LLLL9.Thegovernmentwantstoencourageindividualsonwelfaretobecomeemployed.Itisconsideringtwopossibleincentiveprogramsforfirms.A.Givethefirm$2perhourforeveryindividualonwelfarewhoishired.B.Giveeachfirmthathiresoneormorewelfareworkersapaymentof$1000peryear,irrespectiveofthenumberofhires.Towhatextentiseachoftheseprogramslikelytobeeffectiveatincreasingtheemploymentopportunitiesforwelfareworkers?Firmswillhireadditionallaboraslongastheextrabenefitisgreaterthantheextracostofhiringtheworker,oruntilMRPL=w.OptionAwouldbeeffectivebecauseifthefirmreceives$2perhourforeverywelfareworkerhiredthentheeffectivewagepaid,w,willfallandthefirmwillfinditoptimaltohiremorelaboruntilthebenefits(MRPL)againequalthecosts(w)atthemargin.OptionBwouldbeeffectiveatincreasingemploymentopportunitiesalsointhatifthefirmhiresanindividualwhohasbeenonwelfaretheywillthenreceive$1000.However,planBisnotnecessarilyaseffectiveasplanAgiventhefirmonlyreceivesonelumpsumpaymentregardlessofthenumberofwelfareworkershired.Inthiscasethefirmonlyhasanincentivetohiretheonewelfareworker,thoughtheymayofcoursechoosetohiremorethanonewelfareworker.10.Asmallspecialtycookiecompany,whoseonlyvariableinputislabor,findsthattheaverageworkercanproduce50cookiesperday,thecostoftheaverageworkeris$64perday,andthepriceofacookieis$1.Isthecookiecompanymaximizingitsprofit?Explain.Themarginalproductoflaboris50(cookiesperday)andthepricepercookieis1($percookie)sothemarginalrevenueproductis$50/day.Sincethisislessthanthewageof$64perdaythecookiecompanyisnotmaximizingprofit.Theyareemployingtoomuchlaborsincethecostoflaborisgreaterthanthebenefitoflaboratthemargin,andarethereforeproducingtoomanycookies.11.Afirmusesbothlaborandmachinesinproduction.Explainwhyanincreaseintheaveragewageratecausesbothamovementalongthelabordemandcurveandashiftofthecurve.Anincreaseinthewageratecausesanupwardmovementalongthelabordemandcurve.Foranygivenmarginalrevenueproductcurve,thefirmwillfindthattheywanttohirefewerworkerswhenthewageincreases(anupwardmovement).However,whenthewageincreasesthemarginalcostwillincreasewhichwillreducedesiredoutput.Whenoutputfalls,thefirmwillnotneedasmanymachinesandthemarginalproductoflaborcurvewillshifttotheleft,assumingmachinesandlaborarecomplementary.Thiswillalsoreducethedemandforlabor.1.Supposethatthewagerateis$16perhour,andthepriceoftheproductis$2.Valuesforoutputandlaborareinunitsperhour.q L0 020 135 247 357 465 570 6Findtheprofit-maximizingquantityoflabor.Fromtheinformationgivenabove,calculatethemarginalproductoflabor,theextraoutputproducedbyhiringonemoreunitoflabor,andthenmultiplybypricetogetthemarginalrevenueproductoflabor.Tofindtheprofit-maximizingquantityoflabor,usetherulethatthefirmwantstohirelaboronlyaslongasthemarginalrevenueproductoflaborisgreaterthanthenominalwage,oruptothepointwherethemarginalrevenueproductoflaborisequaltothenominalwage.Fromthetablebelow,thefirmwillhire5unitsoflabor.qLMPLMRPL00--2012040352153047312245741020655816706510Supposethatthepriceoftheproductremainsat$2butthatthewagerateincreasesto$21.Findthenewprofit-maximizingquantityoflabor.Theabovetabledoesnotchangeforthispartoftheproblem.However,thefirmnolongerwantstohire5unitsoflaborbecausethebenefitofthe5thunit($16perhour)islessthanthecostofthe5thunit($21perhour).Thefirmwouldonlyhire3unitsoflaborperhoursinceinthiscasethebenefitstillexceedsthecostatthemargin.Thefirmwouldstickwith3unitsinsteadof4unlessfractionalunitsarepossible.AtL=4thecostisgreaterthanthebenefitsoyouloseprofitbyhiringthe4thunitoflabor.Supposethepriceoftheproductincreasesto$3andthewageremainsat$16perhour.Findthenewprofit-maximizingquantityoflabor.Achangeinthepriceoftheproductwillnotchangethemarginalproductoflabor,butitwillchangethemarginalrevenueproductoflabor.Thenewmarginalrevenueproductoflaborisgiveninthetablebelow.Thefirmwillstillwanttohire5unitsoflabor,asinpartaabove.Itwillnothirethe6thunitbecausetheextrabenefitislessthantheextracost.Profitwillbegreaterthaninparta.qLMPLMRPL00--2012060352154547312365741030655824706515Supposethatthepriceoftheproductremainsat$2andthewageremainsat$16,butthereisatechnologicalbreakthroughthatincreasesoutputby25%foranygivenleveloflabor.Findthenewprofit-maximizingquantityoflabor.Thetechnologicalbreakthroughchangesthenumberofunitsofoutputproducedbyagivennumberofunitsoflabor,andhencechangesthemarginalproductandthemarginalrevenueproductoflabor.Thenewoutputvaluesarefoundbymultiplyingtheoldvaluesby1.25.Thisnewinformationisgiveninthetablebelow.Thefirmwillstillchoosetohire5unitsoflabor.Profitwillbegreaterthaninparta.qLMPLMRPL00--251255043.75218.7537.558.753153071.25412.52581.255102087.566.2512.5Figure14.2LLLLFigure14.6LLSD *10.Afirmusesasingleinput,labor,toproduceoutputqaccordingtotheproductionfunction.Thecommoditysellsfor$150perunitandthewagerateis$75perhour.Findtheprofit-maximizingquantityofL.Therearetwo(equivalent)methodsofsolvingthisproblem.Mostgenerally,definetheprofitfunction,whererevenuesandcostsareexpressedintermsoftheinput,calculatethefirstordernecessarycondition(thefirstderivativeoftheprofitfunction),andsolvefortheoptimalquantityoftheinput.Alternatively,usetherulethatthefirmwillhirelaborupuntilthepointwherethemarginalrevenueproduct(p*MPL)equalsthewagerate.Usingthefirstmethod:Findtheprofit-maximizingquantityofq.Fromparta,theprofitmaximizingquantityoflaboris64sosubstitutethisquantityoflaborintotheproductionfunctiontofind.Whatisthemaximumprofit?Profitistotalrevenueminustotalcostor.Supposenowthatthefirmistaxed$30perunitofoutputandthewagerateissubsidizeda