Chapter 5

Chapter 5

Uncertainty and Consumer Behavior

Chapter 5 2©2005 Pearson Education, Inc.

Topics to be Discussed

Describing Risk

Preferences Toward Risk

Reducing Risk

The Demand for Risky Assets


Introduction

Choice with certainty is reasonably straightforward

How do we make choices when certain variables such as income and prices are uncertain (making choices with risk)?


Describing Risk

To measure risk we must know:

1. All of the possible outcomes

2. The probability or likelihood that each outcome will occur


Describing Risk

Interpreting Probability1. Objective Interpretation

Based on the observed frequency of past events

2. Subjective Interpretation Based on perception that an outcome will

occur


Interpreting Probability

Subjective Probability Different information or different abilities to

process the same information can influence the subjective probability

Based on judgment or experience


Describing Risk

With an interpretation of probability, must determine 2 measures to help describe and compare risky choices

1. Expected value

2. Variability


Describing Risk

Expected Value The weighted average of the payoffs or

values resulting from all possible outcomesExpected value measures the central tendency;

the payoff or value expected on average


Expected Value – An Example

Investment in offshore drilling exploration:

Two outcomes are possible Success – the stock price increases from $30

to $40/share Failure – the stock price falls from $30 to

$20/share



Objective Probability 100 explorations, 25 successes and 75

failures Probability (Pr) of success = 1/4 and the

probability of failure = 3/4



failure) of )(valuePr(failure

success) of )(valuePr(success EV

)($20/share43)($40/share41 EV

$25/share EV


Expected Value

In general, for n possible outcomes: Possible outcomes having payoffs X1, X2, …,

Xn

Probabilities of each outcome is given by Pr1, Pr2, …, Prn

nn2211 XPr...XPrXPr E(X)


Describing Risk

Variability The extent to which possible outcomes of an

uncertain event may differ How much variation exists in the possible

choice


Variability – An Example

Suppose you are choosing between two part-time sales jobs that have the same expected income ($1,500)

The first job is based entirely on commission

The second is a salaried position


There are two equally likely outcomes in the first job: $2,000 for a good sales job and $1,000 for a modestly successful one

The second pays $1,510 most of the time (.99 probability), but you will earn $510 if the company goes out of business (.01 probability)




Outcome 1 Outcome 2

Prob. Income Prob. Income

Job 1: Commission .5 2000 .5 1000

Job 2: Fixed Salary .99 1510 .01 510


1500$ .5($1000).5($2000))E(X1


Income from Possible Sales Job

Job 1 Expected Income

$1500.01($510).99($1510) )E(X2

Job 2 Expected Income


Variability

While the expected values are the same, the variability is not

Greater variability from expected values signals greater risk

Variability comes from deviations in payoffs Difference between expected payoff and

actual payoff



Deviations from Expected Income ($)

Outcome 1

Deviation Outcome 2

Deviation

Job 1 $2000 $500 $1000 -$500

Job 2 1510 10 510 -900


Variability

Average deviations are always zero so we must adjust for negative numbers

We can measure variability with standard deviation The square root of the average of the

squares of the deviations of the payoffs associated with each outcome from their expected value


Variability

Standard deviation is a measure of risk Measures how variable your payoff will be More variability means more risk Individuals generally prefer less variability –

less risk


Variability

The standard deviation is written:

2222

11 )(Pr)(Pr XEXXEX


Standard Deviation – Example 1

Deviations from Expected Income ($)

Outcome 1

Deviation Outcome 2

Deviation

Job 1 $2000 $500 $1000 -$500

Job 2 1510 10 510 -900



Standard deviations of the two jobs are:

500000,250

)000,250($5.0)000,250($5.0

1

1

50.99900,9

)100,980($01.0)100($99.0

2

2

2222

11 )(Pr)(Pr XEXXEX



Job 1 has a larger standard deviation and therefore it is the riskier alternative

The standard deviation also can be used when there are many outcomes instead of only two



Job 1 is a job in which the income ranges from $1000 to $2000 in increments of $100 that are all equally likely

Job 2 is a job in which the income ranges from $1300 to $1700 in increments of $100 that, also, are all equally likely


Outcome Probabilities - Two Jobs

Income

0.1

$1000 $1500 $2000

0.2

Job 1

Job 2

Job 1 has greater spread: greater

standard deviationand greater risk

than Job 2.

