Chapter2TheTheoryofIndividualLaborSupplyChapter2TheTheoryofIndivid1.TheWork-LeisureDecision:BasicModel勞動經濟學課件Individualschoosebetweenworkandleisure.Workistimespentonapayingjob.Leisureincludesactivitieswhereoneisnotpaid.EducationRestWorkwithinthehouseholdAssumptionsIndividualschoosebetweenworIndifferenceCurve

LeisureHrIncome/day240

Theindifferencecurveshows workandleisurecombinations thatyieldthesameamountof totalutility.

Morehoursofleisureimplies fewerhoursofwork.

240WorkHrIndifferenceCurve LeisureNegativeslopeTokeepthelevelofutilitythesame,ifonegetmoreleisure,someofincomemustbegivenup.ConvextooriginWithlowhoursofleisure,individualsarewillingtogiveupalargeamountofincometoget1moreleisurehour.Withhighhoursofleisure,individualsarewillingtogiveupasmallamountofincometoget1moreleisurehour.IndifferenceCurvePropertiesNegativeslopeIndifferenceCuMarginalRate

ofSubstitution

LeisureIncome/day349824041

Themarginalrateof substitution(MRS)istheamount ofincomeonemustgiveupto compensatefor1morehourif leisure.

At3hoursofleisure(21hours ofwork),onemustgiveup4 unitsofincometocompensate for1morehourofleisure.240Work

At8hoursofleisure(16hours ofwork),onemustgiveup1 unitofincometocompensate for1morehourofleisure.

TheMRSfallsasonemoves southeastalonganindifference curve.MarginalRate

ofSubstitutioIndifferenceMap

LeisureIncome/day240

Curvesfurtherfromtheorigin indicatehigherutility.I1I2I3L2L1Y2Y1

CombinationL2Y2ispreferredto combinationL1Y1sinceonegets bothmoreincomeandmore leisure. Apersonwillmaximizeutility bygettingtothehighest attainableindifferencecurve.IndifferenceMap LeisureIncoWork-LeisurePreferences

LeisureIncome/day240

“Leisurelovers”placeahigh valueonleisure.Thehavea steepindifferencecurve.They arewillingtosacrificealarge amountofincometogetasmall increaseinleisure.I1I2 “Workaholics”placealow valueonleisure.Thehavea flatindifferencecurve.They mustbegivenalargeincreasein leisuretocompensatefora smalldecreaseinincome.IAIBWork-LeisurePreferences LeiBudgetConstraint

LeisureIncome/day240

Thebudgetconstraintshowsthe combinationsofincomeand leisurethataworkercouldget givenawagerate.$120 Atawagerateof$5,aworker couldgetamaximumincomeof $120perday($5/hour*24).

Atawagerateof$10,aworker couldgetamaximumincomeof $240perday. Atawagerateof$15,a workercouldgetamaximum incomeof$360perday.$240$360 Theslopeofthebudget constraintis–wagerate.

BudgetConstraint LeisureIncUtilityMaximization

LeisureIncome/day240

Theoptimalorutility maximizingpointiswherethe budgetconstraintistangentto thehighestattainable indifferencecurve

(U).

$240I1I2I316$80U

At

U,theMRS(slopeofthe indifferencecurve)istheequal tothewagerate(slopeofthe budgetconstraint)

At

B,theMRSisgreaterthan thewagerate.Theindividual valuesleisuremorethanthe wagerate.BA

At

A,theMRSislessthan thewagerate.Theindividual valuesleisurelessthanthe wagerate.UtilityMaximization LeisureBackwardBendingLaborSupplyCurve

HoursofWorkWageRate240

Foragivenperson,hoursof workmayincreaseasthewage raterises.810$10$25

Ifthewageraterisesfrom$10to $25perhourhoursofworkrises from8to10hoursperday.

Above$25perhour,hoursof workfall.

