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60CHAPTER99-1.Supposeaworkerwithanannualdiscountrateof10percentcurrentlyresidesinPennsylvaniaandisdecidingwhethertoremainthereortomovetoIllinois.Therearethreeworkperiodsleftinthelifecycle.IftheworkerremainsinPennsylvania,hewillearn$20,000peryearineachofthethreeperiods.IftheworkermovestoIllinois,hewillearn$22,000ineachofthethreeperiods.Whatisthehighestcostofmigrationthataworkeriswillingtoincurandstillmakethemove?TheworkermustcomparethepresentvalueofstayinginPennsylvaniatothepresentvalueofmovingtoIllinois.AworkerwillmoveifthepresentvalueofearningsinIllinoisminusthecostsofmovingthereexceedthepresentvalueofearningsinPennsylvania:74.710,54$)1.1(000,201.1000,20000,202=++=PAPVand82.181,60$)1.1(000,221.1000,22000,222=++=ILPVTheworkerwillmove,therefore,ifPVIL–CPVPA,whereCdenotesmigrationcosts.Thus,theworkermovesifC60,181.82-54,710.74=$5,471.089-2.NickandJanearemarried.TheycurrentlyresideinMinnesota.Nick’spresentvalueoflifetimeearningsinhiscurrentemploymentis$300,000,andJane’spresentvalueis$200,000.TheyarecontemplatingmovingtoTexas,whereeachofthemwouldearnalifetimeincomeof$260,000.Thecouple’scostofmovingis$10,000.Inaddition,NickverymuchpreferstheclimateinTexastothatinMinnesota,andhefiguresthatthechangeinclimateisworthanadditional$2,000tohim.Jane,ontheotherhand,prefersMinnesota’sfrigidwinters,soshefiguresshewouldbe$2,000worseoffbecauseofTexas’sblisteringsummers.ShouldtheymovetoTexas?Yes.The“climatic”aspectsofthemoveexactlybalanceeachother,soweshouldnottakethemintoaccount.Onthemonetaryside,thesumofNick’sandJane’slifetimepresentvalueofearningsinMinnesotais$500,000.ThecorrespondingamountinTexaswillbe$520,000.Thedifferencebetweenthetwo($20,000)exceedsthecostofmoving($10,000),sothemovewillmakethecouplejointlybetteroff.619-3.MickeyandMinnieliveinOrlando.Mickey’snetpresentvalueoflifetimeearningsinOrlandois$125,000.Minnie’snetpresentvalueoflifetimeearningsinOrlandois$500,000.ThecostofmovingtoAtlantais$25,000perperson.InAtlanta,Mickey’snetpresentvalueoflifetimeearningswouldbe$155,000,andMinnie’snetpresentvalueoflifetimeearningswouldbe$510,000.IfMickeyandMinniechoosewheretolivebasedontheirjointwell-being,willtheymovetoAtlanta?IsMickeyatied-moveroratied-stayerorneither?IsMinnieatied-moveroratied-stayerorneither?Asacouple,thenetpresentvalueoflifetimeearningsofstayinginOrlandois$500,000+$125,000=$625,000andofmovingtoAtlantais$510,000+$155,000–$50,000=$615,000.Thus,asacouple,theywouldchoosetostayinOrlando.Thus,therecanonlybeatied-stayer.(Therecannotbeatied-mover,becausethecoupleisnotmoving.)ForMickey,stayinginOrlandoisassociatedwithanetpresentvalueof$125,000,whilemovingtoAtlantawouldyieldanetpresentvalueof$155,000–$25,000=$130,000.SoMickeywouldchoosetomovetoAtlanta.Therefore,Mickeyisatied-stayer.ForMinnie,stayinginOrlandoisassociatedwithanetpresentvalueof$500,000,whilemovingtoAtlantawouldyieldanetpresentvalueof$510,000–$25,000=$485,000.SoMinniewouldchoosetoremaininOrlando.Thus,Minnieisnotatied-stayer.9-4.Supposeaworker’sskilliscapturedbyhisefficiencyunitsoflabor.Thedistributionofefficiencyunitsinthepopulationissuchthatworker1has1efficiencyunit,worker2has2efficiencyunits,andsoon.Thereare100workersinthepopulation.IndecidingwhethertomigratetotheUnitedStates,theseworkerscomparetheirweeklyearningsathome(w0)withtheirpotentialearningsintheUnitedStates(w1).Thewage-skillsrelationshipineachofthetwocountriesisgivenby:w0=700+0.5s,andw1=670+s,wheresisthenumberofefficiencyunitstheworkerpossesses.(a)Assumetherearenomigrationcosts.Whatistheaveragenumberofefficiencyunitsamongimmigrants?Istheimmigrantflowpositivelyornegativelyselected?Theearnings-skillsrelationshipineachcountryisillustratedinthefigurebelow.TheUSlineissteeperbecausethepayofftoaunitofskillsishigherintheUnitedStates.Allworkerswhohaveatleast60efficiencyunitswillmigratetotheUnitedStates.Therefore,thereispositiveselectionandtheaveragenumberofefficiencyunitsintheimmigrantflowisapproximately80(theexactanswerdependsonwhetherthepersonwith60efficiencyunits,whoisindifferentbetweenmovingornot,movestotheUnitedStates).62(b)Supposeitcosts$10tomigratetotheUnitedStates.Whatistheaveragenumberofefficiencyunitsamongimmigrants?Istheimmigrantflowpositivelyornegativelyselected?Ifeveryoneincursacostof$10tomigratetotheUnitedStates,theU.S.wage-skilllinedropsby$10,andonlythosepersonswithmorethan80efficiencyunitswillfinditworthwhiletomigrate.Theimmigrantflowisstillpositivelyselectedandhas,onaverage,90efficiencyunits.(c)Whatwouldhappentotheselectionthattakesplaceifmigrationcostsarenotconstantinthepopulation,butaremuchhigherformoreskilledworkers?Ifmigrationcostsaremuchhigherforskilledworkers,itispossiblethatnoskilledworkerswillfinditworthwhiletomigrate.Wealreadyknowthatevenintheabsenceofmigrationcostsnoworkerwithfewerthan60efficiencyunitsfindsitworthwhiletomigrate.IfhighlyskilledworkersfinditverycostlytomigrateitmightbethecasethatthereisnomigrationtotheUnitedStates.Income70067060EfficiencyUnitsSourceCountryUSIncomeEfficiencyUnits70066080SourceCountryUS639-5.SupposetheUnitedStatesenactslegislationgrantingallwork