Uncertainty and Consumer Behavior

1
Chapter 5

• Uncertainty and Consumer Behavior

2
Topics to be Discussed

• Describing Risk
• Preferences Toward Risk
• Reducing Risk
• The Demand for Risky Assets

3
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)?

4
Describing Risk

• To measure risk we must know
• All of the possible outcomes.
• The probability or likelihood that each outcome
  will occur (its probability).

5
Describing Risk

• Interpreting Probability
• Objective Interpretation
• Based on the observed frequency of past events
• Subjective Interpretation
• Based on perception that an outcome will occur

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Interpreting Probability

• Subjective Probability
• Different information or different abilities to
  process the same information can influence the
  subjective probability
• Based on judgment or experience

7
Describing Risk

• With an interpretation of probability must
  determine 2 measures to help describe and compare
  risky choices
• Expected value
• Variability

8
Describing Risk

• Expected Value
• The weighted average of the payoffs or values
  resulting from all possible outcomes.
• Expected value measures the central tendency the
  payoff or value expected on average.

9
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

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Expected Value An Example

• Objective Probability
• 100 explorations, 25 successes and 75 failures
• Probability (Pr) of success 1/4 and the
  probability of failure 3/4

11
Expected Value An Example
12
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

13
Describing Risk

• Variability
• The extent to which possible outcomes of an
  uncertain even may differ
• How much variation exists in the possible choice

14
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.

15
Variability An Example

• 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).

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Variability An Example
Outcome 1 Outcome 1 Outcome 2 Outcome 2
Prob. Income Prob. Income
Job 1 Commission .5 2000 .5 1000
Job 2 Fixed Salary .99 1510 .01 510
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Variability An Example

• Income from Possible Sales Job
• Job 1 Expected Income

Job 2 Expected Income
18
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

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Variability An Example
Deviations from Expected Income () Deviations from Expected Income () Deviations from Expected Income () Deviations from Expected Income () Deviations from Expected Income ()
Outcome 1 Deviation Outcome 2 Deviation
Job 1 2000 500 1000 -500
Job 2 1510 10 510 -900
20
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.

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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

22
Variability

• The standard deviation is written

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Standard Deviation Example 1
Deviations from Expected Income () Deviations from Expected Income () Deviations from Expected Income () Deviations from Expected Income () Deviations from Expected Income ()
Outcome 1 Deviation Outcome 2 Deviation
Job 1 2000 500 1000 -500
Job 2 1510 10 510 -900
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Standard Deviation Example 1

• Standard deviations of the two jobs are

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Standard Deviation Example 1

• 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.

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Standard Deviation Example 2

• 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.

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Outcome Probabilities - Two Jobs
Job 1 has greater spread greater standard
deviation and greater risk than Job 2.
Probability
0.2
0.1
Income
1000
1500
2000
28
Decision Making Example 1

• What if the outcome probabilities of two jobs
  have unequal probability of outcomes
• Job 1 greater spread standard deviation
• Peaked distribution extreme payoffs are less
  likely that those in the middle of the
  distribution
• You will choose job 2 again

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Unequal Probability Outcomes
The distribution of payoffs associated with Job 1
has a greater spread and standard deviation than
those with Job 2.
Probability
0.2
0.1
Income
1000
1500
2000
30
Decision Making Example 2

• 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

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Decision Making Example 2

• 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

32
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

33
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

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Risk and Crime Deterrence - Example

• Assumptions
• Double-parking saves a person 5 in terms of time
  spent searching for a parking space.
• The driver is risk neutral.
• Cost of apprehension is zero.

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Risk and Crime Deterrence - Example

• 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

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Risk and Crime Deterrence - Example

• The same deterrence effect is obtained by either
• A 50 fine with a .1 probability of being caught
  results in an expected penalty of 5
• or
• A 500 fine with a .01 probability of being
  caught results in an expected penalty of 5.

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Risk and Crime Deterrence - Example

• Enforcement costs are reduced with high fine and
  low probability
• Most effective if drivers dont like to take risks

38
Preferences Toward Risk

• 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

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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

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Preferences Toward Risk - Example

• Utility at 30,000 is 18
• Utility at 10,000 is 10
• Must compare utility from the risky job with
  current utility of 13.5
• To evaluate the new job, we must calculate the
  expected utility of the risky job

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Preferences Toward Risk

• 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)
42
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.