SL Thebackwardbendinglabor supplycurveistheresultofthe incomeandsubstitutioneffects ofawagechange.BackwardBendingLaborSupplyIncomeEffectThechangeindesiredhoursofworkresultingfromachangeinincome,holdingthewageconstant.Leisureisanormalgood,sohigherincomeimpliesadesireformoreleisure(fewerhoursofwork).Forawageincrease,incomeisraisedandsotheincomeeffectlowersdesiredworkhours.IncomeEffectIncomeEffectIncomeEffectSubstitutionEffectThechangeindesiredhoursofworkresultingfromachangeinthewagerate,holdingincomeconstant.Ahigherwagerateraisestherelativepriceofleisure.Forawageincrease,thesubstitutioneffectraisesdesiredworkhours.SubstitutionEffectSubstitutionEffectSubstitutForWageIncreasesIfsubstitutioneffect>incomeeffect,thenhoursofworkrise.Ifincomeeffect>substitutioneffect,thenhoursofworkfall.ForWageDecreasesIfsubstitutioneffect>incomeeffect,thenhoursofworkfall.Ifincomeeffect>substitutioneffect,thenhoursofworkrise.NetEffectForWageIncreasesNetEffectIncomeandSubstitutionEffects

LeisureIncome/day240

Atawagerateof$10/hour,the optimalhoursofleisureis16(8 hoursofwork)atpointU1.$240I1I216U1

Ifthewageraterisesto $15/hour,theoptimalhoursof leisureis15atpoint

U2.

Theincomeeffect(IE)is measuredthroughaparallel shiftoftheoldbudget constraint.TheIEisfrom

U1

to

U2’

(from16to17hoursof leisure).

Thesubstitutioneffect(SE)is measuredbymovementalong I2.TheSEisfrom

U2’

to

U2

(from17to15hoursof leisure).1715U2U2’$360

Theneteffectisanincreaseof hoursofworkby1hour.IncomeandSubstitutionEffectThesubstitutioneffectdominatesatlowwagerates.TheMRSislowbecauseincomeisscarcerelativetoleisure.TheincomeeffectdominatesathigherwageratesTheMRSishighbecauseleisureisscarcerelativetoincome.BackwardBendingLaborSupplyRationaleThesubstitutioneffectdominaThelaborsupplycurveisslightlybackwardbendingformen.Theincomeeffectisslightlygreaterthanthesubstitutioneffect.Thelaborsupplycurveispositiveforwomen.Ifsubstitutioneffectisgreaterthantheincomeeffect.Womensubstitutebetweenworkathomeandmarketworkmorethanmen.EmpiricalEvidenceThelaborsupplycurveissligTheelasticityoflaborsupplymeasurestheresponsivenessofdesiredhoursofworktothewagerate.ElasticityofLaborSupplyElasticity

ofLaborSupply=%Changein

quantityoflaborsupplied%ChangeinthewagerateTheelasticityoflaborsupplyIftheelasticityiszero,itisperfectlyinelastic.Iftheelasticityisnegative,itisbackwardbending.Iftheelasticityispositiveandlessthan1,itisrelativelyinelastic.Iftheelasticityispositiveandmorethan1,itisrelativelyelastic.ElasticityofLaborSupplyIftheelasticityiszero,it1.Showtheeffectofawagedecreaseonanindividual’sincome-leisurechoices.Isolatetheincomeandsubstitutioneffects.Istheworkerontheforward-risingorbackwardbendingportionofthelaborsupplycurve?QuestionsforThought2.Indicateineachofthefollowinginstanceswhetherspecifiedeventswouldcauseaworkertowanttoworkmoreorfewerhours:(a)Thewageratesrisesandthesubstitutioneffectis greaterthantheincomeeffect.(b)Thewageratefallsandtheincomeeffectisgreater thanthesubstitutioneffect.1.Showtheeffectofawaged2.Applyingand ExtendingtheModel勞動經濟學課件Non-LaborIncome

LeisureIncome/day240

Atawagerateof$10/hour withnootherincome,the optimalhoursofleisureis16(8 hoursofwork)atpoint

U1.