Probability


Decision Making – Example 1

What if the outcome probabilities of two jobs have unequal probability of outcomes? Job 1: greater spread and standard deviation Peaked distribution: extreme payoffs are less

likely that those in the middle of the distribution

You will choose job 2 again


Unequal Probability Outcomes

Job 1

Job 2

The distribution of payoffsassociated with Job 1 has a greater spread and standard

deviation than those with Job 2.

Income

0.1

$1000 $1500 $2000

0.2

Probability



Suppose we add $100 to each payoff in Job 1 which makes the expected payoff = $1600 Job 1: expected income $1,600 and a

standard deviation of $500 Job 2: expected income of $1,500 and a

standard deviation of $99.50



Which job should be chosen? Depends on the individual Some may be willing to take risk with higher

expected income Some will prefer less risk even with lower

expected income


Risk and Crime Deterrence

Attitudes toward risk affect willingness to break the law

Suppose a city wants to deter people from double parking

Monetary fines may be better than jail time


Risk and Crime Deterrence

Costs of apprehending criminals are not zero, therefore Fines must be higher than the costs to

society Probability of apprehension is actually less

than one


Risk and Crime Deterrence - Example

Assumptions:1. Double-parking saves a person $5 in terms

of time spent searching for a parking space

2. The driver is risk neutral

3. Cost of apprehension is zero



A fine greater than $5.00 would deter the driver from double parking Benefit of double parking ($5) is less than the

cost ($6.00) equals a net benefit that is negative

If the value of double parking is greater than $5.00, then the person would still break the law



The same deterrence effect is obtained by either A $50 fine with a 0.1 probability of being

caught resulting in an expected penalty of $5

or A $500 fine with a 0.01 probability of being

caught resulting in an expected penalty of $5



Enforcement costs are reduced with high fine and low probability

Most effective if drivers don’t like to take risks



Can expand evaluation of risky alternative by considering utility that is obtained by risk A consumer gets utility from income Payoff measured in terms of utility


Preferences Toward Risk - Example

A person is earning $15,000 and receiving 13.5 units of utility from the job

She is considering a new, but risky job 0.50 chance of $30,000 0.50 chance of $10,000


Preferences Toward Risk - Example

Utility at $30,000 is 18Utility at $10,000 is 10Must compare utility from the risky job

with current utility of 13.5To evaluate the new job, we must

calculate the expected utility of the risky job



The expected utility of the risky option is the sum of the utilities associated with all her possible incomes weighted by the probability that each income will occur

E(u) = (Prob. of Utility 1) *(Utility 1)

+ (Prob. of Utility 2)*(Utility 2)


Preferences Toward Risk – Example

The expected is:E(u) = (1/2)u($10,000) + (1/2)u($30,000)

= 0.5(10) + 0.5(18)

= 14 E(u) of new job is 14, which is greater than

the current utility of 13.5 and therefore preferred



People differ in their preference toward risk

People can be risk averse, risk neutral, or risk loving



Risk Averse A person who prefers a certain given income

to a risky income with the same expected value

The person has a diminishing marginal utility of income

Most common attitude towards riskEx: Market for insurance


Risk Averse - Example

A person can have a $20,000 job with 100% probability and receive a utility level of 16

The person could have a job with a 0.5 chance of earning $30,000 and a 0.5 chance of earning $10,000


Risk Averse – Example

Expected Income of Risky JobE(I) = (0.5)($30,000) + (0.5)($10,000)

E(I) = $20,000

Expected Utility of Risky Job

E(u) = (0.5)(10) + (0.5)(18)

E(u) = 14


Risk Averse – Example

Expected income from both jobs is the same – risk averse may choose current job

Expected utility is greater for certain job Would keep certain job

Risk averse person’s losses (decreased utility) are more important than risky gains


Risk Averse

Can see risk averse choices graphicallyRisky job has expected income =

$20,000 with expected utility = 14 Point F

Certain job has expected income = $20,000 with utility = 16 Point D


Income ($1,000)

Utility

The consumer is risk averse because she would prefer a certain income of

$20,000 to an uncertain expected income =

$20,000

E

10

10 20

14

16

18

0 16 30

A

C

D

Risk Averse Utility Function

F



A person is said to be risk neutral if they show no preference between a certain income, and an uncertain income with the same expected value

Constant marginal utility of income


Risk Neutral

Expected value for risky option is the same as utility for certain outcomeE(I) = (0.5)($10,000) + (0.5)($30,000)

= $20,000

E(u) = (0.5)(6) + (0.5)(18) = 12

This is the same as the certain income of $20,000 with utility of 12


Income ($1,000)10 20

Utility

0 30

6A

E

C

12

18

The consumer is riskneutral and is indifferentbetween certain eventsand uncertain events

with the same expected income.