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Preferences Toward Risk

• People differ in their preference toward risk
• People can be risk averse, risk neutral, or risk
  loving.

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Preferences Toward Risk

• 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 risk
• Ex Market for insurance

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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.

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Risk Averse Example

• Expected Income of risky job
• E(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

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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 persons losses (decreased utility)
  are more important than risky gains

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Risk Averse

• Can see risk averse choices graphically
• Risky job has expected income 20,000 with
  expected utility 14
• Point F
• Certain job has expected income 20,000 with
  utility 16
• Point D

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Risk Averse Utility Function
Utility
The consumer is risk averse because she would
prefer a certain income of 20,000 to an
uncertain expected income 20,000
Income (1,000)
50
Preferences Toward Risk

• 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

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Risk Neutral

• Expected value for risky option is the same as
  utility for certain outcome
• E(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

52
Risk Neutral
Utility
The consumer is risk neutral and is
indifferent between certain events and uncertain
events with the same expected income.
Income (1,000)
0
10
20
30
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Preferences Toward Risk

• 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 activity
• Increasing marginal utility of income

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Risk Loving

• Expected value for risky option point F
• E(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

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Risk Loving
Utility
The consumer is risk loving because she would
prefer the gamble to a certain income.
Income (1,000)
10
20
30
0
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Preferences Toward Risk

• 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.

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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.

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Risk Premium Example

• 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

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Risk Premium Example
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.
Utility
Income (1,000)
0
10
16
20
60
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).

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Risk Aversion and Income

• Example (cont.)
• The expected income is still 20,000, but the
  expected utility falls to 10.
• E(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

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Risk Aversion and Income

• 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.

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Risk Aversion and Income

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

64
Risk Aversion Indifference Curves

• Can describe a persons 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

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Risk Aversion and Indifference Curves
Expected Income
Highly Risk AverseAn increase in
standard deviation requires a large increase in
income to maintain satisfaction.
Standard Deviation of Income
66
Risk Aversion and Indifference Curves
Expected Income
Slightly Risk Averse A large increase in
standard deviation requires only a small
increase in income to maintain satisfaction.
Standard Deviation of Income
67
Reducing Risk

• Consumers are generally risk averse and therefore
  want to reduce risk
• Three ways consumers attempt to reduce risk are
• Diversification
• Insurance
• Obtaining more information

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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?

69
Income from Sales of Appliances
Hot Weather Cold Weather
Air conditioner sales 30,000 12,000
Heater sales 12,000 30,000
70
Diversification Example

• If the firms 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

71
Diversification Example

• 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.

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Diversification Example

• With diversification, expected income is 21,000
  with no risk.
• Better off diversifying to minimize risk
• Firms can reduce risk by diversifying among a
  variety of activities that are not closely related

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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 may different
  stocks or investments
• Ex Mutual funds

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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.

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The Decision to Insure
76
Reducing Risk Insurance

• For 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

77
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

78
Reducing Risk Actuarially Fair

• Insurance company 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.

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Reducing Risk Actuarially Fair

• Some events with very little knowledge of
  probability of occurrence such as floods and
  earthquakes are no longer insured privately
• Cannot calculate true expected values and
  expected loses
• Governments have had to create insurance for
  these types of events
• Ex National Flood Insurance Program

80
The Value of Information

• Risk often exists because we dont know all the
  information surrounding a decision
• Because of this, information is valuable and
  people are willing to pay for it

81
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.

82
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.

83
The Value of Information Example

• 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

84
The Value of Information Example

• 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).

85
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

86
The Demand for Risky Assets

• Assets
• Something that provides a flow of money or
  services to its owner.
• Ex homes, savings accounts, rental property,
  shares of stock
• The flow of money or services can be explicit
  (dividends) or implicit (capital gain).

87
The Demand for Risky Assets

• Capital Gain
• An increase in the value of an asset.
• Capital loss
• A decrease in the value of an asset.

