mgmt104 fall 2010 lecture 03
TRANSCRIPT
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Management1042010ProfessorIwanBarankay 1
Management104
IndustrialRelationsandHumanResourceManagement
ProfessorIwanBarankay
Lecture3
RecapofWorksheet1
Worksheet2
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Management1042010ProfessorIwanBarankay 2
Arecapfromlastlecture
ThePrincipalAgentmodelhasthefollowingcomponents
1) Thetechnologyofproductionconsistingoftheoutput,
theactionstakenbytheagenttoproducetheoutput,and
theeventsthataffectoutputthatareoutsidethecontrolof
theagent.
2) Thesetoffeasiblecontracts
3) Thepayofftotheparties
4) Thetimingofevents
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Management1042010ProfessorIwanBarankay 3
Eventsoutsideofcontrol
exogeneousshockstoproductivity(weather,
technologicalfailure,lawsuits)
unanticipatedchangesindemandforfinalgoods
(financialcrisis)orsupplyofinputs(bankruptcyofsupplier)
fromtheagentsperspective:tosomeextendactionsby
theprincipal
fromtheprincipalsperspective:tosomeextendactions
bytheagent
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Management1042010ProfessorIwanBarankay 4
Contractscantakeonmanyforms
FixedWage/Compensation
Linearcontracts,e.g.piecerates($percrateorkgoffruit
pickedsubjecttoachievingapredefinedqualitylevel)
Nonlinearcontract,e.g.compensationaboveandbelowa
threshold
Bonusschemes
RetentionTournaments
LinkedtoCompanylevelperformance(e.g.stockoptions)
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Management1042010ProfessorIwanBarankay 5
Contractscanbecompleteorincomplete
Completecontractsdescribeacourseofactionand
compensationinallcontingencies
Incomplete
contracts
staydeliberatelysilentonactionsandcompensationinsome
situations
or
itmaybeimpossibleortoocostlytodescribeactionsand
compensationinallcontingencies
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Management1042010ProfessorIwanBarankay 6
Assumptionsweneededtomakewhendiscussingwhich
contractsmightbeused
Whocanobserveactions?
Ifonlytheworkercanseetheactionsthenworkersmight
haveamoralhazardtoengageinactionstheprincipalwouldnotfindoptimal.Iftheactionsmapdirectlytoproductivityandagentsare
riskneutral
(the
case
we
consider
this
week)
then
we
can
stillimplementagoodoutcomefromtheprincipals
perspective.
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Management1042010ProfessorIwanBarankay 7
WorkerHeterogeneity
Somepeoplemightbemoreable(ortalentedetc.)than
others.Weoftenrefertothatasagentstypes.
Whenemployeesworkundercomparableconditionsand
somearemoreproductivethanothersthencontractscanbe
usedtoeffectivelysortagentsbyability.
Underthesamecontract,peoplewithhigherabilitywillbemoreproductive.
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Management1042010ProfessorIwanBarankay 8
PerformanceTargets
Thesecanhavetheundesirableeffectthatthosewhoknow
theycantordontwanttoachievethemwillgiveup.
Thosewhodontknowtheirabilitytypewillexperimentand
learntheirabilityeitherbyobservingtheiroutputdirectlyor
throughfeedbackfromtheprincipal.Wewillreturntothe
questionoffeedbacklaterinthecourse.
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Management1042010ProfessorIwanBarankay 9
Payoffs:
Bythiswemeanwhattheprincipalandtheagentintheend
wanttohavethemostof.
Hereisacommonexampleofapayoffforaprincipal
Principal:profit=output wages
Whatelsemightaprincipalcareabout?
Workersatisfaction,orthepayoffacrossworkers(e.g.equal
payforall;ensuringaminimumwage;capping
compensationatthetop)
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Management1042010ProfessorIwanBarankay 10
Agentspayoff
Theagentwantstomaximizewhateconomistsrefertoas
utility.
Example:U(compensation,costofeffort)
Whatelse,insteadofowncompensationmightaworkercare
about?
Theprincipalspayoff(e.g.inafamilybusiness)
Thepayoffofthefinalconsumerofoutput(e.g.inacharity)
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Management1042010ProfessorIwanBarankay 11
Outsideoption
Opportunitycostisthevalueofwhatyouarewillingtopass
onastheresultofmakingadecision.(goingtothebeach,
party,another
job
etc.)
