E 1035 Veritas University Utility Theory Presentation

Description

Assume that you and your significant other (either real or imagined) are thinking about taking a vacation next year.What can you do to maximize the benefit you’ll get from your overall experience?

2 attachmentsSlide 1 of 2attachment_1attachment_1attachment_2attachment_2.slider-slide > img { width: 100%; display: block; }
.slider-slide > img:focus { margin: auto; }

Unformatted Attachment Preview

Economics E-1035
Behavioral Economics and Decision Making
Utility, Choice, Efficiency, and Happiness
November 4, 2021
© Wilson Alan LLC | +1.978.402.8844 | Jon.Fay@WilsonAlan.com
Decision frameworks, tools and biases
Neoclassical
Economics
Managerial
Economics
Decision
Heuristics
Behavioral
Economics
Economic
ideal
Analytical
approximations
Rules of
thumb
Predictable
biases
Complexity
Optimization
Linear Programming
Uncertainty
Risk Aversion
Decision Tree
Temporality
Discount Rate
Community
Market Efficiency
• Bounded Rationality
• Commitment Strategy
• Mental Accounts
• Decision Strategy
• Mathematical
Shortcuts
• Expert Instincts
• Paradox of Choice
• Anchoring
• Confirmation Bias
• Survivorship Bias
• Availability Bias
• Goldilocks/Decoy Effects
• Halo Effect
• Estimation Heuristics
• Decision Strategies
• Breakeven
• Overage/Underage
• Fast-and Frugal Trees
• Bayesian Probability
• Loss Aversion
• Probability/Certainty
• Fourfold Pattern
• Allais Paradox
Discounted Cash Flow
• NPV
• IRR as breakeven
• Payback Period
• Commitment Strategy
• Negotiate w/ Future Self
• Breaking Up Tasks
• Present Bias
• Sunk Cost Fallacy
• Endowment Effect
• Status Quo Bias
• Dynamic Inconsistency
• Procrastination
Game Theory
• Tit-for-Tat
• Norms, Fairness
• Bright Lines
• Reasonable Expectations
• Collective Commitment
• Bandwagon Effect
• Positional Comparison
• Conspicuous Consumption
• Positional Arms Races
• Group Identification
• Peer pressure
• Altruism
Nash Equilibrium
© DSMcIntosh LLC
Page
1
Session 9: Taking others into account
PEOPLE
MARKETS
Games
First,
See the
Patterns
Consider
the Issues
& Actions
Bubbles
Cooperation
Corrections
• One round or many?
• Accelerating values
• Communication?
• Any natural dampers?
• Look for
opportunities to
cooperate
• Make adjustments for
winner’s curse and
non-Nash behaviors
• Grow the payoffs
• Create guardrails and
circuit breakers
• Share the pie fairly
• Punish defectors
Evaluate
© DSMcIntosh LLC
Am I getting the best likely outcome?
Influences
Comparison
Altruism
Compassion
• Are others influencing
you?
• Understand your
motivation
CONFORMING
• Bandwagon Effect
• Group identification
• Peer pressure
Understand your motivation
• Impact and legacy
• Self-image
• Recognition
COMPETING
• Positional comparison
• Conspicuous consumption
• Positional arms races
Does this really make me happier?
Page
2
Does self interest lead to efficient outcomes?
Markets, Self-Interest, and Efficiency
Games, Self-Interest, and Inefficiency
“Every individual … neither
intends to promote the
public interest, nor knows
how much he is promoting
it … he intends only his
own security; and by directing that industry in
such a manner as its produce may be of the
greatest value, he intends only his own gain,
and he is in this, as in many other cases, led
by an invisible hand to promote an end which
was no part of his intention.”
“Efficient Markets … [are]
driven by enlightened selfinterest (also known as
greed) … It’s worth pointing
out that ‘greed’ isn’t a
pejorative term to an
economist.”
— Andrew Lo, MIT
© DSMcIntosh LLC
Page
3
Utility
Utility is the sum of all
pleasures that result
from an action, minus
suffering that results
from the action
“Utility is taken to be
correlative to Desire or Want.
It has been already argued that
desires cannot be measured
directly, but only indirectly, by
the outward phenomena to
which they give rise: and that
