Deck 12: Naïve Procrastination

Question 1

An infinite horizon model is an attractive way to model consumption decisions because it allows for consumption choices in any given period to interact with preferences for consumption in every other period.

Answer 1

True

Question 2

Consider a fully additive model with one consumption good, $U\left(c_{i}\right)$ , where $i$ indexes time.
$u\left(c_{i}\right)=u\left(c_{j}\right) \forall i \neq j$ if and only if $c_{i}=c_{j}$ .

Answer 2

True

Question 3

The full additive model does not assume exponential time discounting.

Answer 3

False

Question 4

Graham gets 10 units of utility from consuming an apple today, but needs 3 apples
tomorrow to achieve the same level of utility. Graham's discount factor is only $\frac{1}{3}$ if he is riskneutral.

Question 5

The discount factor, $\delta$ , is a measure of patience because it indicates how much an individual must be compensated in order to postpone utility.

Question 6

Consider a fully additive model with one consumption good, $U\left(c_{i}\right)$ , where $i$ indexes time. If $\delta<1$ then the fully additive model predicts $c_{i}<c_{j} \forall i<j$ .

Question 7

Exponential time discounting implies stationarity.

Question 8

Time preferences that do not satisfy stationarity are a form of projection bias: the individual is unable to predict how their preferences will change when they reach a future time period.

Question 9

Consumption smoothing implies that if the discount factor is close to 1 , then optimal consumption across time will be nearly constant.

Question 10

An individual with present biased preferences must be a hyperbolic discounter.

Question 11

Quasi-hyperbolic discounting is a two-part time discount function: one part is identical to exponential time discounting and the second part adds an additional discount to near future time periods.

Question 12

One behavioral feature of a naïve quasi-hyperbolic discounter is that they always plan to bear a utility cost "tomorrow" in order to reap the benefits in the "day after", but tomorrow arrives, their utility- maximizing choice is to postpone costs until the following the day.

Question 13

Delay-speedup asymmetry refers to the finding that individuals must be compensated more to delay consumption than they are willing to pay to speed up consumption.

Question 14

The absolute magnitude effect identifies that empirical discount factors are smaller when larger magnitudes of money are being considered.

Question 15

Hyperbolic discounting means that the function form of the discount factor changes over time.

Question 16

Procrastination and the hot-cold empathy gap can both result from

A) Loss aversion.
B) Risk aversion.
C) Time inconsistent preferences.
D) Overconfidence.

Question 17

An infinite planning horizon refers to

A) An infinite number of tasks to complete.
B) An infinite number of time periods over which to plan consumption.
C) An infinite amount of wealth.
D) An infinite number of individuals making a decision today.

Question 18

A fully additive model of the utility function $U\left(c_{1, i}, c_{2, i}\right)$ , where $i$ indexes time and $c_{1}$ and $c_{2}$ are two different goods, has which features?

A) Utility is additive across $i$ (time).
B) Utility is additive across goods 1 and 2, but not across $i$ (time).
C) Utility is neither additive across goods or time.
D) Utility is additive across $i$ (time), but the function form may change in each time period.

Question 19

Consider a fully additive model with two consumption goods, $U\left(c_{1, i}, c_{2, i}\right)$ , where $i$ indexes time. Suppose in the first period, $i=0, U\left(c_{1,0}, c_{2,0}\right)=u\left(c_{1,0}\right)+u\left(c_{2,0}\right)$ and $\frac{u^{\prime}\left(c_{1,0}\right)}{u^{\prime}\left(c_{2,0}\right)}=k$ , then which of the following is an assumption of the fully additive model?