Itisvery(!)importanttobeawareofthelevelandthe
changeinoutsideoptions.
Thiswilldetermineifpeoplewillacceptorrejectcontracts
Outsideoptionscanalsochangewhenthedemandforlabor
changes
(Note:
Companies
demand
labor
and
workers
supply
labor)
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Management1042010ProfessorIwanBarankay 12
Theselectioneffectofcontractswhetherpeopleaccepta
contract isoftenjustasimportantastheincentiveeffect
howmuchefforttheyputin.
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Management1042010ProfessorIwanBarankay 13
TheCostFunctionofEffort
Itisintuitivetoassumethecostfunctionofefforttohave
thefollowingproperties:
(i) puttinginmoreeffortisalwaysmorecostlythanputtinginless,and(Ifnotworkerwouldbewillingto
payforbeingallowedtoworke.g.altruisticpeople,
those enrollingineducationetc.(ii) initiallyitisreallyeasytoputinmoreeffortbuteach
additionalamountofeffortgetsharderandharder.
(whatifnot?Thenundersomeconditionsworkers
wouldputinendlesseffort,e.g.whenthemarginal
costiszero)
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Management1042010ProfessorIwanBarankay 14
Q7)Agentisbeingofferedalinearcontract
w=a+b*y
wisthewage,
aisafixedpayment(e.g.$5000),
bisapiecerate(e.g.$0.50)
y=e+ isoutput(e.g.kgoffruitpicked)determinedbytheeffortoftheemployee,e,andsomerandomshock beyond
thecontroloftheagent.
Theoutsideoptionandthedegreeofriskaversionwill
determineifthesizeandthesignofthefixedpartof
compensationa.
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Management1042010ProfessorIwanBarankay 15
Whatistheimplicationofalargepieceratebforthe
principal?
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Management1042010ProfessorIwanBarankay 16
Whatistheimplicationofalargepieceratebforthe
principal?
Theimplicationfortheprincipalhingesuponwhatitwilldotoprofits.Thefarmerfacesthefollowingtradeoff:ahigher
piecerateinducestheworkertopickmorefruitbutthenthe
principalalsohastospendmoremoneyonwages.Inthenextworksheetweshowthatgiventhistradeoffhowthe
principalshouldchoosethepiecerate.
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Management1042010ProfessorIwanBarankay 17
Supposenowthatthepiecerateislargebutalso the
randomshockislarge:Howandwhenwillalarge affectthe
actionsoftheagent?
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Management1042010ProfessorIwanBarankay 18
Supposenowthatthepiecerateislargebutalso the
randomshockislarge:Howandwhenwillalarge affectthe
actionsoftheagent?
Alargeerrortermmatterswhentheworkercaresaboutrisk.
Whentheworkerisriskaverse,thenhewillchoosealower
levelofeffortthanwhenhewouldberiskneutral.Theintuitionisthatariskaversepersondoesnotlikethatthe
returntoeffortisuncertain,thereforehefeelsthereturnto
effortislower.(Thisisdifferentwhenpeoplesetthemselvesincometargets.Inthatcasetheywillworkhardertoensure
theyreachtheincometarget.)
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Management1042010ProfessorIwanBarankay 19
Worksheet2
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Management1042010ProfessorIwanBarankay 20
Letsthinkofthefarmerandthefruitpickeragain.
Assumptions
Productiontechnology:Norandomshocksi.e. =0.
(alternativelywecouldassumetheworkersareriskneutral)
Contracts:Thefarmeroffersalinearcontractw=a+b*yPayoffs:Thefarmerwantstomaximizeprofit=output
wages.
Thepickerwantstomaximizeutility=wagecostofeffort
Letsassumethatcostofeffort=0.5e2
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Management1042010ProfessorIwanBarankay 21
Timingofevents:
Theprincipaloffersthecontractwhichtheagentaccepts;
theagentthenchooseshowmuchefforttoexertbutthe
principal
cant
see
the
effort;
as
the
agent
implements
his
effortchoicetherandomshockoccursresultinginthe
output;theoutputisobservedbytheprincipalandtheagent
getspaid.