in those cases with which
economics is chiefly concerned
the measure is found in the
price which a person is willing
to pay for the fulfillment or
satisfaction of his desire.”
Alfred Marshall
1842-1924
Founder of
Neoclassical
Economics
Jeremy Bentham
1748-1832
Founder of
Utilitarianism
© DSMcIntosh LLC
What was different about Marshall’s
reformulation of “Utility”?
Page
4
Modeling utility: Assumption #1
>
If
>
And
Transitivity
© DSMcIntosh LLC
Then
>
Page
5
Modeling utility: Assumption #2
If
Then
Decreasing Rate of
Marginal Substitution
© DSMcIntosh LLC
Page
6
Modeling utility: Assumption #3
Given a set of options …
You know which one you prefer …
… or at least which ones you are indifferent between
Completeness
© DSMcIntosh LLC
Page
7
Neoclassical economic definition of rationality
Behavioral biases cause
inconsistent choices
As a neoclassical economist
• I can’t judge your preference function
• I can judge the consistency of your choices
Which are irrational from
an economic perspective
Because they represent
arbitrage opportunities
Choosing peach, instead
of buying nothing …
but then buying nothing,
instead of choosing peach
Reducing
financial
risk …
Deciding to run …
© DSMcIntosh LLC
… and then sleeping in
while
also
buying
lottery
tickets
Page
8
Neoclassical utility theory: Summary
In economics, “Utility” Theory is about Preference Ordering, not utility
• When a person is faced with a choice of A or B, do they choose A, or B, or are
they indifferent between them?
Happiness
“Utils”
• All that matters is what you choose – no need to measure the “utility” of that choice
Preference Ordering is about Choice, not preference
• We can’t let people actually make all possible choices
• And stated preferences may not map to actual choices
Preferences
Choices
Utility Index
• So “Revealed Preference” theory models preference functions from the limited
choices we do see
To build these models, the Preference Function is assumed to have certain properties:
• Your preference function is given (and your brain knows it even if you don’t
consciously)
• The arguments of the preference function are product quantities and attributes –
market prices and endowments define the constraints
• Preference ordering is complete and transitive
• Preferences exhibit diminishing marginal rate of substitution, so indifference curves
bow towards the origin (not strictly necessary, but it makes the models work better)
© DSMcIntosh LLC
Page
9
Markets are built up from preference functions
Utility maximization by consumers:
Preference Function
(indifference curves)
Y
Demand Curves
$
Drive market prices
and adjustments
$
X
X
And profit maximization by firms:
X
Production Function
(cost curves)
Y
$
X
© DSMcIntosh LLC
Supply Curves
X
Page 10
What if transitivity isn’t always true?
Non-transitive dice
Die #1: 1, 2, 5, 6, 7, 9
Die #2: 1, 3, 4, 5, 8, 9
Die #3: 2, 3, 4, 6, 7, 8
#2 beats #1 : 19/36
#3 beats #2 : 19/36
#1 beats #3 : 19/36
© DSMcIntosh LLC
Page 11
Available choices can drive decision criteria
Preference
between two
fruit desserts …
>
Preference between
two chocolate
desserts …
>
>
© DSMcIntosh LLC
Preference
between two
pie desserts …
Page 12
The rationality spectrum
Rationality
Economics
Psychology
Managerial &
Behavioral
Economics
Irrationality
Assumes a high degree of Rationality
Rational
Perfect
Rationality
Irrational
Documents a high degree of Irrationality
Analytical
Rationality
Neoclassical Economics
provides a rigorous if idealized
definition of Rationality
Reasonable
Rationality
Genuine
Irrationality
Behavioral Economics
explains when it’s dangerous
to assume Rational behavior
Managerial Economics and Heuristics provide tools
for making pretty good decisions, most of the time
© DSMcIntosh LLC
Page 13
Should I go to Europe for vacation next year?
Past
Remembered Utility
Satisfaction
“I’ll have a
lifetime of