Risk Neutral



A person is said to be risk loving if they show a preference toward an uncertain income over a certain income with the same expected value Examples: Gambling, some criminal activities

Increasing marginal utility of income


Risk Loving

Expected value for risky option – point FE(I) = (0.5)($10,000) + (0.5)($30,000)

= $20,000

E(u) = (0.5)(3) + (0.5)(18) = 10.5

Certain income is $20,000 with utility of 8 – point C

Risky alternative is preferred


Income ($1,000)

Utility

0 10 20 30

The consumer is riskloving because she

would prefer the gamble to a certain income.

Risk Loving

3A

E

C8

18

F10.5



The risk premium is the maximum amount of money that a risk-averse person would pay to avoid taking a risk

The risk premium depends on the risky alternatives the person faces


Risk Premium – Example

From the previous example A person has a .5 probability of earning

$30,000 and a .5 probability of earning $10,000

The expected income is $20,000 with expected utility of 14



Point F shows the risky scenario – the utility of 14 can also be obtained with certain income of $16,000

This person would be willing to pay up to $4000 (20 – 16) to avoid the risk of uncertain income

Can show this graphically by drawing a straight line between the two points – line CF


Income ($1,000)

Utility

0 10 16

Here, the risk premium is $4,000 because a certain income of $16,000 gives the person

the same expected utility as the

uncertain income with expected value

of $20,000.

10

18

30 40

20

14

A

CE

G

20

Risk Premium

F



Risk Aversion and Income

Variability in potential payoffs increases the risk premium

Example: A job has a .5 probability of paying $40,000

(utility of 20) and a .5 chance of paying 0 (utility of 0).



Example (cont.): The expected income is still $20,000, but the

expected utility falls to 10E(u) = (0.5)u($0) + (0.5)u($40,000)

= 0 + .5(20) = 10 The certain income of $20,000 has utility of

16 If person must take new job, their utility will

fall by 6



Example (cont.): They can get 10 units of utility by taking a

certain job paying $10,000 The risk premium, therefore, is $10,000 (i.e.

they would be willing to give up $10,000 of the $20,000 and have the same E(u) as the risky job



The greater the variability, the more the person would be willing to pay to avoid the risk, and the larger the risk premium


Risk Aversion and Indifference Curves

Can describe a person’s risk aversion using indifference curves that relate expected income to variability of income (standard deviation)

Since risk is undesirable, greater risk requires greater expected income to make the person equally well off

Indifference curves are therefore upward sloping



Standard Deviation of Income

ExpectedIncome

Highly Risk Averse: Anincrease in standarddeviation requires a large increase in income to maintainsatisfaction.

U1

U2

U3



Standard Deviation of Income

ExpectedIncome

Slightly Risk Averse:A large increase in standarddeviation requires only a small increase in incometo maintain satisfaction.

U1

U2

U3


Reducing Risk

Consumers are generally risk averse and therefore want to reduce risk

Three ways consumers attempt to reduce risk are:

1. Diversification

2. Insurance

3. Obtaining more information


Reducing Risk

Diversification Reducing risk by allocating resources to a

variety of activities whose outcomes are not closely related

Example: Suppose a firm has a choice of selling air

conditioners, heaters, or both The probability of it being hot or cold is 0.5 How does a firm decide what to sell?


Income from Sales of Appliances

Hot WeatherCold

Weather

Air conditioner sales

$30,000 $12,000

Heater sales 12,000 30,000


Diversification – Example

If the firm sells only heaters or air conditioners their income will be either $12,000 or $30,000

Their expected income would be: 1/2($12,000) + 1/2($30,000) = $21,000



If the firm divides their time evenly between appliances, their air conditioning and heating sales would be half their original values

If it were hot, their expected income would be $15,000 from air conditioners and $6,000 from heaters, or $21,000

If it were cold, their expected income would be $6,000 from air conditioners and $15,000 from heaters, or $21,000



With diversification, expected income is $21,000 with no risk

Better off diversifying to minimize riskFirms can reduce risk by diversifying

among a variety of activities that are not closely related


Reducing Risk – The Stock Market

If invest all money in one stock, then take on a lot of risk If that stock loses value, you lose all your

investment value

Can spread risk out by investing in many different stocks or investments Ex: Mutual funds


