MGMT104 Fall 2010 Lecture 03

8/8/2019 MGMT104 Fall 2010 Lecture 03

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Management1042010ProfessorIwanBarankay 1

Management104

IndustrialRelationsandHumanResourceManagement

ProfessorIwanBarankay

Lecture3

RecapofWorksheet1

Worksheet2


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Arecapfromlastlecture

ThePrincipalAgentmodelhasthefollowingcomponents

1) Thetechnologyofproductionconsistingoftheoutput,

theactionstakenbytheagenttoproducetheoutput,and

theeventsthataffectoutputthatareoutsidethecontrolof

theagent.

2) Thesetoffeasiblecontracts

3) Thepayofftotheparties

4) Thetimingofevents


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Eventsoutsideofcontrol

exogeneousshockstoproductivity(weather,

technologicalfailure,lawsuits)

unanticipatedchangesindemandforfinalgoods

(financialcrisis)orsupplyofinputs(bankruptcyofsupplier)

fromtheagentsperspective:tosomeextendactionsby

theprincipal

fromtheprincipalsperspective:tosomeextendactions

bytheagent


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Contractscantakeonmanyforms

FixedWage/Compensation

Linearcontracts,e.g.piecerates($percrateorkgoffruit

pickedsubjecttoachievingapredefinedqualitylevel)

Nonlinearcontract,e.g.compensationaboveandbelowa

threshold

Bonusschemes

RetentionTournaments

LinkedtoCompanylevelperformance(e.g.stockoptions)


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Contractscanbecompleteorincomplete

Completecontractsdescribeacourseofactionand

compensationinallcontingencies

Incomplete

contracts

staydeliberatelysilentonactionsandcompensationinsome

situations

or

itmaybeimpossibleortoocostlytodescribeactionsand

compensationinallcontingencies


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Assumptionsweneededtomakewhendiscussingwhich

contractsmightbeused

Whocanobserveactions?

Ifonlytheworkercanseetheactionsthenworkersmight

haveamoralhazardtoengageinactionstheprincipalwouldnotfindoptimal.Iftheactionsmapdirectlytoproductivityandagentsare

riskneutral

(the

case

we

consider

this

week)

then

we

can

stillimplementagoodoutcomefromtheprincipals

perspective.


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WorkerHeterogeneity

Somepeoplemightbemoreable(ortalentedetc.)than

others.Weoftenrefertothatasagentstypes.

Whenemployeesworkundercomparableconditionsand

somearemoreproductivethanothersthencontractscanbe

usedtoeffectivelysortagentsbyability.

Underthesamecontract,peoplewithhigherabilitywillbemoreproductive.


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PerformanceTargets

Thesecanhavetheundesirableeffectthatthosewhoknow

theycantordontwanttoachievethemwillgiveup.

Thosewhodontknowtheirabilitytypewillexperimentand

learntheirabilityeitherbyobservingtheiroutputdirectlyor

throughfeedbackfromtheprincipal.Wewillreturntothe

questionoffeedbacklaterinthecourse.


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Payoffs:

Bythiswemeanwhattheprincipalandtheagentintheend

wanttohavethemostof.

Hereisacommonexampleofapayoffforaprincipal

Principal:profit=output wages

Whatelsemightaprincipalcareabout?

Workersatisfaction,orthepayoffacrossworkers(e.g.equal

payforall;ensuringaminimumwage;capping

compensationatthetop)


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Agentspayoff

Theagentwantstomaximizewhateconomistsrefertoas

utility.

Example:U(compensation,costofeffort)

Whatelse,insteadofowncompensationmightaworkercare

about?

Theprincipalspayoff(e.g.inafamilybusiness)

Thepayoffofthefinalconsumerofoutput(e.g.inacharity)


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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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Theselectioneffectofcontractswhetherpeopleaccepta

contract isoftenjustasimportantastheincentiveeffect

howmuchefforttheyputin.


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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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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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Whatistheimplicationofalargepieceratebforthe

principal?


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Whatistheimplicationofalargepieceratebforthe

principal?

Theimplicationfortheprincipalhingesuponwhatitwilldotoprofits.Thefarmerfacesthefollowingtradeoff:ahigher

piecerateinducestheworkertopickmorefruitbutthenthe

principalalsohastospendmoremoneyonwages.Inthenextworksheetweshowthatgiventhistradeoffhowthe

principalshouldchoosethepiecerate.


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Supposenowthatthepiecerateislargebutalso the

randomshockislarge:Howandwhenwillalarge affectthe

actionsoftheagent?


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Supposenowthatthepiecerateislargebutalso the

randomshockislarge:Howandwhenwillalarge affectthe

actionsoftheagent?

Alargeerrortermmatterswhentheworkercaresaboutrisk.

Whentheworkerisriskaverse,thenhewillchoosealower

levelofeffortthanwhenhewouldberiskneutral.Theintuitionisthatariskaversepersondoesnotlikethatthe

returntoeffortisuncertain,thereforehefeelsthereturnto

effortislower.(Thisisdifferentwhenpeoplesetthemselvesincometargets.Inthatcasetheywillworkhardertoensure

theyreachtheincometarget.)


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Worksheet2


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Letsthinkofthefarmerandthefruitpickeragain.

Assumptions

Productiontechnology:Norandomshocksi.e. =0.

