Deck 11: Disagreeing With Ourselves: Projection and Hindsight Biases

Question 1

Hindsight bias occurs when we do not perfectly remember the information our past self had at the time of making a decision.

Answer 1

True

Question 2

Time inconsistent preferences are a bias.

Answer 2

False

Question 3

Hindsight bias, projection bias and time inconsistent preferences can only occur in situations in which decisions are made in at least two time periods.

Answer 3

True

Question 4

Suppose you wanted to write down a model of addiction, where $c_{1}$ is drug use today and $c_{2}$ is drug use tomorrow. You want to model the idea that more drug use today increases the utility of drug use tomorrow. One way to capture this relationship is to model $c_{1}$ and $c_{2}$ as complements.

Question 5

In the college admissions example, projection bias occurs because the prospective student does not incorporate the utility of their future-self under alternative weather.

Question 6

Consider the following inter-temporal choice problem, where $s^{\prime}$ is the state today and $s$ is the state tomorrow. $\max _{c_{1}} u\left(c_{1}, s^{\prime}\right)+\delta\left[(1-\alpha) u\left(w-c_{1}, s\right)+\alpha u\left(w-c_{1}, s^{\prime}\right)\right.$ . This problem reduces to the rational model of inter-temporal choice when $\alpha=1$ .

Question 7

Consider the following inter-temporal choice problem, where $s^{\prime}$ is the state today and $s$ is the state tomorrow. $\max _{c_{1}} u\left(c_{1}, s^{\prime}\right)+\delta\left[(1-\alpha) u\left(w-c_{1}, s\right)+\alpha u\left(w-c_{1}, s^{\prime}\right)\right.$ . This problem reduces to the rational model of inter-temporal choice when $\delta=1$ .

Question 8

Time inconsistent preferences means that $\delta<1$ .

Question 9

Using projection bias to describe addictive behaviors allows us to model the idea that individuals were not aware of how consumption today would affect their desire to consume tomorrow.

Question 10

Rational models of addiction assume that the effect of today's consumption on tomorrow's consumption is predictable. This is in contrast to the projection bias models of consumption, in which the addictive property is not predictable.

Question 11

Visceral factors may drive individuals to make decisions in a similar fashion to projection bias.

Question 12

The hot state is today "today" in inter-temporal choice with projection bias, as the cold state is to "tomorrow" in inter-temporal choice with projection bias.

Question 13

One way to model the hot-cold empathy gap is to put the visceral state directly into the utility function as a continuous variable $s$ . As $s$ increases, the individual becomes "hotter."

Question 14

The hot-cold empathy gap refers to individual's inability to understand other's feelings.

Question 15

Consider equation 11.33 and the model presented above. The interpretation of equation 11.33 is that for $\left(\overline{x_{1}}, \overline{x_{2}}\right)$ utility decreases as the individual's state becomes hotter. That is, without adjusting consumption of $x_{1}$ and $x_{2}$ , the individual becomes worse off as they experience a hotter visceral state.

Question 16

Consider equation 11.34 and the model presented above. The interpretation of equation 11.34 is that for a given $x_{2}$ , the marginal utility I receive from $x_{1}$ increases as my visceral state becomes hotter. That is, without adjusting consumption of $x_{2}$ , as my visceral state becomes hotter than the marginal utility I get from an increase in $x_{1}$ increases.

Question 17

Projection bias occurs when

A) An individual believes that others currently share his preferences.
B) An individual believes that others have the same income as he.
C) An individual believes his future self will have the same preferences as his current self.
D) An individual believes that others' future selves will have the same preferences as his current self.

Question 18

Inter-temporal choice refers to

A) Scenarios in which decisions made today affect the possible choices that can be made tomorrow.
B) Scenarios in which you much decide on which day to consume.
C) Scenarios in which you make consumption decisions today and another individual makes consumption decisions tomorrow.
D) Scenarios in which all decisions about consumption are made simultaneously.

Question 19

Consider a model of inter-temporal choice, with utility function $u\left(c_{1}, c_{2}\right)$ . If $c_{1}$ and $c_{2}$ are substitutes then which of the following must be true?

A) $\frac{\partial u\left(c_{1}, c_{2}\right)}{\partial c_{1}}>0$ .
B) $\frac{\partial u\left(c_{1}, c_{2}\right)}{\partial c_{2}}<0$
C) $\frac{\partial^{2} u\left(c_{1}, c_{2}\right)}{\partial c_{1} \partial c_{2}}>0$ .
D) $\frac{\partial^{2} u\left(c_{1}, c_{2}\right)}{\partial c_{1} \partial c_{2}}>0$

Question 20

Consider a model of inter-temporal choice, with utility function $u\left(c_{1}, c_{2}\right)$ . If $c_{1}$ and $c_{2}$ are complements then which of the following must be true?