memories”
© DSMcIntosh LLC
Present
Experienced Utility
Future
Expected Utility
Enjoyment
Anticipation
“I’ll have so
much fun”
“I love both the
planning and
just knowing
that it’s going to
happen”
Page 14
Six components of utility
Past
Remembered Utility
© DSMcIntosh LLC
Present
Experienced Utility
Future
Expected Utility
Satisfaction
Enjoyment
Anticipation
Regret
Displeasure
Dread
Page 15
Past: Remembered utility
© DSMcIntosh LLC
Past
Present
Future
Remembered Utility
Experienced Utility
Expected Utility
Satisfaction
Enjoyment
Anticipation
Regret
Displeasure
Dread
Page 16
Regret and rationality
• The two easily applied tests of rationality
are arbitrage and regret
– Arbitrage exists (in neoclassical economics)
because of a failure of consistency, across
prices, risks, or time
– Regret exists (in behavioral economics) when
we look back at a decision we made and
realize that if we were to do it again, we
would make a different choice
• Not because a gamble didn’t pay off
• Not because we didn’t have enough time to
think through the problem
• But rather, because a behavioral bias or blind
spot led to a careless decision
• Regret illuminates decisions that can be
seen, in hindsight, as irrational
© DSMcIntosh LLC
Photo credit : BBC.com
Page 17
Redelmeier, Katz, Kahneman (2003)
© DSMcIntosh LLC
Page 18
Redelmeier, Katz, Kahneman (2003)
Which patient experienced more discomfort?
Which patient reported a worse experience?
Which patient was more likely to schedule their next colonoscopy?
What behavioral bias that we’ve studied is at play here?
© DSMcIntosh LLC
Page 19
Past: Remembered utility
Past
Remembered Utility
Experienced Utility
Future
Expected Utility
Satisfaction
Enjoyment
Anticipation
Regret
Displeasure
Dread
Imperfect memory
Availability bias
Peak-end bias
IKEA effect
Behavioral
Biases
•
•
•
•
Impact of
Other People
• Social comparison
• Fairness
• Altruism
Strategies
•
•
•
•
© DSMcIntosh LLC
Present
Resilience
Selective memory
Framing
Ignoring sunk costs
Page 20
Present: Experienced utility
Past
Remembered Utility
© DSMcIntosh LLC
Present
Experienced Utility
Future
Expected Utility
Satisfaction
Enjoyment
Anticipation
Regret
Displeasure
Dread
Page 21
Present: Experienced utility
How do you define happiness?
Past
Remembered Utility
Present
Experienced Utility
Future
Expected Utility
Compared to …
• Past experiences
• Hoped-for outcome
• Expected outcome
• What you enjoy
• What others have
© DSMcIntosh LLC
Page 22
Does only money make us happy?
Would you perform a
given task for:
175
Effort (circles moved)
? No payment
? $.50
? $5.00
200
150
125
Candy
100
Cash
$ Candy
75
50
25
0
None
Low
High
Reward
Source: Predictably Irrational, by Dan Ariely
© DSMcIntosh LLC
Page 23
Does only money make us happy?
Would you perform a
given task for:
? No payment
? Candy bar
? Box of chocolates
175
Effort (circles moved)
? No payment
? $.50
? $5.00
200
150
125
Candy
100
Cash
$ Candy
75
50
25
0
None
Low
High
Reward
Source: Predictably Irrational, by Dan Ariely
© DSMcIntosh LLC
Page 24
Does only money make us happy?
Would you perform a
given task for:
? No payment
? Candy bar
? Box of chocolates
No payment
$.50 bar of candy
$5.00 box of
chocolates
175
Effort (circles moved)
? No payment
? $.50
? $5.00
200
150
125
Candy
100
Cash
$ Candy
75
50
25
0
None
Low
High
Reward
Source: Predictably Irrational, by Dan Ariely
© DSMcIntosh LLC
Page 25
Incentives and monetization
Monetary incentives:
No monetary incentives:
The AARP asked a group of
lawyers to provide legal services
to needy retirees, offering to pay
them $30 / hour.
The AARP asked a group of
lawyers to provide legal services
to needy retirees, asking them to
volunteer their time.
Which offer got the greater response from the lawyers?
Why do you think that was the case?
The monetization of certain activities can crowd out the intrinsic
motivations that would lead people to perform the tasks
