For each of the circuits shown in Figure P14.22, assume

Session 16 Tuesday,March1,2016 10:27AM Table1 L Q MPL APL 1 2 2 2 2 7 5 3.5 3 14 7 4.6 4 20 6 5 5 25 5 5 6 29 4 4.8 7 32 3 4.57 8 34 2 4.25 9 35 1 3.88 10 35 0 3.5 11 34 -1 3.09 Theobjectiveistomaximizerent. Wageis$20perday. Thepriceofashirtis$10. • Profitmaximizationandfirm'semploymentdecision: o Anentrepreneurintendingtoproduceagoodhasalotofdecisionstomake. • Whattoproduce • Howmuchtoproduce • Wheretolocatetheirproductionfacility • Howlargeaspacetorent • Howmanymachines • Howmanyworkers • Whattopayforeachtypeoffactor • Atwhatpricetoselltheirgood o Thefirmisacompetitiveproducerinalargemarketforboththeproducts(shirts) andfactors(labor). o Disregardallexceptthreedecisions: • Howmanyworkerstoemploy • Howmuchtopayeachworker • Atwhatpricetoselltheirgood Table2 L P*Q$ VMPL$ VAPL$ LaborCost$ Rent$ 1 20 20 20 20 0 2 70 50 35 40 30 3 140 70 46 60 80 4 200 60 50 80 120 5 250 50 50 100 160 6 290 40 48 120 170 7 320 30 45.7 140 180 8 340 20 42.5 160 180 9 350 10 38.8 180 170 10 350 0 35 200 150 11 340 -10 30.9 210 120 1 1:Unitsoflabor 2:Revenue:pricexquantity 3:pricexmpl 4:pricexvapl 5:laborcost:costofemployment 6:Laborcost-Revenue=rent • Rentsarewhatafirmmakes • Accordingtotheobjectiveofrentmaximization,howmanyworkersdoesthisfirmhire o Therule:Hirelaboruptowherethewageequalsthevalueofthemarginalproduct oflabor. o Hires8laborers. o AtVMPL=$20,there's8workers • AtL=2theoutputad dedfromemployingthe2ndunitoflaboris$50. • Thatis,the2ndworkeradds$whiletheworkercosts$20. • Thererentsincreaseby$30whenthe2ndworkerisadded. • Addinganotherworker,itscontributionis$70,whileitcosts$20,sorentsincreaseby$ 50. • WecontinuewiththisexpansiontillwegetL=8.Herethisworkerwillad$20anditwill cost$20. • Forthe9thUnitoflaborthislaboradds$10totheoutputwhileitcosts$20.Willthe9th workerbeemployedatthisfirmWhy o No,becauseiftheyemploythe9thperson,therentswillfall,by$10.There'saloss. Derivingafirm'soptionalchoiceoflaboremployment(forexpositiononly) Q=quantityofoutput L=quantityoflaborusedtoproducetheoutput P=Pricepershirt W=wageperunitof labor • Firm'sdecision:chooseLsoastomaximizerents=PQ -WL. • WeknowthatQ=f(L) • So,chooseLsoastomaximizerents=Pf(L) -WL • TakethederivativewithrespecttoLandequatetozero.ThensolveforoptimalL: o Pdf(L)/dL-W=0orPMPL=worVMPL=W WhynotusetheAveragerule • TheValueofAverageProductofthe9thworkersis$38.88.Thatis,asanaverage,the9th workerproduces$38.88whilethisworkercostsonly$20. • Iftheemployeraddsthe9thworker,thisworkeradds$ 10tothetotalvalueofoutput. • Onaverage,theemployergets$38.88ofoutputoutofeachofthe9workersandpays each$20sobyemployingthe9thworker,theemployergetsalmost$19ofbenefit/rent. • However,thearrivalofthe9thworkerslowsdownt herestoftheworkers. • Thecostoftheslowdownoftheprevious8workersis($2.50 -$38.88)*8andisequalto $28.96. • Sotheemployer,byaddingthe9thworker,gets$19ofbenefitbutloses$29.Helosesin net$29-$19-$10.Thisisindeedthereduction inrents(from$180to$170). Derivingthedemandscheduleforlabor(byafirm): • Atwageof$20,wedecidedthattherentmaximizingfirmwouldhire 