive with certainty in order to attain the same level of expected utility as the gamble.

Question 12

If my preferences are given by $U=\ln (x)$ then my coefficient of relative risk aversion increases as my income increases.

Question 13

Choice bracketing refers to:

A) The sequence in which decisions are made.
B) How choices are grouped together.
C) The mental account where choices are placed.
D) Segmenting choices to make decisions less complex.

Question 14

Segmentation Independence refers to which concept?

A) The available choices do not change based on how they are grouped together.
B) When all decision-makers make choices simultaneously they make the same choices.
C) Decisions of a single individual do not change based on how they are grouped together.
D) Elements of your choice set can be broken into smaller pieces.

Question 15

Sherry has two choices. She can either receive $\$ 8$ or a lottery ticket that pays $\$ 40$ with a $50 \%$ chance and $\$ 10$ with a $50 \%$ chance. Sherry rejects the lottery ticket unless her preferences are given by which of the following?

A) $U(x)=2 \exp ^{-.01 x}$
B) $\quad U(x)=\ln (x)$
C) $U(x)=\sqrt{x}$
D) $U(x)=\frac{x^{\frac{1}{4}}}{\frac{1}{4}}$

Question 16

Suppose I know that Holly always has a certainty equivalent $\left(x_{C E}\right)$ equal to 0 . Which of the following utility functions describes Holly's preferences?

A) $\mathrm{U}(\mathrm{x})=\ln (\mathrm{x})$
B) $\mathrm{U}(\mathrm{x})=\mathrm{x}$
C) $\mathrm{U}(\mathrm{x})=\mathrm{x}$ if $\mathrm{x}>0$ and $\mathrm{U}(\mathrm{x})=-2 \mathrm{x}$ if $\mathrm{x}<=0$
D) $U(x)=\sqrt{x}$

Question 17

The following statements about excepted utility theory are all equivalent except:

A) For all gambles an individual's certainty equivalent equals $0, x_{C E}=0$
B) $\mathrm{E}(\mathrm{u}(\mathrm{x}))=\mathrm{u}(\mathrm{E}(\mathrm{x}))$
C) The individual is risk averse.
D) The individual is risk-neutral.

Question 18

The following statements about excepted utility theory are all equivalent except:

A) For all gambles an individual's certainty equivalent is always greater than $0, x_{C E}>0$
B) If $x^{\prime}>x^{\prime \prime}$ then the slope of $u(x)$ is greater at $u\left(x^{\prime \prime}\right)$ then at $u\left(x^{\prime}\right)$ .
C) The individual is risk averse.
D) The individual is risk-neutral.

Question 19

An individual is risk-loving if his utility function is given by which of the following functional forms:

A) $U(x)=x^{2}$
B) $U(x)=x$
C) $U(x)=2 x$
D) $U(x)=100 x$

Question 20

When an individual focuses on short-term aspects of a decision at the expense of the longterm aspects, then this is called:

A) Addiction.
B) Melioration.
C) Loss Aversion.
D) Risk Aversion.

Question 21

Narrow bracketing of investments in a portfolio of risk assets can lead to which of the following except:

A) Excess exposure to risk.
B) Under exposure to risk.
C) Optimal exposure to risk.
D) No risk in the portfolio.

Question 22

A tendency to broadly bracket decisions may be evidence of

A) A diversification bias.
B) Melioration.
C) A status quo bias.
D) A default option bias.

Question 23

All of the following have been suggested as causes for narrow bracketing except:

A) Timing of decisions
B) Social heuristics.
C) Not knowing one's utility function.
D) Motivation.

Question 24

Why did the CEO fire the president in the first example? Can you replicate the calculations on page 1 and 2 and show that it is likely you would come to the same conclusion?

Question 25

I live for two time periods: today and tomorrow. At the beginning of today, I must choose to smoke cigarettes or not smoke cigarettes. On the first day that I smoke cigarettes, I receive a utility of $2 \bar{u}$ and pay a cost of $c$ . I only receive a utility $\bar{u}$ from smoking on the second day and still pay cost $c$ . But, I also receive a fraction of utility from yesterday's smoking $\delta \in$ $(0,1)$ . If I choose not to smoke on a given day, then my utility is 0 . Let $\bar{u}=10$ , and $c=22$ . I am risk neutral.
a. If I do not choose to start smoking today, will I choose to smoke tomorrow? No. My utility from today is 0 and my utility tomorrow will be -12 if I choose to smoke and 0 if I choose not to smoke.
b. Suppose $\delta=0$ , that is, I carry no utility from smoking today into tomorrow. If I choose to smoke today, will I quit tomorrow?
No. $U($ smoke, smoke $)=u($ today $)+u($ tomorrow $)=(2 * 10-22)+$ $(20+10-22)=6 \cdot U($ smoke, no smoke $)=(2 * 10-22)+0=-2$ .
d. What is the minimum level of $\delta$ that I will smoke today and tomorrow.
$(20-22)+\delta 20+10-22 \geq 0$ . This is always true if $\delta \geq \frac{7}{10}$ .

Question 26

On page 6-21 and 6-22, there is a discussion about how people have under-invested in stocks relative to bonds which can be explained by bracketing. Explain the argument?

Question 27

Suppose my preferences are given by $U=\ln (x)$ .
a. What is my coefficient of absolute risk aversion?
$R_{R}=1$

Question 28

If Sherry's preferences are given by $U(x)=\sqrt{x}$ what is her certainty equivalent of taking a gamble that consists of $\$ 100$ with a $25 \%$ chance and $\$ 25$ with a $75 \%$ chance?

Question 29

Raul is trying to plan what to do on Saturday. He will do one leisure activity in the afternoon and one chore in the morning. His two leisure activity choices are a movie and hiking and his two chore choices are paying bills and mowing the law. He prefers hiking to going to the movies only if it's sunny. And prefers mowing the lawn over paying the bills only if it's sunny. However, what's most important to Raul is to not over-exert himself: mowing the lawn and hiking on the same day is too much activity for Raul.
a. Raul wakes up on Saturday and sees that it's sunny. If the decision for the Saturday's activities is taken simultaneously, how does Raul rank the activities: U(morning activity, afternoon activity)? (Hint: there may be more than one correct answer). $\max _{\text {morning activity } \in(\text { mow,bills })} U$ (morning activity). Choice of morning activity is to mow.
c. It is still sunny in the afternoon when Raul must decide which leisure activity to do. Write down Raul's decision problem in the afternoon and his choice.
$\max _{\text {afternoon activity } \in(\text { hike,movie })} U($ afternoon activity|morning activity). Choice of afternoon activity is to go to the movies.
d. Is Raul better off making decisions sequentially or simultaneously?
Simultaneously. If he had known that it would be sunny all day he would have preferred to do the bills in the morning and then go hiking in the afternoon.
However, he wasn't sure whether the sun would stay out and so he made his choice in the morning only based off his preference for mowing and paying the bills.