without compensation.
Source: Predictably Irrational, by Dan Ariely
© DSMcIntosh LLC
Page 26
What’s the incentive?
© DSMcIntosh LLC
Page 27
Engagement
A state of focused
concentration and
absorption in a task
where you lose track
of time. It comes about
when you are engaged
in a challenge that you care about
and that you have a decent
possibility of succeeding at.
High
Arousal
Anxiety
Challenge
Control
Worry
Low
Apathy
Low
Relaxation
Boredom
Skills
High
Source: Flow: The Psychology of Optimal Experience, by Mihaly Csikszentmihalyi (1990); Wired September 1996
© DSMcIntosh LLC
Page 28
Csikszentmihalyi describing flow
”…being completely involved in an
activity for its own sake. The ego
falls away. Time flies. Every action,
movement, and thought follows
inevitably from the previous one,
like playing jazz. Your whole being
is involved, and you’re using your
skills to the utmost.”
Source: “Go with the Flow,” Wired, September 1996
© DSMcIntosh LLC
Page 29
Maximizing flow
Situations where flow arises
Behavioral hacks
• Sports (playing > watching)
• Be clear about the goal
• Art (making > enjoying)
• Remove distractions
• Cooking and other hobbies
• Deadlines are your friend
• Social interactions
• Leverage peer pressure
• Work
• Feel moments of progress
Underlying behavioral factors
• Switching costs for engaging System 2
• Availability bias
• Now bias and hyperbolic discounting
• Commitment strategy
• Peer pressure
• Past, present, and future utility
© DSMcIntosh LLC
Page 30
Present: Experienced utility
Past
Present
Remembered Utility
Experienced Utility
Expected Utility
Satisfaction
Enjoyment
Anticipation
Regret
Displeasure
Dread
Behavioral
Biases
•
•
•
•
Imperfect memory
Availability bias
Peak-end bias
IKEA effect
•
•
•
•
Endowment effect
Group identification
Hedonic treadmill
Status quo bias
Impact of
Other People
• Social comparison
• Fairness
• Altruism
•
•
•
•
Social comparison
Fairness
Altruism
FOMO
Strategies
•
•
•
•
© DSMcIntosh LLC
Future
Resilience
Selective memory
Framing
Ignoring sunk costs
• Resilience
• Flow / Engagement
• Calibrate and
commiserate
Page 31
Future: Expected utility
Past
Remembered Utility
© DSMcIntosh LLC
Present
Experienced Utility
Future
Expected Utility
Satisfaction
Enjoyment
Anticipation
Regret
Displeasure
Dread
Page 32
Should I go to Europe for vacation next year?
Past
Remembered Utility
Satisfaction
“I’ll have a
lifetime of
memories”
© DSMcIntosh LLC
Present
Experienced Utility
Future
Expected Utility
Enjoyment
Anticipation
“I’ll have so
much fun”
“I love both the
planning and
just knowing
that it’s going to
happen”
Page 33
Should I go to Europe for vacation next year?
Satisfaction
U = u0 +
© DSMcIntosh LLC
? u1
(1 + ?)1
+
Enjoyment
? u2
(1 + ?)2
+
? u3
(1 + ?)3
Anticipation
+
? u4
(1 + ?)4
+ …
Page 34
But we don’t know today what will make us happier tomorrow
U = u0 +
?
? ut / (1 + ?)t
t
Choosing for Today
Fruit
U = 3 + (.5)(0) / (1+0)1
=3+0
=3
? = .5
?=0
Immediate
Utility (u0)
Subsequent
Utility (ut)
Fruit
3
0
Chocolate
6
-4
Choosing for Tomorrow
U = 0 + (.5)(3) / (1+0)1 + (.5)(0) / (1+0)2
= 0 + 1.5 / 1 + 0 / 1
= 0 + 1.5 + 0
= 1.5
U = 6 + (.5)(- 4) / (1+0)1
Chocolate
= 6 + (- 2) / 1
=6–2
=4
U = 0 + (.5)(6) / (1+0)1 + (.5)(- 4) / (1+0)2
= 0 + 3 + (- 2) / 1
=0+3–2
=1
Experiment: Read and van Leeuwen (1998); Example: Prof. Laibson, Ec 1030
© DSMcIntosh LLC
Page 35
Magnitude effect
Small
Prefer:
Gain
Prefer:
$10 today
$11 in a year
$1,000 today
$1,050 in a year
HIGH discount rate
Normal discount rate
Prefer:
Loss
LARGE
What motivates us to
“rip off the Band-Aid”?
Prefer:
($10) today
($9.70) in 6 months
($1,000) today
($1,070) in 6 months
NEGATIVE discount rate
Normal discount rate
People use System 2 when making decisions about larger gains and losses.
For smaller gains or losses, the System 1 instinct is to deal with it now (due to present bias)