Reducing Risk – Insurance

Risk averse are willing to pay to avoid risk

If the cost of insurance equals the expected loss, risk averse people will buy enough insurance to recover fully from a potential financial loss


The Decision to Insure


Reducing Risk – Insurance

For the risk averse consumer, guarantee of same income regardless of outcome has higher utility than facing the probability of risk

Expected utility with insurance is higher than without


The Law of Large Numbers

Insurance companies know that although single events are random and largely unpredictable, the average outcome of many similar events can be predicted

When insurance companies sell many policies, they face relatively little risk


Reducing Risk – Actuarially Fair

Insurance companies can be sure total premiums paid will equal total money paid out

Companies set the premiums so money received will be enough to pay expected losses


Reducing Risk – Actuarially Fair

Some events with very little probability of occurrence such as floods and earthquakes are no longer insured privately Cannot calculate true expected values and

expected losses Governments have had to create insurance

for these types of eventsEx: National Flood Insurance Program


The Value of Information

Risk often exists because we don’t know all the information surrounding a decision

Because of this, information is valuable and people are willing to pay for it


The Value of Information

The value of complete information The difference between the expected value

of a choice with complete information and the expected value when information is incomplete


The Value of Information – Example

Per capita milk consumption has fallen over the years

The milk producers engaged in market research to develop new sales strategies to encourage the consumption of milk



Findings Milk demand is seasonal with the greatest

demand in the spring Price elasticity of demand is negative and

small Income elasticity is positive and large



Milk advertising increases sales most in the spring

Allocating advertising based on this information in New York increased profits by 9% or $14 million

The cost of the information was relatively low, while the value was substantial (increased profits)


Demand for Risky Assets

Most individuals are risk averse and yet choose to invest money in assets that carry some risk Why do they do this? How do they decide how much risk to bear?

Must examine the demand for risky assets



Assets Something that provides a flow of money or

services to its ownerEx: homes, savings accounts, rental property,

shares of stock The flow of money or services can be explicit

(dividends) or implicit (capital gain)



Capital Gain An increase in the value of an asset

Capital loss A decrease in the value of an asset


Risky and Riskless Assets

Risky Asset Provides an uncertain flow of money or

services to its owner Examples

Apartment rent, capital gains, corporate bonds, stock prices

Don’t know with certainty what will happen to the value of a stock


Risky and Riskless Assets

Riskless Asset Provides a flow of money or services that is

known with certainty Examples

Short-term government bonds, short-term certificates of deposit



People hold assets because of the monetary flows provided

To compare assets, one must consider the monetary flow relative to the asset’s price (value)

Return on an asset The total monetary flow of an asset, including

capital gains or losses, as a fraction of its price



Individuals hope to have an asset that has returns larger than the rate of inflation Want to have greater purchasing power

Real Return of an Asset (inflation adjusted) The simple (or nominal) return less the rate

of inflation



Since returns are not known with certainty, investors often make decisions based on expected returns

Expected Return Return that an asset should earn on average In the end, the actual return could be higher

or lower than the expected return


Investments – Risk and Return (1926-1999)



The higher the return, the greater the riskInvestors will choose lower return

investments in order to reduce riskA risk-averse investor must balance risk

relative to return Must study the trade-off between return and

risk


Trade-offs: Risk and ReturnsExample

An investor is choosing between T-Bills and stocks:

1. T-bills – riskless

2. Stocks – risky

Investor can choose only T-bills, only stocks, or some combination of both



Rf = risk-free return on T-bill Expected return equals actual return on a

riskless asset

Rm = the expected return on stocks

rm = the actual returns on stock

Assume Rm > Rf or no risk averse investor would buy the stocks



How do we determine the allocation of funds between the two choices? b = fraction of funds placed in stocks (1-b) = fraction of funds placed in T-bills

Expected return on portfolio is weighted average of expected return on the two assets

fmP RbbRR )1(



Assume, Rm = 12%, Rf = 4%, and b = 1/2

%8

%)4)(2/11(%)12)(2/1(

)1(

P

P

fmP

R

R

RbbRR



How risky is the portfolio? As stated before, one measure of risk is

standard deviation Standard deviation of the risky asset, m

Standard deviation of risky portfolio, p

Can show that:

mp b



We still need to figure out the allocation between the investment choices

A type of budget line can be constructed describing the trade-off between risk and expected return



