img/" width="695" height="1066" useMap="#Map">
Microeconomics ­ECO402
VU
Lesson 14
PREFERENCESTOWARD RISK
ChoosingAmong RiskyAlternatives
­ Assume
­ Consumption of a single commodity
­ Theconsumer knows allprobabilities
­ Payoffsmeasured in terms of utility
­ Utilityfunction given
Example
­ A person is earning $15,000 andreceiving 13 units of utilityfrom the job.
­ She is considering a new, but riskyjob.
Shehas a .50 chance of increasing her income to $30,000 and a .50 chance of decreasing
herincome to $10,000.
Shewill evaluate the position by calculating the expectedvalue (utility) of theresulting
income.
Theexpected utility of the newposition is the sum of theutilities associated withall her
possibleincomes weighted by theprobability that each incomewill occur.
Theexpected utility can be written:
­ E(u) = (1/2)u($10,000) + (1/2)u($30,000)
= 0.5(10) + 0.5(18)
= 14
­ E(u) of newjob is 14 which is greaterthan the current utility of 13 and therefore
preferred.
DifferentPreferences TowardRisk
­ People can be
· Riskaverse
· Risk neutral or
· Riskloving
­ RiskAverse:
­ A person whoprefers a certain givenincome to a risky incomewith the sameexpected
value.
­ A person is considered risk averse if they have a diminishingmarginal utility of income
­ Theuse of insurance demonstratesrisk aversive behavior.
RiskAverse: A Scenario
­ A person canhave a $20,000 job with100% probability and receive a utility level of 16.
­ The personcould have a job with a .5 chance of earning $30,000and a .5 chance of
earning$10,000.
ExpectedIncome =
(0.5)($30,000) + (0.5) ($10,000) = $20,000
Expectedincome from both jobs is the same -- risk aversemay choose currentjob
Theexpected utility from thenew job is found:
­ E(u) = (1/2)u($10,000) + (1/2)u($30,000)
­ E(u) = (0.5)(10) + (0.5)(18) = 14
­ E(u) of Job 1 is 16 which is greaterthan the E(u) of Job 2 which is 14.
68
img/" width="695" height="1066" useMap="#Map">
Microeconomics ­ECO402
VU
Thisindividual would keep theirpresent job since it provides them with moreutility than the
riskyjob.
Theyare said to be riskaverse.
RiskAverse
Theconsumer is risk
Utility
aversebecause she
E
wouldprefer a certain
18
income of $20,000 to a
D
gamble with a .5 probability
16
of $10,000 and a .5
C
probability of $30,000.
14
13
B
A
10
Income ($1,000)
0
15 16 20
10
30
RiskNeutral
­ A person is said to be riskneutral if theyshow no preference between a certain
income,and an uncertain one withthe same expectedvalue.
RiskNeutral
E
18
Utility
Theconsumer is risk
neutraland is indifferent
C
betweencertain events
12
anduncertain events
with the same
expectedincome.
A
6
Income ($1,000)
0
10
20
30
RiskLoving
­ A person is said to be riskloving if theyshow a preference toward an uncertain income
over a certain income with thesame expected value.
· Examples:Gambling, some criminalactivity
69
img/" width="695" height="1066" useMap="#Map">
Microeconomics ­ECO402
VU
Utility
E
RiskLoving
18
Theconsumer is risk
lovingbecause she
wouldprefer the gamble
to a certain income.
C
8
A
3
Income ($1,000)
10
20
30
0
RiskPremium
­ Theriskpremium is theamount of money that a risk-averse person would pay to avoid
taking a risk.
RiskPremium: A Scenario
­ The personhas a .5 probability of earning$30,000 and a .5 probability of earning
$10,000(expected income = $20,000).
­ The expectedutility of these twooutcomes can be found:
­ E(u) = .5(18) + .5(10) = 14
Question
­ How muchwould the person pay to avoid risk?
RiskPremium
Here , the risk premium is
RiskPremium
$4,000because a certain
Utility
income of $16,000gives the
personthe same expected
utility as the uncertain
incomethat has an
G
expectedvalue of $20,000.
20
18
E
C
14
F
A
10
Income($1,000)
0
20
10
16
40
30
RiskAversion and Income
­ Variability in potential payoffs increasesthe risk premium.
70
img/" width="695" height="1066" useMap="#Map">
Microeconomics ­ECO402
VU
­ Example:
·  A job has a .5 probability of paying $40,000(utility of 20) and a .5 chance of paying 0
(utility of 0).
Theexpected income is still$20,000, but the expectedutility falls to 10.
Expectedutility = .5u($) + .5u($40,000)
= 0 + .5(20) = 10
Thecertain income of $20,000has a utility of 16.
If the person is required to take the new position,their utility will fall by 6.
Therisk premium is $10,000(i.e. they would be willing to give up $10,000 of the$20,000
andhave the same E(u) as the risky job.
Therefore, it can be said that thegreater the variability, thegreater the riskpremium.
IndifferenceCurve
­ Combinations of expected income & standarddeviation of income thatyield the
sameutility.
RiskAversion and IndifferenceCurves
U3
HighlyRisk Averse: An
Expected
increase in standard
U2
Income
deviationrequires a
largeincrease in
income to maintain
U1
satisfaction.
StandardDeviation of Income
Expected
SlightlyRisk Averse:
Income
A large increase in
standard
deviationrequires only a
smallincrease in income
to maintain satisfaction.
U3
U2
U1
71
img/" width="695" height="1066" useMap="#Map">
Microeconomics ­ECO402
VU
BusinessExecutives and the Choice of Risk
Example
­ Study of 464executives foundthat:
·  20% wererisk neutral
·  40% wererisk takers
·  20% wererisk averse
·  20% didnot respond
Thosewho liked risky situationsdid so when losses wereinvolved.
Whenrisks involved gains thesame, executives opted forless riskysituations.
Theexecutives made substantialefforts to reduce or eliminaterisk by delayingdecisions
andcollecting moreinformation.
72