A) $\frac{\partial u\left(c_{1}, c_{2}\right)}{\partial c_{1}}>0$
B) $\frac{\partial u\left(c_{1}, c_{2}\right)}{\partial c_{2}}<0$
C) $\frac{\partial^{2} u\left(c_{1}, c_{2}\right)}{\partial c_{1} \partial c_{2}}>0$
D) $\frac{\partial^{2} u\left(c_{1}, c_{2}\right)}{\partial c_{1} \partial c_{2}}<0$

Question 21

In the college admissions example, which of the following describes a student who exhibits time inconsistent preferences?

A) Joe visited UState on a sunny day. Despite the great parties at UState, Joe knows he needs to study hard to keep is scholarship. Joe decides to attend UState.
B) Joe visited UState on a sunny day and saw how much fun he would have there. He decides to attend UState and soon realizes that UState is only fun in the summer and spring and during other times of the year there is nothing to do. He finds himself
Constantly traveling to UCity to visit friends because there is so much more to do in the city. He wishes he would have attended UCity.
C) Joe visited UCity on a cold day. He liked UCity because it was close to the museums and there were lots of restaurants, but he decides to attend UState.
D) Joe visited UCity on a sunny day. The weather in the city felt really hot and he wished he was on a big, grassy campus so that he could relax in the shade. But, Joe attends UCity anyways.

Question 22

Which of the following statements about the projection bias is true?

A) There are instances when the solution to the optimization problem of an individual with a projection bias coincides with the solution to the optimization problem if the individual did not exhibit the projection bias.
B) Some individuals gain additional utility from a projection bias.
C) Individuals who make decisions with a projection bias are always worse off than in the absence of such a bias.
D) Individuals who make decisions with a projection bias are sometimes better off than in the absence of such a bias.

Question 23

Consider equations 11.20 and 11.21. When $\alpha=1$ , which of the following gives a correct interpretation of the $x_{c, 1}$ and $x_{c, 2}$ ?

A) $\quad x_{c, 1}=x_{c, 2}$ because the individual is unable to predict how coffee consumption in $\mathrm{t}=1$ will affect their preference to drink coffee in $\mathrm{t}=2$ .
B) $x_{c, 1}=x_{c, 2}$ because the individual is unable to afford additional coffee in $\mathrm{t}=2$ because he consumed too much coffee in $\mathrm{t}=1$ .
C) $x_{c, 1}<x_{c, 2}$ because the individual drank coffee in $\mathrm{t}=1$ he formed an addiction and now must drink more coffee in $\mathrm{t}=2$ to be satisfied.
D) $\quad x_{c, 1}>x_{c, 2}$ because the individual drank a lot of coffee in $\mathrm{t}=1$ and thought he would become addicted, but then when he reached $\mathrm{t}=2$ he realized he was not actually addicted to coffee.

Question 24

Consider example 4. The authors wanted to know whether people had a tendency to buy cold-weather clothes through catalogs when the current weather in their location was cold due to a projection bias. Showing that purchases of winter gear increased during cold
Weather provide confirmatory information. What piece of information provides disconfirmatory information?

A) Knowing whether they were less likely to enjoy the gear they bought during the cold weather.
B) Knowing whether they were more likely to also purchase warm weather gear during the cold weather.
C) Knowing whether they were more likely to purchase warm weather gear on hot days.
D) Knowing whether they were more likely to enjoy the cold weather gear they bought during warm weather.

Question 25

The hot state refers to which of the following:

A) When individuals make decision based on the hot weather today and they fail to predict that it might be cold tomorrow.
B) When a visceral factor is active.
C) When a visceral factor is inactive.
D) When individuals are unable to predict future hot weather.

Question 26

All of the following are types of preferences and behaviors that can be attributed to the hotcold empathy except

A) Feelings of regret.
B) Self-control problems.
C) Extreme risk preferences.
D) Ambiguity aversion.

Question 27

Consider Figure 11.1. Billy has a utility function given by $u\left(c_{1}, c_{2}\right)=\ln \left(c_{1}\right)+\delta \ln \left(c_{2}\right)$ and a budget constraint given by $c_{1}+c_{2} \leq 100$ . Where $c_{1}=$ hamburgers today and $c_{2}=$ hamburgers tomorrow, and $p_{1}=p_{2}=1$ .
a. What is the slope of Billy's indifference curve at any point $\left(c_{1}, c_{2}\right)$ ?
b. What is the slope of Billy's budget line?
c. At any optimal solution to Billy's utility maximization problem, it must be true that $\frac{c_{2}}{\delta c_{1}}=1$ .
d. Suppose Billy spends all of his income on hamburgers today and tomorrow. If $\delta=1$ , what percentage of his income is spent on hamburgers tomorrow?
e. If $\delta=.8$ , what percentage of his income is spent on hamburgers tomorrow?
f. In general, as $\delta$ decreases, hamburger consumption tomorrow increases.

Question 28

Using the utility function given in 11.35 , show that 11.33 is true.

Question 29

Using the utility function given in 11.35 , show that 11.34 is true.