Expected return on the portfolio, rp increases as the standard deviation, p of that return increases

pm

fmfp

fmp

RRRR

RbbRR

)(

)1(



The slope of the line is called the price of risk Tells how much extra risk an investor must

incur to enjoy a higher expected return

mfm )/R(R Slope


Choosing Between Risk and Return

If all funds are invested in T-bills (b=0), expected return is Rf

If all funds are invested in stocks (b=1), expected return is Rm but with standard deviation of m

Funds may be invested between the assets with expected return between Rf and Rm, with standard deviation between m and 0



We can draw indifference curves showing combinations of risk and return that leave an investor equally satisfied

Comparing the payoffs and risk between the two investment choices and the preferences of the investor, the optimal portfolio choice can be determined

Investor wants to maximize utility within the “affordable” options



p Return, of

Deviation Standard

ExpectedReturn,Rp

U2 is the optimal choice since it gives the highest return for a given risk and is still affordable

Rf

Budget Line

m

Rm

R*

U2

U1

U3



Different investors have different attitudes toward risk

If we consider a very risk averse investor (A) Portfolio will contain mostly T-bills and less in stock,

with return slightly larger than Rf

If we consider a riskier investor (B) Portfolio will contain mostly stock and less T-bills, with

a higher return Rb but with higher standard deviation


The Choices of Two Different Investors

ExpectedReturn,Rp

p Return, of

Deviation Standard

Given the same budget line, investor A

chooses low return/low risk, while investor B

chooses high return/high risk.

UA

RA

A

UB

Rf

Budget line

m

Rm

RB

B


Investing in the Stock Market

In 1990’s many people began investing in the stock market for the first time Percent of US families who had directly or

indirectly invested in the stock market1989 = 32%1998 = 49%

Percent with share of wealth in stock market1989 = 26%1998 = 54%


Investing in the Stock Market

Why were stock market investments increasing during the 90’s? Ease of online trading Significant increase in stock prices during

late 90’s Employers shifting to self-directed retirement

plans Publicity for “do it yourself” investing


Behavioral Economics

Sometimes individuals’ behavior contradicts basic assumptions of consumer choice More information about human behavior

might lead to better understanding This is the objective of behavioral

economicsImproving understanding of consumer choice by

incorporating more realistic and detailed assumptions regarding human behavior



There are a number of examples of consumer choice contradictions You take at trip and stop at a restaurant that

you will most likely never stop at again. You still think it fair to leave a 15% tip rewarding the good service.

You choose to buy a lottery ticket even though the expected value is less than the price of the ticket



Reference Points Economists assume that consumers place a

unique value on the goods/services purchased

Psychologists have found that perceived value can depend on circumstances

You are able to buy a ticket to the sold out Cher concert for the published price of $125. You find out you can sell the ticket for $500 but you choose not to, even though you would never have paid more than $250 for the ticket.



Reference Points (cont.) The point from which an individual makes a

consumption decision From the example, owning the Cher ticket is

the reference pointIndividuals dislike losing things they ownThey value items more when they own them

than when they do notLosses are valued more than gainsUtility loss from selling the ticket is greater than

original utility gain from purchasing it



Experimental Economics Students were divided into two groups Group one was given a mug with a market

value of $5.00 Group two received nothing Students with mugs were asked how much

they would take to sell the mug backLowest price for mugs, on average, was $7.00



Experimental Economics (cont.) Group without mugs was asked minimum

amount of cash they would except in lieu of the mug

On average willing to accept $3.50 instead of getting the mug

Group one had reference point of owning the mug

Group two had reference point of no mug



Fairness Individuals often make choices because they

think they are fair and appropriateCharitable giving, tipping in restaurants

Some consumers will go out of their way to punish a store they think is “unfair” in their pricing

Manager might offer higher than market wages to make for happier working environment or more productive worker



The Laws of Probability Individuals don’t always evaluate uncertain

events according to the laws of probability Individuals also don’t always maximize

expected utility Law of small numbers

Overstate probability of an event when faced with little information

Ex: overstate likelihood they will win the lottery



Theory up to now has explained much but not all of consumer choice

Although not all of consumer decisions can be explained by the theory up to this point, it helps us understand much of it

Behavioral economics is a developing field to help explain and elaborate on situations not well explained by the basic consumer model

Chapter 5

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