People’s intertemporal choices can be nudged by:
• Rolling up a payoff as a lump sum, today
• Breaking up a payment into smaller pieces, spread out over time
Source: David Hardisty, Kirstin Appelt, & Elke Weber (2009, 2012)
© DSMcIntosh LLC
Page 36
Wages and the Ratchet Effect
Contract negotiations, as a whole, have demonstrated that workers
prefer wages that increase over time:
• Wages increase, even if less than inflation
• Layoffs for some, rather than wage cuts for all
• Pay based on seniority, not (just) productivity
Is this related to the hedonic treadmill?
What behavioral biases / factors might be at play here?
© DSMcIntosh LLC
Page 37
It Gets Better
• In 2010, advice columnist Dan Savage
and his partner Terry Miller posted a
YouTube video
• The goal was to reduce suicide and self
harm among LGBTQ youths faced with
bullying, exclusion, and hopelessness
• To date, 70,000 others have posted their
own “it gets better” story, including
Barack and Michelle Obama, George
Takei, Lady Gaga, and Joe Biden
“I wish I could have talked to this kid for
five minutes. I wish I could have told Billy
that it gets better. I wish I could have told
him that, however bad things were,
however isolated and alone he was, it gets
better.”
— Dan Savage
© DSMcIntosh LLC
Page 38
Future: Expected utility
Past
Present
Remembered Utility
Future
Expected Utility
Experienced Utility
Satisfaction
Enjoyment
Anticipation
Regret
Displeasure
Dread
Behavioral
Biases
•
•
•
•
Imperfect memory
Availability bias
Peak-end bias
IKEA effect
•
•
•
•
Endowment effect
Group identification
Hedonic treadmill
Status quo bias
•
•
•
•
•
•
Present self vs. Future self
(Quasi) Hyperbolic discounting
Assessing probabilities and payoffs
Loss aversion
Choice fatigue
Gambler’s bias
Impact of
Other People
• Social comparison
• Fairness
• Altruism
•
•
•
•
Social comparison
Fairness
Altruism
FOMO
•
•
•
•
Social comparison
Bandwagon effect
Altruism
FOMO
Strategies
•
•
•
•
• Resilience
• Flow / Engagement
• Calibrate and
commiserate
•
•
•
•
Commitment strategies
Satisficing
Limiting available choices
Certainty / possibility effect
© DSMcIntosh LLC
Resilience
Selective memory
Framing
Ignoring sunk costs
Page 39
Let’s talk about happiness
© DSMcIntosh LLC
Page 40
Mean Happiness
2.2
2.4
21000
1.8
2
18000
15000
Real GDP per Capita
24000
2.6
Happiness vs. Income (a time series)
1975
1980
1985
Year
Real GDP per Capita
1990
1995
Mean Happiness
Why have increases in income and wealth
not led to increases in happiness?
Source: Andrew Oswald, Cited in Prof. Laibson Ec 1030
© DSMcIntosh LLC
Page 41
So why aren’t people happier?
• Pandemics
• Positional comparison
• Choice fatigue and FOMO
• “Present self” made decisions for “future self”
• Hedonic treadmill
© DSMcIntosh LLC
Page 42
Positional comparison
© DSMcIntosh LLC
Page 43
Choice fatigue and FOMO
•Increased search costs
•Lower probability of
choosing single best
option
•Expected opportunity
costs increase with
number of choices
not taken (FOMO)
© DSMcIntosh LLC
Page 44
“Present self” made decisions for “future self”
Source: Money, March 14, 2016
© DSMcIntosh LLC
Page 45
Hedonic Treadmill
Increased
Happiness
Good News!
Adaptation
Original
New
Set Point
What behavioral biases or factors might contribute to this?
© DSMcIntosh LLC
Page 46
The Resilience Effect: It Gets Better
Divorce
Number of years before and after the event
Birth of a Child
Number of years before and after the event
Widowhood
Number of years before and after the event
Unemployment
Number of years before and after the event
Source: Andrew Clark, cited by Andrew Oswald,”The Economics of Health and Happiness”
© DSMcIntosh LLC
Page 47
Resilience
U.S. Happiness, by Age
3.8
Scale:
1-4
3.7
3.6
3.5
3.4
18
21
24
27
30
33
36
39
42
45
48
51
54
57
60
63
66
69
72
Source: Blanchflower and Oswald (2017)
© DSMcIntosh LLC
Page 48
What leads to longevity and happiness?
