PREFERENCES TOWARD RISK:Risk Premium, Indifference Curve

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Microeconomics ECO402

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.

Microeconomics ECO402

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

wouldprefer a certain

income of $20,000 to a

gamble with a .5 probability

of $10,000 and a .5

probability of $30,000.

Income ($1,000)

15 16 20

RiskNeutral

A person is said to be riskneutral if theyshow no preference between a certain

income,and an uncertain one withthe same expectedvalue.

RiskNeutral

Utility

Theconsumer is risk

neutraland is indifferent

betweencertain events

anduncertain events

with the same

expectedincome.

Income ($1,000)

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

Microeconomics ECO402

Utility

RiskLoving

Theconsumer is risk

lovingbecause she

wouldprefer the gamble

to a certain income.

Income ($1,000)

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

expectedvalue of $20,000.

Income($1,000)

RiskAversion and Income

Variability in potential payoffs increasesthe risk premium.

Microeconomics ECO402

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

HighlyRisk Averse: An

Expected

increase in standard

Income

deviationrequires a

largeincrease in

income to maintain

satisfaction.

StandardDeviation of Income

Expected

SlightlyRisk Averse:

Income

A large increase in

standard

deviationrequires only a

smallincrease in income

to maintain satisfaction.

Microeconomics ECO402

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.

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