8workers. • Howmanyworkerswillthefirmhireifthewagegoesdownto$10perday o 9workers • Howmanyworkerswillthefirmhireifthewagegoesupto$40perday 20 10 Anexampleoftheuseofmarginalanalysisinproductionandemploymentoflabor: • JaneandJillaretwinsisters.TheyhavegraduatedwiththesameGPAandthesameskills fromthesamedepartment. • Assumethatthegoingwageforfreshgraduatesfromthisdepartsis$40Kayear. • Janegoesdowntowntoafurnituredesignfirmtoapplyforajob.Shecomeshomea nd tellsJillthatshegotthejob. • Nextday,Jillgoestothesamefirm(sheisasgoodasJane)andsheisturneddown. • Why • WhatisthevalueofemployingJanetothefirm(whatistheVMPLofemployJane) o $40K. • WhatisthevalueofemployingJillIs ithigherorlowerthan$40K o Lessthan$40K. • Animportantinsight:Whyisitthatourskilledgraduatesdonotreceive5millionjob offersupongraduation o ItisduetothefallingMPL.IftheMPLwasnotfallingsay,ifitwasincreasing,then firmswouldhaveinfinitedemandforworkers. Allocationofresourcesunderprivateproperty • Supposethereisapieceoflandownedbysomeone.Theownerhiresworkerstoworkon thelandtoproducefood.Thegoingwageis$20perworkerperday.Thepriceofa unitof foodis$10.Thetableoflaborinputsandoutputsisproducedbelow. L Output(Q) 1 2 2 7 3 14 4 20 5 25 6 29 7 32 8 34 9 35 10 35 11 34 12 32 13 30 14 28 15 25 Table4-Decisionofthefirmunderprivateproperty L P*Q($) VMPL($) VAPL($) LaborCost($) Rent($) 1 20 20 20 20 0 2 70 50 35 40 30 3 140 70 46 60 80 4 200 60 50 80 120 5 250 50 50 100 150 6 290 40 48 120 170 7 320 30 45.7 140 180 8 340 20 42.5 160 180 9 350 10 38.8 180 170 10 350 0 35 200 150 11 340 -10 30.9 220 120 12 320 -20 26.67 240 80 13 300 -20 25 260 40 14 280 -20 20 280 0 15 250 -30 16.67 300 -50 • Howmanyworkersdoesthisfirm -withprivatepropertyrights -hire o 8 • The$20wagemeansthata workerisabletoproduce$20worthofgoodsperday somewhereelseintheeconomy. • Thereforewhenthisindividualdecidestoworkfor$20atafarm,itmeansthat$20worth ofothergoodsdisappearelsewhereintheeconomy. • Underprivateproperty,thefa ctory/businessowneremploysworkersuptowherethe contributionofthelastworkeremployedinhisbusinessisnolessthantheywouldhave producedelsewhereintheeconomy(whichis$20perday). Considerthe6thworker: 6thworker: Shoes$20 WheatFarm$40 7thWorker: Shoes$20 WheatFarm$30 8thWorker Shoes$20 WheatFarm$20 9thWorker Shoes$20 WheatFarm$10 Session 17 Thursday,March3,2016 10:29AM Thebehavioroffirmsunderdifferentsystemsofpropertyrights:inallocatingresources,the systemofpropertyrightsmattersagreatdeal. • Underprivateproperty,rentsaremaximized.Howdoesthisprocessalsoensureefficient allocationofresourcesfortheeconomy o The$20wagemeansthataworkerisabletoproduce$20ofgoodsperday somewhereelseintheeconomy. o Whenthisindividualdecidestoworkfor$20atafarm,itmeansthat$20worthof othergoodsdisappearelsewhereintheeconomy. o Thewageraterepresentstheopportunitycostofthislabortothesociety. • Rentsrepresentthenetgainsinthevalueofoutput -requiringuseofscarceresources-in wheatproductionoverandabovethesameresourcesbeingusedelsewhere. ProductionandInputUseUnderCommonProperty • Consideragainapieceoflandonwhich foodisproduced.Now,assumethereisno "owner"andnoonecanbedeniedaccesstothisland.Eachworkergetsanequalshare - theValueofAverageProductofLabor.Goingwageis$20perworkerperday. • Priceis$10perbushelofwheat: L P*Q($) VMPL($) VAPL($) LaborCost($) Rent($) 1 20 20 20 20 0 2 70 50 35 40 30 3 140 70 46 60 80 4 200 60 50 80 120 5 250 50 50 100 150 6 290 40 48 120 170 7 320 30 45.7 140 180 8 340 20 42.5 160 180 9 350 10 38.8 180 170 10 350 0 35 200 150 11 340 -10 30.9 220 120 12 320 -20 26.67 240 80 13 300 -20 25 260 40 14 280 -20 20 280 0 15 250 -30 16.67 300 -50 • Undernoprivateproperty,howmanyworkerswillbeworkingonthislandWhatarethe rents o 14workers o Here,theVAPLis$20whichisequaltothewage. o Rentsare$0. • Whyarerents" dissipated"undercommonproperty o Excessoutputisgone. o The$20wagemeansthataworkerisabletoproduce$20worthofgoods somewhereelse. th • Forthe10 worker,thisworkerdoesnotaddanythingtooutputonthefarmandbybeing there,$20worthofothergoodsandservicesarenotbeingproduced.Sonetlossforthe 10 workeris$20. o AtL=11,VMPL=$-10,netlossis$30 o AtL=12,VMPL=$-20,netlossis$40 o AtL=13,VMPL=$-20,netlossis$40 o AtL=14,VMPL=$-20,netlossis$40 • Soaddingallthenetlosses:$180. • ThisisthemaximumrentthatcouldhavebeenearnedbychoosingworkerswhereVMPL =W.Thatis,inthesystemofcommonproperty,"dissipation"ofrentstakesplace.The rentrepresentsthenetgaininthevalueofoutput -requiringuseofscarceresources-in anactivityoverandabovethesameresourcesusedelsewhereintheeconomy.Thisnet gainisdissipatedbytheabsenceofpropertyrights. • TheMPLdiffersfromtheAPLbecauseMPLtakesintoaccounttheimpactof adding anotherworkeronpreviousworkers'averageproduct. • Ifthisimpactisignored,thenindividualsdonotownthefullconsequencesoftheiractions ,thisisthesourceoflostgainsfromtrade. • Anapplicationofthecommonpropertyoutcome:Whyis thatsalmonisarguedandfeared tobeonthebrinkofextinctionbutnotbeeforchicken ClickerQuestion:Undercommonproperty,workersaddthemselvesinuntilVAPL=W.Atthis levelofemploymentwagerentsfalltozerosinceworkersignoretheir pactonotherworkers' work. ProductionandInputUseunder"SocialistCooperatives":theworkers -whocollectivelyownthe land-decidewhocanjoinin.Eachworkergetsanequalshare. • P=$10 • W=$20 L P*Q($) VMPL($) VAPL($) LaborCost($) Rent($) 1 20 20 20 20 0 2 70 50 35 40 30 3 140 70 46 60 80 4 200 60 50 80 120 5 250 50 50 100 150 6 290 40 48 120 170 7 320 30 45.7 140 180 8 340 20 42.5 160 180 9 350 10 38.8 180 170 10 350 0 35 200 150 11 340 -10 30.9 220 120 12 320 -20 26.67 240 80 13 300 -20 25 260 40 14 280 -20 20 280 0 15 250 -30 16.67 300 -50 • Howmanyworkerswillbeworkingtheland o Only5workers o That'swherethevalueoftheaverageproductisthehighest o Therentsarenotmaximized. • Therentsare$150. • Butthe6thworkercouldadd $40onthislandandisonlyproducing$20elsewhere.The netgaintoconsumersof$20islostbyexcludingthisworker. • Thoseonthefarmwillget$50andotherworkersqueueuptogettherighttoworkthere andearnsomeofthe"rents" capturedbythemembersofcooperatives. • Sincecompetitionisfierce,somerationingtakesplace.Themembersofthecooperative