Grant Study of Adult Development
• One-of-a-kind, longitudinal study
• Maintained over 75 years
• 286 sophomores from the Harvard College
classes of 1938, 1939, 1940 and 1941
• As a prospective study, it
– Avoided survivorship bias
– Shed light on causality, via chronology
• Relationships
What factors
meaningfully and
reliably predict
the good life?
• Resilience
• Gratifying career
“Happiness is love.
Full stop.”
• Healthy lifestyle
• Social interaction
© DSMcIntosh LLC
Page 49
Maximizing longevity and happiness
Things to remember
• Happiness and mental health
contribute to longevity
Behavioral hacks
• Continue to care about the future
• What we value changes over time
• Invest in other people and your
relationships with them
• A gratifying career is about more
than maximizing income
• “Ignore sunk costs” means letting
go of regret and past unhappiness
• Resilience is the reverse of the
hedonic treadmill
• Know your own utility functions, and
minimize social comparison
• Longevity is a social comparison
Underlying behavioral factors
• Sunk costs
• Social comparison
• Now bias and hyperbolic
discounting
• Hedonic treadmill and resilience
• Altruism
© DSMcIntosh LLC
Page 50
Behavioral biases affecting utility
Past
Present
Remembered Utility
Experienced Utility
Future
Expected Utility
Satisfaction
Enjoyment
Anticipation
• Availability bias
• Peak-end bias
• Social comparison
• Magnitude effect
• (Quasi) Hyperbolic
discounting
Regret
Displeasure
Dread
• Resilience
• Selective memory
• IKEA effect
• Present self vs.
Future self
• Sunk cost bias
© DSMcIntosh LLC
•
•
•
•
•
Flow / Engagement
Resilience
Endowment effect
Status quo bias
Group Identification
• Hedonic treadmill
• Peer pressure
• FOMO
• Present self vs.
Future self
• Gambler’s bias
• Commitment strategy
• Certainty /
Possibility effect
• Loss Aversion
• Choice fatigue
• FOMO
Page 51
Behavioral strategies for maximizing utility
Past
Present
Remembered Utility
Future
Expected Utility
Experienced Utility
Satisfaction
Enjoyment
Anticipation
Regret
Displeasure
Dread
Behavioral
Biases
•
•
•
•
Imperfect memory
Availability bias
Peak-end bias
IKEA effect
•
•
•
•
Endowment effect
Group identification
Hedonic treadmill
Status quo bias
•
•
•
•
•
•
Present self vs. Future self
(Quasi) Hyperbolic discounting
Assessing probabilities and payoffs
Loss aversion
Choice fatigue
Gambler’s bias
Impact of
Other People
• Social comparison
• Fairness
• Altruism
•
•
•
•
Social comparison
Fairness
Altruism
FOMO
•
•
•
•
Social comparison
Bandwagon effect
Altruism
FOMO
Strategies
•
•
•
•
© DSMcIntosh LLC
Resilience
Selective memory
Framing
Ignoring sunk costs
• Resilience
• Flow / Engagement
• Calibrate and
commiserate
• Commitment strategies
• Calibrate with others’
experience
• Satisficing
• Limiting available choices
• Certainty / possibility effect
Page 52
Homework 9
Assume that you and your significant other (either real or
imagined) are thinking about taking a vacation next year.
What can you do to maximize the benefit you’ll get from your
overall experience?
Due Tuesday, November 9
Format: PowerPoint, ?12 point fonts, one page, horizontal
(landscape), page setup formatted to “letter size” and your
name on a second page
© DSMcIntosh LLC
Page 53
Term Paper
• Due December 14
• Approximately 1500-2000 words (6-8 pages)
• “…apply the analytic concepts developed in the course
to a situation of their choosing, explaining the apparent
irrationalities in stakeholders’ behaviors and suggesting
ways that one or more stakeholders could reframe the
situation to their advantage.”
© DSMcIntosh LLC
Page 54
Title
• Text
Name

Purchase answer to see full
attachment

Explanation & Answer:
1 Slide

Tags:
vacation

BENEFIT

Utility Theory

User generated content is uploaded by users for the purposes of learning and should be used following Studypool’s honor code & terms of service.