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MovementofLaborandCapitalbetweenCountries1.Intheshort-runspecific-factorsmodel,examinetheimpactonasmallcountryfol-lowinganaturaldisasterthatdecreasesitspopulation.Assumethatlandisspecifictoagriculture,capitalisspecifictomanufacturing,andlaborisfreetomovebetweenthetwosectors.a.InadiagramsimilartoFigure5-2,determinetheimpactofthedecreaseinwork-forceontheoutputofeachindustryandtheequilibriumwage.Answer:Thefollowingdiagramdepictsadecreaseinpopulation(labor)inthespecific-factorsmodel.Theoriginforagricultureshiftsinwardbyexactlytheamountofthechangeinpopulation,carryingwithitthecurverepresentingthemarginalproductoflaborinagriculture.(Note:onecouldequivalentlyshifttheoriginandMPLcurveinmanufacturingandarriveatthesameresult.)ThenewequilibriumisdeterminedattheintersectionofPMMPLMand(PAMPLA),whichcorrespondstoahigherwageW.Inmanufacturing,theamountoflabordecreasesfromOMLtoOMLandtheamountofcapitalremainsthesame.Asaresult,theoutputofmanufacturingdecreases.Inagriculture,theamountoflaborhasdecreasedfromOALtoOAL(notethat(LL)isnecessarilylessthan(OAOA)andtheamountoflandremainsthesame.Asaresult,theoutputofagriculturealsodecreases).S-395b.Whathappenstotherentalsoncapitalandland?Answer:Becausethequantityoflaborinbothindustriesdecreasesduetothenat-uraldisaster,themarginalproductoflaborincreasesinbothindustriesandthemar-ginalproductsoftheindustry-specificfactorsdecrease.Becauseitisasmallcoun-try,thefinaloutputpricesPAandPMremainunchanged;hence,therentalrateforcapital,PMMPK,decreasesandtherentalrateforland,PAMPT,decreases.2.Howwouldyouranswertoproblem1changeifinsteadweusethelong-runmodel,withshoesandcomputersproducedusinglaborandcapital?Answer:Inthelong-runmodel,adecreaseinlabordoesnotaffectfactorpricesatall.Rather,theoutputofshoesandcomputersadjusts:accordingtotheRybczynskitheorem,theoutputofthelabor-intensiveindustry(shoes)decreasesandtheoutputofthecapital-intensiveindustry(computers)increases.Thispointcanbeillustratedgraphicallyaswell,asinproblem3.3.Consideranincreaseinthesupplyoflaborduetoimmigration,andusethelong-runmodel.Figure5-8showstheboxdiagramandtheleftwardshiftoftheoriginfortheshoeindustry.Redrawthisdiagram,butinstead,shifttotherighttheoriginforcomput-ers.Thatis,expandthelaboraxisbytheamountL,butshiftittotherightratherthantotheleft.Withthenewdiagram,showhowtheamountoflaborandcapitalinshoesandcomputersisdetermined,withoutanychangeinfactorprices.Carefullyexplainwhathashappenedtotheamountoflaborandcapitalusedineachindustryandtotheoutputofeachindustry.Answer:Keepingfactorpricesconstant(i.e.,WandRKconstant),theK/Lratioineachindustryremainsunchanged.Inthediagrambelow,thismeansthattheslopeofthearrowsemanatingfromeachoriginstaysthesameevenwhenthetotalendow-mentsofcapitalorlaborchange.Shiftingtheoriginforcomputerstotherightex-pandsthehorizontalaxisandsignifiestheincreaseinlaborduetoimmigration.Findinganewequilibriuminvolvesscalingthearrowsupordownfromtheirre-spectiveoriginstofindauniqueintersection.Inthiscase,theonlypossibleintersec-tioninvolveslengtheningtheshoesarrowandcontractingthecomputersarrow.ThisillustratestheRybczynskitheorem:theoutputofthelabor-intensiveindustryin-creaseswithadditionallaborintheeconomy(viceversaforthecapital-intensivein-dustry).ThenewequilibriumisidenticaltothatinFigure5-8,soitdoesnotmattertowhichindustrytheextralaborisinitiallyadded.S-40Solutions■Chapter5MovementofLaborandCapitalbetweenCountriesWage,WPA·MPLA(PA·MPLA)PM·MPLMABW1WOMOALLLOA4.Intheshort-runspecific-factorsmodel,consideradecreaseinthestockofland.Forexample,supposeanaturaldisasterdecreasesthequantityofarablelandusedforplantingcrops.a.Redrawpanel(a)ofFigure5-11startingfromtheinitialequilibriumatpointA.Answer:b.Whatistheeffectofthischangeinlandonthequantityoflaborineachindus-tryandontheequilibriumwage?Answer:Withlesslandperlaborerintheagriculturesector,MPLAdecreases.ThisisrepresentedbyaninwardshiftinthewagecurveforagricultureandleadstoanewequilibriumatpointB.Inwords,wagesintheagriculturesectordrop,drawinglaborintothemanufacturingsector.TheincreasedlaborsupplyintheSolutions■Chapter5MovementofLaborandCapitalbetweenCountriesS-41KOSLSKSKCOCLCOCKLKKBALLLWage,WPA·MPLAPA·MPLAPM·MPLMABWOMOALWLmanufacturingsectorputsdownwardpressureonthewage.Inthenewequilib-rium,wagesareonceagainequalizedacrossindustriesatWW,manufactur-inglaborincreasesfromOMLtoOML,andagriculturelabordecreasesfromOALtoOAL.c.Whatistheeffectontherentalonlandandtherentaloncapital?Answer:Inthemanufacturingindustry,thequantityoflaborincreasesandtheamountofcapitalremainsthesame(i.e.,thelabor/capitalratioincreases).There-fore,themarginalproductofcapitalincreasesduetothenaturaldisasterbecauseeachunitofcapitalhasmorelaborersworkingwithit.Asaresult,therentaloncapital,PMMPK,increases.Inagriculture,theresultseemsambiguousatfirst.Ononehand,thenaturaldisasterdecreasesthestockofland,whichincreasesthemarginalproductofland.Ontheotherhand,themovementoflaborfromagri-culturetomanufacturingdecreasesthemarginalproductofland.Whichoneoftheseeffectsisstronger?Itispossibletoanswerthisques