havetodecidewhogetsinandwhodoesnot.Asextraresourcesarespenttogetin,a dissipationofrentstakesplace. ClickerQuestion:Whenworkers'socialistcooperativescontrolthelevelofemployment,they employworkerssuchthateachworkerispaidthehighestVAPL.Atthislevel,toofewworkers areemployed. Section7.4ApplicationsoftheLawofDiminishingMargin alProduct:Allocatingtwoormore variableinputsinproduction: • Withonlyoneinputchoice,welearnedthattherent(benefit)maximizingruleistohire laboruptowhere: o VMPL=WageoflabororP*MPL=W L • Now,supposethefirmalsoneedstomakedecisio nsaboutcapital(Machinery).INthis casetheruleformaximumbenefitfromemploymentofmachinesis:buyequipmentupto where o VMPK=WageofcapitalorP*MPK=W k • Theabovetworelationshipsimply: o P*MPL/W -P*MPK/W L K • Benefitsaremaximizedwhenemployme ntoflaborandcapitaltakeplaceuptowhere: themarginalbenefitofthelast$spentonlabor -themarginalbenefitofthelast$spent oncapital. • Forsimplicity,let'sassumewageforbothfactorsis$1.Thentheaboverulebecomes: employunitsoflaborandcapitaluptowhereMPL=MPK • INthissimplifiedcase,theruleistoemployLandKtillthemarginalproductivityoflabor employed=themarginalproductivityofcapitalemployed. • Ifresourcesareemployedsuchthat,MPL>MPK,itimpliesthat additiontooutputofone moreunitoflaboremployedarehigherthanthebenefitsofonemoreunitofcapital. Example • Supposeaclothingfirmcurrentlyemploys4.5hoursofdesigners/tailorstimeand4.5 hoursofadriver'stimeperday. • Thefirmhastotalof9hourofresourcestoemployperday. • Anadditionalhalfanhourofdesignerworkproduces$100worthofoutputwhilean additionalhalfhourofthedrivertimeproduces$150worthofoutput/service. • Shouldthisfirmchangetheallocationofitsr esources o Yes.Byreallocatinghalfanhourfromdesignertodriver,thefirmislosing$100but gaining$150,increasingitsrevenues. o Therefore,whereMPL>MPK,thefirmneedstomakeadjustmentsinitsemployment ofthesefactors. o Whereanemploymentof factorsaresuchthatMPL-MPK,nofurtheradjustmentis necessary(thisiswherethetotalbenefitsfromemploymentofbothfactorsarethe highest.) Example1: InM*A*S*HunitsduringtheKoreanwar,doctorsandnurseshadtodecidehowmuchattention togivetoeachwoundedsoldier.Thegoal(implicitly)istomaximizehumanlife. Theyspendtheirtimeandeffortonpatientssuchthat: Marginalbenefits(ofanhourofsurgery)onpatient1=Marginalbenefits(ofanhourofsurgery) onpatient2andsoon… Ifapatientistooseverelyinjuredandrequires10hoursofsurgerytosavehislife,thedoctors mayoptfornottreatinghim.Inthose10hours,theycouldsaveperhaps5lives.Inthismanner, themarginalbenefit(MB)ofspendingefforton theveryseverelywoundedislessthantheMB ofresourcesspentonthelessseverelywoundedpatients. Example2: Incasinos,itisthecasethatthe$machinesaremoreprofitablethannickelmachines.Thatis, theaverageprofitper$machineishighe rthantheaverageprofitpernickelmachine.Should thecasinoonlyinstall$machines SupposetheDollarmachineandNickelmachineseachcost$1000.Thetable1and2providethe marginalandaverageprofitsfor$andfornickelmachines. Supposethiscasinohasspacefor5machines. Shoulditinstallonly$machines,onlynickelmachines,oracombinationofthetwo