Utility Streams and Discounting Models

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What does the discount factor δ represent in the context of utility streams?

The absolute value of all future utilities

The increase in utility over time

The diminishing value of future utility (correct)

The total utility received today

How is the utility of receiving a dollar tomorrow calculated?

$u + δ$

$δ × u$ (correct)

$u × δ^2$

$u / δ$

If today's utility is represented as $u_0$, what does $u_2$ represent?

Utility received today

Utility received two days from now (correct)

Utility received tomorrow

Utility received three days from now

What is the relationship between exponential discounting and the evaluation of utility streams?

Utility streams are discounted uniformly over time. Signup and view all the answers

Which model accounts for the discrepancy between predicted and actual decision-making in relation to future utilities?

Hyperbolic Discounting Signup and view all the answers

What is the formula for utility U0(u) according to the delta model?

$U_0(u) = u_0 + ext{δ}u_1 + ext{δ}^2u_2 + ext{δ}^3u_3 + ...$ Signup and view all the answers

Which utility stream corresponds to the highest present value according to exponential discounting in the delta model?

$4$ at t=2 Signup and view all the answers

What does the parameter δ represent in the context of the delta model?

The discounting factor for future utilities Signup and view all the answers

What are the implications of hyperbolic discounting contrasted with exponential discounting?

Hyperbolic discounting may result in inconsistent preference for immediate rewards over time. Signup and view all the answers

Which of these options best describes the term 'Present-Bias' within the delta model?

A preference for immediate gratification over delayed rewards Signup and view all the answers

What is the primary focus of intertemporal choice?

Evaluating trade-offs between different time periods Signup and view all the answers

What model serves as a behavioral economic alternative to the standard exponential discounting model?

Beta-delta model Signup and view all the answers

Which of the following concepts relates to the perceptions of value over time?

Present-bias Signup and view all the answers

What term describes the decrease in perceived value of future rewards?

Discount rate Signup and view all the answers

What does hyperbolic discounting suggest about people's decision-making?

People prefer immediate rewards over future rewards systematically Signup and view all the answers

In what context might a person experience immediate benefits and deferred costs?

Going for a movie with friends Signup and view all the answers

Which of these is NOT a limitation associated with the exponential discounting model?

Accounts for immediate gratification responses Signup and view all the answers

Which aspect does the delta model primarily examine?

Preferences over time and utility maximization Signup and view all the answers

What characterizes the beta-delta model in behavioral economics?

It combines hyperbolic discounting with a linear form Signup and view all the answers

What value does the discount factor δ take when indifferent between $100 now and $160 in 1 year?

0.79 Signup and view all the answers

When comparing a present value of $100 and a future value of $1000, what does a calculated discount factor of δ = 0.32 imply about the individual?

The individual is relatively impatient. Signup and view all the answers

Which model incorporates both immediate and delayed rewards in intertemporal choice?

Beta-delta model Signup and view all the answers

What is the relationship established when an individual is indifferent between two monetary options?

U 0 (a) = U 0 (b) Signup and view all the answers

How is discounting sometimes expressed instead of using the discount factor?

Discount rate Signup and view all the answers

What utility value does $1000 yield when applying the utility function 0.5?

10 Signup and view all the answers

What is indicated by a higher discount factor in intertemporal choice?

A preference for delayed rewards Signup and view all the answers

Which scenario represents a situation of present bias based on the beta-delta model?

$100 now is preferred over $600 in 2 years Signup and view all the answers

What is a significant limitation of exponential discounting?

It fails to account for temporal loss aversion. Signup and view all the answers

What does the delay speed-up asymmetry illustrate in behavioral economics?

People show a preference for delayed tasks when they align with larger future benefits. Signup and view all the answers

Which effect indicates that people often change their preferences over time?

The date-delay effect Signup and view all the answers

In the beta-delta model, what does β represent?

The weight assigned to the first utility in a utility stream. Signup and view all the answers

What behavior does time inconsistency describe in individuals?

Planning future actions that are later abandoned or altered. Signup and view all the answers

Which of the following is a feature of hyperbolic discounting as opposed to exponential discounting?

It allows for significant changes in preferences as deadlines approach. Signup and view all the answers

What does the 'magnitude effect' refer to in behavioral economics?

The impact of the size of outcomes on people's patience levels. Signup and view all the answers

Which characteristic is NOT associated with quasi-hyperbolic discounting?

Individuals show consistent preference across different time frames. Signup and view all the answers

What is a defining feature of the beta-delta model in comparison to the delta model?