Ifthepersongetsaninheritance thatgenerates$60adayofnon- laborincome,thebudget constrainthasaparallelshift.

Theoptimalhoursofleisure risesto17atpoint

U2

.$240I116U1I217U2$300

Withanincreaseinnon-labor income,onlytheincomeeffect occursandsohourswork

must

fall.

Non-LaborIncome LeisureIncoNon-Participants

LeisureIncome/day240

Ifapersonhasalowwagerate (WNisflat),highernon-labor income(NH),orsteep indifferencecurves(I1),heis lesslikelytoparticipateinthe laborforce(U1).HNW

Ifapersonhasahighwage rate(HW’),lownon-labor income(0),orflatindifference curves(I2),sheismorelikelyto participate(U2).I1I2U2U1W’

The

reservationwage

isthe lowestwagenecessaryto inducesomeonetowork.10

Collegestudentsarelesslikely toparticipateinthelaborforce thanotherpersons.Why?

Non-Participants LeisureIncOver-Employment

LeisureIncome/day240

Ifanindividualisfreetochoose thenumberofhoursofwork,she wouldchoosepoint

U1,with18 hoursofleisureand6hoursof work.HNWU1

Iftheindividualisconstrained toworkastandardworkdayof 8hoursornotall,shewill choosepoint

U2.U21618

At

U2,herMRSismorethan thewagerateandsoshefeels

overemployed.

Whatisapotentialsolutionto heroveremploymentsituation?

Over-Employment LeisureIncomUnder-Employment

LeisureIncome/day240

Ifanindividualisfreetochoose thenumberofhoursofwork,she wouldchoosepoint

U1,with14 hoursofworkand10hoursof leisure.HNWU1

Iftheindividualisconstrained toworkastandardworkdayof 8hoursornotall,shewill choosepoint

U2.U21610

At

U2,herMRSislessthanthe wagerateandsoshefeels

underemployed.

Whatisapotentialsolutionto herunderemployment situation?

Under-Employment LeisureIncoThereareavarietyofincomemaintenanceprogramssuchasfoodstamps,Medicaid,TemporaryAssistancetoNeedyFamilies.Wewillexaminetheworkincentivesofsuchprograms.IncomeMaintenanceProgramsThereareavarietyofincomeIncomeGuarantee(B)Benefitreceivedifindividual/familyhasnoearnedincome.BenefitReductionRate(t)Ratebywhichthebenefitisreducedasincomeisincreased.Att=.50,benefitsarereducedby$.50foreverydollarearned.Break-EvenLevelofIncome(Yb)Thelevelofearnedincomeatwhichtheindividual/familyreceivesnobenefit.IncomeMaintenanceProgramFeaturesIncomeGuarantee(B)IncomeMai TheactualsubsidypaymentS

illustratestheseconceptsasshownbelow.BenefitExampleS

=B–tYIfB=$80,t=.5,earnedincome(Y)=$60then..S=$80-.5*$60=$50 TheactualsubsidypaymentS Thebreak-evenlevelofincomeformulaisshownbelow:BenefitExampleYb

=B/tIfB=$80,t=.5,thenYb=$160 Thebreak-evenlevelofincomIncomeMaintenanceProgram

LeisureIncome/day240

Atawagerateof$10/hour,the optimalhoursofleisureis16(8 hoursofwork)atpoint

U1.$240I1I216U1

Ifthereisawelfareprogramis startedwithaBof$80aday, t=.5,thenYb=$160.

Theincomeeffect(IE)is measuredthroughaparallel shiftoftheoldbudget constraint.TheIEisfrom

U1

to

U2’

(from16to18hoursof leisure).

Thesubstitutioneffect(SE)is measuredbymovementalong I2.TheSEisfrom

U2’

to

U2

(from18to22hoursof leisure).Thetaxlowersthe “price”ofleisure.1822U2U2’

Incontrasttoawagechange, boththeIEandSEreduce desiredhoursofwork.$160$80IncomeMaintenanceProgram LThemainelementsofthe1996WelfareR