88
Risky Riskless Assets

• Risky Asset
• Provides an uncertain flow of money or services
  to its owner.
• Examples
• apartment rent, capital gains, corporate bonds,
  stock prices
• Dont know with certainty what will happen to the
  value of a stock.

89
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

90
The Demand for Risky Assets

• People hold assets because of the monetary flows
  provided
• To compare assets, must consider the monetary
  flow relative to the assets price (value)
• Return on an Asset
• The total monetary flow of an asset, including
  capital gains or losses, as a fraction of its
  price.

91
The Demand for Risky Assets

• 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.

92
The Demand for Risky Assets

• 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

93
Investments Risk and Return (1926-1999)
94
The Demand for Risky Assets

• The higher the return, the greater the risk.
• Investors will choose lower return investments in
  order to reduce risk
• A risk-averse investor must balance risk relative
  to return
• Must study the trade-off between return and risk

95
Trade-offs Risk and ReturnsExample

• An investor is choosing between T-Bills and
  stocks
• T-bills riskless
• Stocks risky
• Investor can choose only T-bills, only stocks, or
  some combination of both

96
Trade-offs Risk and ReturnsExample

• 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 gt Rf or no risk averse investor would
  buy the stocks

97
Trade-offs Risk and ReturnsExample

• 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

98
Trade-offs Risk and ReturnsExample

• Assume, Rm 12, Rf 4, and b 1/2

99
Trade-offs Risk and ReturnsExample

• 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

100
Trade-offs Risk and ReturnsExample

• We still need to figure out how the allocation
  between the investment choices
• A type of budget line can be constructed
  describing the trade-off between risk and
  expected return

101
Trade-offs Risk and ReturnsExample

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

102
Trade-offs Risk and ReturnsExample

• 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

103
Choosing Between Risk Return

• If all funds are invested in T-bills (b0),
  expected return is Rf
• If all funds are invested in stocks (b1),
  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

104
Choosing Between Risk Return

• We can draw indifference curves showing
  combinations of risk and return that leave an
  investor equally satisfied
• Comparing the pay-offs 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

105
Choosing Between Risk Return
Expected Return,Rp
U2 is the optimal choice since it gives the
highest return for a given risk and is still
affordable
106
Choosing Between Risk Return

• 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

107
The Choices of Two Different Investors
Expected Return,Rp
Given the same budget line, investor A chooses
low return- low risk,
while investor B chooses high return-high risk.
108
Investing in the Stock Market

• In 1990s 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 market
• 1989 32
• 1998 49
• Percent with share of wealth in stock market
• 1989 26
• 1998 54

109
Investing in the Stock Market

• Why were stock market investments increasing
  during the 90s?
• Ease of online trading
• Significant increase in stock prices during late
  90s
• Employers shifting to self-directed retirement
  plans
• Publicity for do it yourself investing

110
Behavioral Economics

• Sometimes individuals behavior contradict basic
  assumptions of consumer choice
• More information about human behavior might lead
  to better understanding
• This is the objective of behavioral economics
• Improving understanding of consumer choice by
  incorporating more realistic and detailed
  assumptions regarding human behavior

111
Behavioral Economics

• 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

112
Behavioral Economics

• Reference Points
• Economists assumes 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.

113
Behavioral Economics

• Reference Points
• The point from which an individual makes a
  consumption decision
• From the example, owning the Cher ticket is the
  reference point
• Individuals dislike losing things they own
• They value items more when they own them than
  when they do not
• Losses are valued more than gains
• Utility loss from selling the ticket is greater
  than original utility gain from purchasing it

114
Behavioral Economics

• Experimental Economics
• Students were divided into two groups
• Group one was given a mug with market value of
  5.00
• Group two received nothing
• Students with mugs were asked how much they would
  take to sell the mug back
• Lowest price for mugs, on average, was 7.00

115
Behavioral Economics

• 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

116
Behavioral Economics

• Fairness
• Individuals often make choice because they think
  they are fair and appropriate
• Charitable 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

117
Behavioral Economics

• The Laws of Probability
• Individuals dont always evaluate uncertain
  events according to the laws of probability
• Individuals also dont 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

118
Behavioral Economics

• Theory up to now has explained much but not all
  of consumer choice
• Although not all of consumer decisions can be
  explained by theory up to this point, it helps
  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