Chapter 3 Micro2 Choice Under Uncertainty

Chapter 3
CHOICE UNDER UNCERTAINTY
Chapter outline
1.
2.
3.
4.
5.
Describing Risk
Preference toward risk
Reducing Risk
The Demand for Risk Assets
Behavioral Economics
Uncertainty and Consumer behavior

To examine the ways that people can compare and
choose among risky alternatives, we take the following
steps:
1. In order to compare the risk of alternative choices, we
need to quantify risk
2. We will examine peoples preference toward risk
3. We will se how people can sometimes reduce or
eliminate risk.
4. In some situations, people must choose the amount of
risk they wish to bear.
In the final section of this chapter, we offer an overview
of the flouring field of behavioral economics
3.1 DESCRIBING RISK
To measure risk, must know:
Interpreting Probability
1.
2.
All possible outcomes

Probability/likelihood each outcome will occur
Objective interpretation: based on observed
frequency or past events
Subjective interpretation: based on perception
that outcome will occur.
Two measures help describe ans compare

risky choices:
1.
2.
Expected Value
Variability
3.1.1 Expected Value
Expected Value
For n possible outcomes:
Probability- weight average of payoffs or values

resulting from all possible outcomes
V1 , V2 ,..., Vn
Payoffs
P1 , P2 ..., Pn
Probabilities of each outcomes:
Pi 1
i 1
The EV measures the central tendency- the

payoff or value that we would expected on
the average
n
EV
Pi.Vi
i 1
3.1.1 Expected Value

E.g. two outcomes possible:
Success- stock price increase $30 to

$40/share => V1 = $40
Failure- Stock price fall $30 to
$20/share=> V2 = $20
100 trials: 25 successes and 75
failures=> P1 = 0.25 and P2 = 0.75
EV =?
3.1.2 Variability
Extent to which possible outcomes of

an uncertain event may differ
How much variation exists in possible
choice
Table 1
Income from Sales jobs

Outcome 1
Outcome 2
Expected
Income ($)
Proba
bility
Income
($)
Probab
ility
Income
($)
Job1:
Commission
0.5
2000
0.5
1000
1500
Job2: Fixed
Salary
0.99
1510
0.01
510
1500
3.1.2 Variability
Greater variability from expected values

signals greater risk
Variability comes from deviations in
payoffs
Deviation: difference between expected

payoff and actual payoff (V-E(V))
Var ( X ) (Vi EV ) .Pi

2
3.1.2 Variability
Standard Deviation
Squared root of average of squares of

deviations of payoffs associated with
each outcome from expected value
Greater standard deviation signals greater

risk
2
Pi
(
Vi
EV
)
i 1
3.1.2 Variability
Table 2
Deviation from Expected Income ($)

Outcome 1
Deviation
Outcome 2
Deviation
Job 1
2000
500
1000
- 500
Job 2
1510
10
510
- 990
Table 3
Calculating Variance ($) and Standard Deviation

Outcome
1
Deviation
Squared
Probabilit
y
Outcome
2
Deviation
Squared
Probabilit
y
Variance
Standard
Deviation
Job 1
2000
500
0.5
1000
250,000
0.5
250,000
500
Job 2
1510
10
0.99
510
980,100
0.01
9900
99.5
3.1.3 Decision Making
Suppose add $100 to each payoff in job 1

which makes expected income = $1,600
Job 1: EI = $1,600 and standard deviation $500

Job 2: EI = $1,510 and standard deviation $99.5
Which job should be chosen?
Depends on individual
Some willing to take risk with higher expected

income
Some prefer less risk even with lower expected

income
3.2 PREFERENCES TOWARD RISK
Different Preferences
Risk Averse
Condition of preferring a certain income to a

risky income with the same expected value
Risk Neutral
Condition of being indifferent between a certain

income and un uncertain income with the same
expected value
Risk Loving
Condition of preferring a risky income to a

certain income with the same expected value
Expected Utility
EU of risky option is sum of utilities associated

with all possible incomes weighted by probability
of each
n
EU Pri .U i
i 1
E.g. Risky job with 50% chance of $10,000

(utility 10) and 50% chance of $30,000 (utility
18)
EI =?
EU=?
3.2.1 Risk Averse

Utility
18
EU=1
4
10
B
F
10 16 20
I* EI
30
Consumer is risk
averse because he
would prefer certain
income of $20,000 to
uncertain expected
income = $20,000
Income
Risk Premium
Maximum amount that risk-averse

person would pay to avoid risk
3.2.2 Risk Neutral

Utility
18
12
6
10 20
30
Income
3.2.3 Risk Loving

Utility
18
U(EI)=
8
3
A
10
20 25 30
EI I*
Income
3.3 REDUCING RISK
Consumers generally risk averse and

want to reduce risk
3.3.1 Diversification
Practice of reducing risk by allocating

resources to a variety of activities
whose outcomes are not closely
related.
Table 4
Income form Sales of Appliances ($)

