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68CHAPTER1010-1.Supposeblacksandwhitesarenotperfectsubstitutesinproduction.Thefirmwouldliketominimizethecostsofproducing100unitsofoutput.Showthatemployerswhodiscriminateagainstblacksearnlowerprofits.Doesyourconclusiondependonwhetherthemarket-determinedblackwageislowerthanthewhitewage?Asdrawninthefigurebelow,theprofit-maximizingpositionforanon-discriminatingemployeroccursatpointPwherethe100-unitisoquantistangenttothelowestpossibleisocostlinegivenbyX.Discriminationagainstblacksimpliesthattheutility-adjustedblackwageisrelativelyhigh,andhenceemployerswouldmovetoapointlikeA,whichistangenttotheutility-adjustedisocostgivenbylineY.Note,however,thatatpointAthetruecostsofproductionaregivenbyisocostlineZ,whichisclearlyhigherthanisocostlineX.Asaresult,discriminationiscostly.Itisworthnotingthatthisanalysisassumesnothingaboutwhichwage,theblackorthewhite,ishigher.10-2.Supposeblackandwhiteworkersarecomplementsinthesensethatthemarginalproductofwhitesincreaseswhenmoreblacksarehired.Supposealsothatwhiteworkersdonotlikeworkingalongsideblackworkers.Doesemployeediscriminationleadtocompletesegregation?Doesitcreateawagedifferentialbetweenblackandwhiteworkers?Ifblacksandwhitesareperfectsubstitutes,employeediscriminationleadstocompletesegregation.If,however,blacksandwhitesarecomplementsasinthisproblem,thenthereisanincentiveforemployerstoemployblacksandwhitestogetherintheworkplaceiftheincreaseinproductivityachievedbyintegratingtheworkforceishigherthantheextrawagesemployersmustpaywhiteworkerstocompensatethemforworkingalongsideblacks.Theinterpretationofthewagedifferentialbetweenblackandwhiteworkersismoredifficult.Thewagedifferentialbetweenthetwogroupswillreflectnotonlytheeffectofdiscrimination(ahigherwageforwhitestoencouragethemtoworkalongsideblacks),butalsotheeffectofdifferencesinproductivity.Overall,however,itisclearthatwhitesmustbepaidacompensatingdifferential.CapitalEmploymentXZY100PA6910-3.In1960,theproportionofblacksinSouthernstateswashigherthantheproportionofblacksinNorthernstates.Theblack-whitewageratioinSouthernstateswasalsomuchlowerthaninNorthernstates.Doesthedifferenceintherelativeblack-whitewageratiosacrossregionsindicatethatSouthernemployersdiscriminatedmorethanNorthernemployers?Supposeemployersinneitherregiondiscriminate,sothattheequilibriumblack-whitewagedifferentialinbothregionsisdeterminedbythe(relative)demandforandsupplyofblackworkers.IftherearerelativelymanymoreblackworkersintheSouththanintheNorth,thentheblack-whitewageratiowillbelowerintheSouththanintheNorth,asthemarginalblackhiredintheSouthislessvaluablethanthemarginalblackhiredintheNorth.Thus,thefactthatblacksearnrelativelylessintheSouthneednotindicatethatSouthernemployersdiscriminatemorethanNorthernemployers.Rather,thelargedifferentialmaysimplyreflecttherelativelylargenumberofblackworkersintheSouth.(Thisdoesassumethatblacksandwhitesarenotperfectsubstitutes.)10-4.Supposeyearsofschooling,s,istheonlyvariablethataffectsearnings.Theequationsfortheweeklysalariesofmaleandfemaleworkersaregivenby:wm=500+100sandwf=300+75s.Onaverage,menhave14yearsofschoolingandwomenhave12yearsofschooling.(a)Whatisthemale-femalewagedifferentialinthelabormarket?Thewagedifferentialcanbewrittenas:∆w−=w−m–w−f=500+100s−m–(300+75s−f)=500+100(14)–300–75(12)=$700(b)UsingtheOaxacadecomposition,calculatehowmuchofthiswagedifferentialisduetodiscrimination?Therawwagedifferentialis4342144443444421SkillsinDifferencetoDuealDifferentitionDiscriminatoDuealDifferenti)()()(fmmffmfmsssw−+−+−=∆βββαα700$200$500$)1214(10012)75100()300500(SkillsinDifferencetoDuealDifferentitionDiscriminatoDuealDifferenti=+=−+−+−=4342144443444421.Thewagedifferentialthatisduetodiscriminationequals$500,or5/7thsoftherawdifferential.70(c)CanyouthinkofanalternativeOaxacadecompositionthatwouldleadtoadifferentmeasureofdiscrimination?Whichmeasureisbetter?Supposeinsteadofaddingandsubtractingβmfstotheexpressiongivingtherawwagedifferential,βfmshadbeenaddedandsubtractedtotheexpression.TheOaxacadecompositionwouldthenbegivenby∆wsssmfmfmfmf=−+−+−()()()ααβββDifferentialDuetoDiscriminationDifferentialDuetoDifferenceinSkills1244443444412434700150$550$)1214(7514)75100()300500(SkillsinDifferencetoDuealDifferentitionDiscriminatoDuealDifferenti=+=−+−+−=4342144443444421.Underthismethod,$550ofthe$700wagedifferentialisduetodiscrimination.Thedifferencebetweenmethodsarisesbecauseofthewayinwhichdiscriminationisdefined.Inone,discriminationismeasuredbycalculatinghowmuchawomanwouldearnifsheweretreatedlikeaman(asinthetext),andintheseconditismeasuredbycalculatinghowmuchamanwouldearnifheweretreatedlikeawoman.Onthesurface,neitherisabettermeasure.Itcanbeshown,however,thatthesecondapproach(asinpartc)attributesmorevariationtodiscrimination.10-5.Supposethefirm’sproductionfunctionisgivenbyqEEwb=+10,whereEwandEbarethenumberofwhitesandblacksemployedbythefirmrespectively.ItcanbeshownthatthemarginalproductoflaboristhenMPEEEwb=+5.Supposethemarketwageforblackworkersis$10,themarketwageforwhitesis$20,andthepriceofeachunitofoutputis$100.(a)Howmanyworkerswouldafirmhireifitdoesnotdis