(alternativelywecouldassumetheworkersareriskneutral)

Contracts:Thefarmeroffersalinearcontractw=a+b*yPayoffs:Thefarmerwantstomaximizeprofit=output

wages.

Thepickerwantstomaximizeutility=wagecostofeffort

Letsassumethatcostofeffort=0.5e2


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Timingofevents:

Theprincipaloffersthecontractwhichtheagentaccepts;

theagentthenchooseshowmuchefforttoexertbutthe

principal

cant

see

the

effort;

as

the

agent

implements

his

effortchoicetherandomshockoccursresultinginthe

output;theoutputisobservedbytheprincipalandtheagent

getspaid.


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Howhardwillthepickerworki.e.howmuchfruitwillshe

pickwhensheisofferedthiscontract

w=$5+$1*y


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w=$5+$1*y

recallourassumptionaboutthepickerspayoff

u =wc


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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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Sounderthiscontractthepickerwillpick1kgoffruit.

Supposeinsteadof

w=$5+$1*y

sheisbeingoffered

w=$10+$1*y

or

w=$5+$2*y

howmuchfruitwillshepicknow?


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Howmuchfruitwillshepicknow?

u(e) =wc

=$a+$b*e0.5*e2

Now

,sosetting

yields

Aworkerwillworkuntilthemarginalrewardforeffort

equalsthemarginalcostofeffort.Sowhataboutthe$5additionalfixedwages?

Whataboutthehigherpiecerate?


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Changinga,thefixedwagecomponentdoesnotaffectthe

amountoffruitpickedhere.

Changingthepieceratebdoes.


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Solvingthegeneralcase

Letusnowfindoutwhatpieceratethefarmershouldset

givenourassumptions.

Iwillsolvethegeneralcaseandwecanlaterreplacethevariableswithnumbers.


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Thetechnologyofproductionissuchthatefforttranslates

directlyintooutput,y=e.

Nowrecallthatthepickerwillmaximizeutility,whichis

compensationminusthecostofeffort:

Now

,sosetting

yields


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Giventhetermsofthecompensationpackage,theworker

willpick

(1)


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Thefarmersprofitmaximizationproblem

Letusnotturntothefarmersproblem.Weassumedthat

thefarmerwantstomaximizeprofits.

Thequestionis:whatshouldbethepieceratetomaximizeprofits?

Inourcase:

Nowthefarmerknowsthatthepickerwillchooseeffortsuch

that Replacingthiswehavethat


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Tofindtheoptimalpiecerateheneedstoset:

(2)

Theprofitmaximizingpiecerateisrelatedtothemarginal

product.


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Againthisresultisintuitive.Whenthereisalotofmoneyto

bemadebysellingfruit,thefarmerwantstoenticethe

pickertopickmorefruit.


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Nowwearereadytocalculatethefarmersprofits,given

prices:

(3)


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Sofinallywecanalsosaywhatthemaximumlevelofthe

fixedwagecomponent,a,isthatthefarmershouldofferthe

picker.Lookatequation(3)onthepreviouspage.Inorderto

makeanyprofitandsotostayinbusinesshecanonlyoffera

fixedwagecomponentsuchthat

asotherwisehewouldmakealoss.


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Tosummarizethewholeissuecanbesummarizedintothree

equations:

Theprofitmaximizingpiecerateis

;

Theworkerseffortwillbe

Andthefarmersprofitgiventhat

.


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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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Bonusquestion1:

Whataboutthefixedwagecomponenta?Whatistheprofit

maximizinglevelofa?


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Bonusquestion1:

Whataboutthefixedwagecomponenta?Whatistheprofit

maximizinglevelofa?

Recallourdiscussionabouttheroleofthefixedwage

component.Inmanysituationsitwillrespondtotheoutside

optionoftheworker.

Giventhatawillnotaffecttheamountoffruitpickedinour

modelwithriskneutralagents,thefarmershouldsetaas

lowaspossible.Why?Asotherwiseitwilleatintohisprofits.

Seetheprecedingslidesforthecalculations.


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Recallthat

u(e) =wc

=$a+$b*e0.5**e2

ebeu

setting

0

eu

yields


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Nowthefarmercontinuestomaximizeprofits:

** beape

Butnowe*=b/.So:

2

**bapbbeape

Nowhesets

.0

b

,

bp

b

2

sotheprofitmaximizingpiecerateisstill 2*

pb

.


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Hangonaminute.

Didnothingchange?


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Notethataworkerwillworkuntilthemarginalrewardfor

effortequalsthemarginalcostofeffort.

Youcanseethishere: 0

eu

yields

Thismeansthatpickerswithdifferentcostfunctionswillpick

differentamountsoffruit!Thisisintuitive.Fasterpickerstireoutlessquicklysowillpickmorefruituntilthemarginalcost

ofeffortisequaltothemarginalbenefitthepiecerateb.

Whatelseischanging?


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Whatelseischanging?

Theprofit:

ebapbbeape2

**

Notethat isinthedenominator.Soalargermarginalcost

willmakethosefractionssmallerandthiswillmakeprofits

smaller.


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Drawafigurewiththepieceratebonthehorizontalandprofit ontheverticalaxis.

Whatdoestherelationshipbetweenpiecerateandprofit

looklike?


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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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Whatwillhappen?

Whowillleaveandwhowillstayatthefarm?


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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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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.

Documents

MGMT104 Fall 2010 Lecture 03