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Management1042010ProfessorIwanBarankay 22
Howhardwillthepickerworki.e.howmuchfruitwillshe
pickwhensheisofferedthiscontract
w=$5+$1*y
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Management1042010ProfessorIwanBarankay 23
Howhardwillthepickerworki.e.howmuchfruitwillshe
pickwhensheisofferedthiscontract
w=$5+$1*y
recallourassumptionaboutthepickerspayoff
u =wc
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Management1042010ProfessorIwanBarankay 24
Howhardwillthepickerworki.e.howmuchfruitwillshe
pickwhensheisofferedthiscontract
w=$5+$1*y
recallourassumptionaboutthepickerspayoff
andrecallthaty=e
u(e) =wc
=$5+$1*e0.5*e2
ee
u
1
setting0
e
u
yields e=1
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Management1042010ProfessorIwanBarankay 25
Sounderthiscontractthepickerwillpick1kgoffruit.
Supposeinsteadof
w=$5+$1*y
sheisbeingoffered
w=$10+$1*y
or
w=$5+$2*y
howmuchfruitwillshepicknow?
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Management1042010ProfessorIwanBarankay 26
Howmuchfruitwillshepicknow?
u(e) =wc
=$a+$b*e0.5*e2
Now
,sosetting
yields
Aworkerwillworkuntilthemarginalrewardforeffort
equalsthemarginalcostofeffort.Sowhataboutthe$5additionalfixedwages?
Whataboutthehigherpiecerate?
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Management1042010ProfessorIwanBarankay 27
Changinga,thefixedwagecomponentdoesnotaffectthe
amountoffruitpickedhere.
Changingthepieceratebdoes.
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Management1042010ProfessorIwanBarankay 28
Solvingthegeneralcase
Letusnowfindoutwhatpieceratethefarmershouldset
givenourassumptions.
Iwillsolvethegeneralcaseandwecanlaterreplacethevariableswithnumbers.
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Management1042010ProfessorIwanBarankay 29
Thetechnologyofproductionissuchthatefforttranslates
directlyintooutput,y=e.
Nowrecallthatthepickerwillmaximizeutility,whichis
compensationminusthecostofeffort:
Now
,sosetting
yields
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Management1042010ProfessorIwanBarankay 30
Giventhetermsofthecompensationpackage,theworker
willpick
(1)
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Management1042010ProfessorIwanBarankay 31
Thefarmersprofitmaximizationproblem
Letusnotturntothefarmersproblem.Weassumedthat
thefarmerwantstomaximizeprofits.
Thequestionis:whatshouldbethepieceratetomaximizeprofits?
Inourcase:
Nowthefarmerknowsthatthepickerwillchooseeffortsuch
that Replacingthiswehavethat
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Management1042010ProfessorIwanBarankay 32
Tofindtheoptimalpiecerateheneedstoset:
(2)
Theprofitmaximizingpiecerateisrelatedtothemarginal
product.
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Management1042010ProfessorIwanBarankay 33
Againthisresultisintuitive.Whenthereisalotofmoneyto
bemadebysellingfruit,thefarmerwantstoenticethe
pickertopickmorefruit.
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Management1042010ProfessorIwanBarankay 34
Nowwearereadytocalculatethefarmersprofits,given
prices:
(3)
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Management1042010ProfessorIwanBarankay 35
Sofinallywecanalsosaywhatthemaximumlevelofthe
fixedwagecomponent,a,isthatthefarmershouldofferthe
picker.Lookatequation(3)onthepreviouspage.Inorderto
makeanyprofitandsotostayinbusinesshecanonlyoffera
fixedwagecomponentsuchthat
asotherwisehewouldmakealoss.
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Management1042010ProfessorIwanBarankay 36
Tosummarizethewholeissuecanbesummarizedintothree
equations:
Theprofitmaximizingpiecerateis
;
Theworkerseffortwillbe
Andthefarmersprofitgiventhat
.
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Management1042010ProfessorIwanBarankay 37
Example:
Iftheprizeofferedtothefarmerbythesupermarketis
$2/kg,hewillofferapiecerateof$1/kgtotheworker.The
workerwillpick1kg.Toavoidmakingaloss,thefarmerhas
tosetthefixedwagecomponentsuchthat
or .