It includes the parameter β. Signup and view all the answers

Under what condition does the beta-delta model reduce to the delta model?

When β = 1. Signup and view all the answers

What happens when β < 1 in the beta-delta model?

Present-biased preferences are exhibited. Signup and view all the answers

In the example involving cake, what utility does eating the cake provide on Saturday?

4 Signup and view all the answers

What is the utility gained from skipping the cake on Saturday if β = 0.5 and δ = 0.67?

3 Signup and view all the answers

What does it mean if a person has present-biased preferences?

They often regret choosing immediate rewards. Signup and view all the answers

Which of the following actions illustrates impulsivity based on the beta-delta model?

Choosing to watch a favorite show instead of studying. Signup and view all the answers

Which limitation is mentioned regarding the beta-delta model?

It cannot explain preferences for improving sequences. Signup and view all the answers

What phenomenon does quasi-hyperbolic discounting help to explain?

Inconsistent future planning behavior. Signup and view all the answers

What is the expected utility of choosing to skip the cake on Friday according to the beta-delta model?

1.67 Signup and view all the answers

Which of the following actions would exhibit time inconsistency?

Choosing a small immediate reward over a future larger reward. Signup and view all the answers

In the context of the beta-delta model, what does the parameter δ refer to?

The discount rate for future utilities. Signup and view all the answers

What type of bias is explained by the beta-delta model?

Present bias in preference. Signup and view all the answers

Which statement about utility streams is accurate within the beta-delta model?

Utility changes based on present versus future choices. Signup and view all the answers

Study Notes

Behavioural Economics

Behavioural economics examines preferences, time, and utility maximisation in standard economic models.
Intertemporal choice refers to decisions involving trade-offs between costs and benefits at different points in time.
Examples include choosing between immediate benefits (e.g., a movie with friends) and deferred costs (e.g., cleaning the house) or vice-versa.
Another example is purchasing a one-year warranty on a new computer, which involves a current loss (warranty cost) versus a possible future loss (repairing the computer).

Exponential Discounting

Exponential discounting models preferences using a discount factor.
In exponential discounting, the utility (U) is multiplied by the discount factor(δ to the power of t).
The discount factor (δ) is a parameter between 0 and 1, representing the rate at which future utility diminishes relative to present utility.
Values closer to 1 indicate greater patience, while values closer to 0 suggest significant impatience.
The utility (U) of receiving a dollar today is multiplied by the discount factor (δ).
Examples calculating the present value of future utility streams using this model are provided in the notes.

Utility Streams

Utility streams represent a sequence of utilities over time.
Uº(u) = u₀ + δu₁ + δ²u₂ + δ³u₃ + ... = Σ δ¹u₁ t=1
't' represents time, = 0 for today, t =1 tomorrow, etc.
u₀ represents utility you receive today, u₁ is utility received tomorrow and so on.

Delta Model

The δ-function is used to calculate the utility of a stream of future utilities at a starting time t=0, resulting in Uº(u)
U°(u) = u₀ + δu₁ + δ²u₂ + δ³u₃ + ..
Examples of how to apply the δ-function are presented.
If δ = 0.9 then Uº(a)=1+2.7+3.24=6.94, Uº(b)=1.33 and for Uº(c)= 1.67.

Discount Rates

Discount rates represent the rate at which future utility declines relative to present utility.
The relationship between discount rates and discount factors is r = (1 - δ) / δ
if δ = 0.79, r=0.27.
Examples demonstrating the conversion between discount factors, and rates are provided in the notes

Limitations of Exponential Discounting

The exponential discounting model, while useful, has limitations.
The model assumes time-consistent preferences.
Individuals' preferences over time may change, or they might value immediate gratification over a future reward, implying time inconsistency.
Further shortcomings to the model are the "sign effect", "magnitude effect", "temporal loss aversion", "delay speed-up asymmetry & preference for improving sequences", and "date-delay effect & violations of independence."

Quasi-Hyperbolic Discounting (Beta-Delta Model)

The beta-delta model extends the exponential model by introducing a present-bias parameter, β.
This model can explain situations where a person's preferences are inconsistent over time. It assumes that future rewards are discounted less than other situations.
The present bias implies more weight is given to rewards that occur immediately than future ones, meaning the future is often devalued. It assumes that the preference for a smaller, earlier reward is higher compared to a larger, later reward.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz explores key concepts related to utility streams, discount factors, and intertemporal choice models like the delta model. Participants will answer questions regarding the calculation of utility and the differences between exponential and hyperbolic discounting. Gain insight into decision-making processes related to future utilities and present-bias within economic theories.