A) $\frac{u^{\prime}\left(c_{1,2}\right)}{u^{\prime}\left(c_{2,2}\right)}=2 k$
B) $\frac{u^{\prime}\left(c_{1,2}\right)}{u^{\prime}\left(c_{2,2}\right)}=k$
C) $\frac{u^{\prime}\left(c_{1,2}\right)}{u^{\prime}\left(c_{2,2}\right)}=k^{2}$
D) $\frac{u^{\prime}\left(c_{1,2}\right)}{u^{\prime}\left(c_{2,2}\right)}=k+2$

Question 20

Let $\delta^{t-t^{\prime}}$ be the discount factor between $t$ and $t^{\prime}$ , where $t>t^{\prime}$ . Stationarity implies which of the following must be true?

A) $\delta^{200-191}<\delta^{109-100}$
B) $\delta^{200-191}=\delta^{110-100}$
C) $\delta^{200-191}>\delta^{109-100}$
D) $\delta^{200-191}=\delta^{109-100}$

Question 21

Lucas must make consumption decisions over three time periods, $t=0,1,2$ . His preferences do not satisfy stationarity and he values current consumption more than future consumption. Let $\delta_{1}$ be the discount factor on consumption that is one period in the future and $\delta_{2}$ be the discount factor on consumption that is two periods into the future. Which of the following is true?

A) $\delta_{1}=\delta_{2}$
B) $\delta_{1}>\delta_{2}$
C) $\delta_{1}=1$
D) $\delta_{1}<\delta_{2}$

Question 22

Hyperbolic discounting was introduced as a solution to which violation of the fully additive model:

A) Stationarity.
B) Regret.
C) Time inconsistent preferences.
D) Loss aversion.

Question 23

Let $\delta^{t-t^{\prime}}$ be the discount factor between $t$ and $t^{\prime}$ , where $t>t^{\prime}$ . Naïve hyperbolic discounting implies which of the following is true?

A) $\delta^{200-191}<\delta^{9-0}$
B) $\delta^{200-191}=\delta^{10-0}$
C) $\delta^{200-191}>\delta^{9-0}$
D) $\delta^{200-191}=\delta^{9-0}$

Question 24

The common difference effect is:

A) A preference reversal.
B) Loss aversion.
C) Violation of transitivity.
D) Violation of stationarity.

Question 25

An individual's empirical discount factor and "true" discount factor coincide when the individual is

A) Risk averse only.
B) Risk neutral only.
C) Time consistent.
D) Loss Averse.

Question 26

The finding that individuals are willing to delay losses more than they are willing to delay gains is known as

A) The absolute magnitude effect.
B) The common difference effect.
C) Gain-loss asymmetry.
D) Prospect theory.

Question 27

The model presented in 12.67 and 12.68 combines hyperbolic discounting with prospect theory in order to address all of the following anomalies EXCEPT

A) The common difference effect.
B) Gain-loss asymmetry.
C) Loss aversion.
D) The absolute magnitude effect.

Question 28

In the model presented in 12.67 and 12.68 , which parameter addresses the common difference effect?

A) $\alpha$
B) $\beta$
C) $v(c \mid k)$
D) $t$

Question 29

In the model presented in 12.67 and 12.68 , which parameter addresses the gain-loss asymmetry?

A) $\alpha$
B) $\beta$
C) $v(c \mid k)$
D) $t$

Question 30

Equation 12.26 shows that $\Psi(j, k)=\left(\frac{1+\alpha k}{1+\alpha j}\right)^{-\left(\frac{\beta}{\alpha}\right)}$ . Use this equation to show that $\Psi(90,100)>\Psi(0,10)$ if $\alpha \neq 0$ .

Question 31

Graham gets 10 units of utility from consuming an apple today, but needs 3 apples tomorrow to achieve the same level of utility. What is Graham's discount factor?

Question 32

One property of exponential time discounting is that when an individual is making a decision today about consumption in the future, they put very little weight on their utility in the distant future.
Find $\lim _{t \rightarrow \infty} \delta^{t}$

Question 33

The text states that equation 12.14 will always be consistent with 12.11 if $\delta_{3}=\delta_{2}^{2}$ . Why?