Iftheworkerdemandsafixedwagecomponentofa=$5,
thenthefarmerwouldmakealossof$4.Soheshouldeither
lowerato$1orbeloworheshouldquitthefruitharvesting
business.
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Management1042010ProfessorIwanBarankay 38
Bonusquestion1:
Whataboutthefixedwagecomponenta?Whatistheprofit
maximizinglevelofa?
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Management1042010ProfessorIwanBarankay 39
Bonusquestion1:
Whataboutthefixedwagecomponenta?Whatistheprofit
maximizinglevelofa?
Recallourdiscussionabouttheroleofthefixedwage
component.Inmanysituationsitwillrespondtotheoutside
optionoftheworker.
Giventhatawillnotaffecttheamountoffruitpickedinour
modelwithriskneutralagents,thefarmershouldsetaas
lowaspossible.Why?Asotherwiseitwilleatintohisprofits.
Seetheprecedingslidesforthecalculations.
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Management1042010ProfessorIwanBarankay 41
Recallthat
u(e) =wc
=$a+$b*e0.5**e2
ebeu
setting
0
eu
yields
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Management1042010ProfessorIwanBarankay 42
Nowthefarmercontinuestomaximizeprofits:
** beape
Butnowe*=b/.So:
2
**bapbbeape
Nowhesets
.0
b
,
bp
b
2
sotheprofitmaximizingpiecerateisstill 2*
pb
.
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Management1042010ProfessorIwanBarankay 43
Hangonaminute.
Didnothingchange?
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Notethataworkerwillworkuntilthemarginalrewardfor
effortequalsthemarginalcostofeffort.
Youcanseethishere: 0
eu
yields
Thismeansthatpickerswithdifferentcostfunctionswillpick
differentamountsoffruit!Thisisintuitive.Fasterpickerstireoutlessquicklysowillpickmorefruituntilthemarginalcost
ofeffortisequaltothemarginalbenefitthepiecerateb.
Whatelseischanging?
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Management1042010ProfessorIwanBarankay 45
Whatelseischanging?
Theprofit:
ebapbbeape2
**
Notethat isinthedenominator.Soalargermarginalcost
willmakethosefractionssmallerandthiswillmakeprofits
smaller.
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Management1042010ProfessorIwanBarankay 46
Drawafigurewiththepieceratebonthehorizontalandprofit ontheverticalaxis.
Whatdoestherelationshipbetweenpiecerateandprofit
looklike?
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Management1042010ProfessorIwanBarankay 47
Finalquestion:Outsideoption
Asbeforeassumethatthepriceofstrawberriesis$2.
Andthatinitiallythefarmeroffersthiscontract:
w=b*y=y(i.e.nofixedwageandthepiecerateissetto
maximizeprofits,inthiscasep=1).
Supposethatthetherearetwoworkers.
Fastworker =1:costofeffort=0.5e2
Slowworker =2:costofeffort=0.52e2=e
2
Supposenowthatbothofthemareofferedajobata
differentcompanywithafixedwageof$0.45.
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Management1042010ProfessorIwanBarankay 48
Whatwillhappen?
Whowillleaveandwhowillstayatthefarm?
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Management1042010ProfessorIwanBarankay 49
Whatwillhappen?
Rememberthattheworkerwillpicksothat
0
e
u
whichyields
Theutilityofworkersatthefarmare:
forthefastpicker, =1,u=w c=e* .5e*2=$.5
fortheslowpicker, =2,u=w c=e* .5*2*e*2=$0.25
Theslowpickerwillleaveandthefastpickerwillstay.
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Management1042010ProfessorIwanBarankay 50
Hereisagraphthatlinksthepieceratetoprofits(tomake
thegraphsimplerIseta=0).
fast
picker
slow
picker
0
b
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Readingfornextweek
Worksheet3Tournament(Netflix)
FixingBankersPay,byLucianBebchukappearedinThe
EconomistsVoice,
December
2009.
ShouldBankerPayBeRegulated?byStevenN.Kaplan
appearedonTheEconomistsVoice,December2009.