Hot weather
Cold weather
Air conditioner
sales
30,000
12,000
Heater Sales
12,000
30,000
3.3.2 Insurance
If cost of insurance equals expected

loss, risk averse people buy enough
insurance to recover fully from
potential loss
If risk averse, guarantee of same
income regardless of outcome has
utility than facing risk
Expected utility with insurance higher
than without
3.3.3 Value of information
Risk often exists because dont know

all information surrounding decision
Information is valuable and peole
willing to pay for it
Value of complete information
Difference between expected value of

choice with complete information and
expected value with incomplete
information.
3.4 DEMAND FOR RISKY ASSETS

3.4.1 Risky and risk less assets
Risky assets
Provides uncertain flow of money or

services to its owner
E.g.:
Risk less assets
Provides flow of money or service that is

known with certainty
E.g.:
3.4.1 Risky and risk less assets
Return on assets
Total money flow of an assets, including capital

gain or losses, as a fraction of its price
Real return: Simple (or nominal) return on an
assets less the rate of inflation
Expected Return
Return that asset should earn on average

Actual return could be higher or lower
Risk averse investor balances risk relative to
return.
3.4.2 The investors choice
Trade-off: Risk and Return
Investor is dividing her funds between

two assets- Treasury bills and stocks. To
receive higher return, she must incur
some risk
Rf: risk-free return on bill
Rm: expected return on stocks
rm: actual return on stocks
Assume Rm>Rf
How determine allocation of funds?
b: fraction of funds placed in stocls

(1-b): fraction of funds placed in T-bills
Expected Return on the investment

porfolio:
R p bRm (1 b) R f
How risky is porfolio?
Standard deviation of stocks:

Standard deviation of portfolio:
p m. m
Budget line describing trade-off between

risk and expected return
Rp R f
( Rm R f )
Price of risk: extra risk that an investor must

incur to enjoy a higher expected return Rm R f
m
Choosing between risk and return

R
p
U3
U2
U1
Budget line
R*
3.5 BEHAVIOURAL ECONOMICS
Objectives:
Improving understanding of consumer

choice by incorporating more realistic,
detailed assumptions regarding human
behavior
Developing field to explain situations not
well explained by basic consumer model
Fairness
People often make choices that they

think are fair
Behavioral economics
Reference points
Economists assume consumers place unique

value on goods/services purchased
Psychologists found that perceived value depend
on circumstances
Law of Probability
Individual dont always evaluate uncertain

events according to law of probability
Dont always maximize expected utility
Law of small numbers

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Chapter 3

CHOICE UNDER UNCERTAINTY

Uncertainty and Consumer behavior

3.1 DESCRIBING RISK

To measure risk, must know:

All possible outcomes

Two measures help describe ans compare

3.1.1 Expected Value

For n possible outcomes:

Probability- weight average of payoffs or values

The EV measures the central tendency- the

3.1.1 Expected Value

Success- stock price increase $30 to

Extent to which possible outcomes of

Income from Sales jobs

Greater variability from expected values

Deviation: difference between expected

Var ( X ) (Vi EV ) .Pi

Squared root of average of squares of

Greater standard deviation signals greater

Deviation from Expected Income ($)

Calculating Variance ($) and Standard Deviation

3.1.3 Decision Making

Suppose add $100 to each payoff in job 1

Job 1: EI = $1,600 and standard deviation $500

Which job should be chosen?

Some willing to take risk with higher expected

Some prefer less risk even with lower expected

3.2 PREFERENCES TOWARD RISK

Condition of preferring a certain income to a

Condition of being indifferent between a certain

Condition of preferring a risky income to a

EU of risky option is sum of utilities associated

E.g. Risky job with 50% chance of $10,000

3.2.1 Risk Averse

Maximum amount that risk-averse

3.2.2 Risk Neutral

3.2.3 Risk Loving

3.3 REDUCING RISK

Consumers generally risk averse and

Practice of reducing risk by allocating

Income form Sales of Appliances ($)

If cost of insurance equals expected

3.3.3 Value of information

Risk often exists because dont know

Difference between expected value of

3.4 DEMAND FOR RISKY ASSETS

Provides uncertain flow of money or

Risk less assets

Provides flow of money or service that is

3.4.1 Risky and risk less assets

Total money flow of an assets, including capital

Return that asset should earn on average

3.4.2 The investors choice

Trade-off: Risk and Return

Investor is dividing her funds between

Trade-off: Risk and Return

How determine allocation of funds?

b: fraction of funds placed in stocls