chapter 3 micro2 choice under uncertainty
DESCRIPTION
Microeconomics 1TRANSCRIPT
Chapter 3
CHOICE UNDER UNCERTAINTY
Chapter outline
1. Describing Risk2. Preference toward risk3. Reducing Risk4. The Demand for Risk Assets5. Behavioral Economics
Uncertainty and Consumer behaviorTo examine the ways that people can compare andchoose among risky alternatives, we take the followingsteps:1. In order to compare the risk of alternative choices, we
need to quantify risk2. We will examine people’s preference toward risk3. 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:
All possible outcomes Probability/likelihood each outcome will occur
Interpreting Probability1. Objective interpretation: based on observed frequency o
r past events2. Subjective interpretation: based on perception that outc
ome will occur. Two measures help describe ans compare risky c
hoices:1. Expected Value2. Variability
3.1.1 Expected Value Expected Value
Probability- weight average of payoffs or values resulting from all possible outcomes
For n possible outcomes: Payoffs Probabilities of each outcomes:
The EV measures the central tendency- the payoff or value that we would expected on the average
1 2, ,..., nV V V1 2P ,P ..., Pn
1
1n
i
Pi
1
.n
i
EV PiVi
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
bilityIncome
($)Probab
ilityIncome
($)
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))
22( ) ( ) .i
Var X Vi EV Pi
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
n
i
EVViPi1
2)(
3.1.2 VariabilityTable 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
Probability
Outcome 2
Deviation
Squared
Probability
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
E.g. Risky job with 50% chance of $10,000 (utility 10) and 50% chance of $30,000 (utility 18) EI =? EU=?
1
Pr .n
i ii
EU U
3.2.1 Risk Averse
Consumer is risk averse because he would prefer certain income of $20,000 to uncertain expected income = $20,000
10
EU=14
20EI
10
Income
Utility
18
30
A
B
EF
16I*
Risk Premium
Maximum amount that risk-averse person would pay to avoid risk
3.2.2 Risk Neutral
10 20 30
6
12
18
Utility
Income
3.2.3 Risk Loving
10 20EI
U(EI)=8
3
Income
Utility
18
30
A
B
E
25I*
3.3 REDUCING RISK
Consumers generally risk averse and want to reduce risk
3.3.1 Diversification Practice of reducing risk by allocating
resources to a variety of activities whose outcomes are not closely related.
Table 4 Income form Sales of Appliances ($)
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 don’t 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 wi
th 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 investor’s choice
Trade-off: Risk and Return Investor is dividing her funds between two asse
ts- 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
Trade-off: Risk and Return 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:
(1 )p m fR bR b R
Trade-off: Risk and Return How risky is porfolio?
Standard deviation of stocks: Standard deviation of portfolio:
Budget line describing trade-off between risk and expected return
Price of risk: extra risk that an investor must incur to enjoy a higher expected return
m.p mm
( )m fp f p
m
R RR R
m f
m
R R
Choosing between risk and return
σ*
Rp
σp
U1U2U3
R*
Budget line
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 don’t always evaluate uncertain
events according to law of probability Don’t always maximize expected utility Law of small numbers