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ProblemSet4-Solutions Question1 SupposewhenRussiaopenstotrade,itimportsautomobiles,acapital-intensivegood. a) According to the Heckscher-Ohlin theorem, is Russia capital abundant or labor abundant? Briefly explain. AccordingtotheHOtheoremacountryexportsthegoodthatusesitabundantfactor intensively ThereforeRussiaislaborabundantbecauseitimportsthecapital-intensivegood. b) WhatistheimpactofopeningtradeontherealwageinRussia? § Russiawillspecializeinthelabor-intensiveproduct,whichwillleadtoanincrease therelativedemandforlaborinthelabor-intensiveindustry(lookatRD/RSfor laborgraph). § Thiscausesanincreaseintherelativewage. § Therebyreducingthelabor/capitalratioinbothindustries. Thedecreaseinthelabor/capitalratioleadstoariseinthemarginalproductoflabor.Thus, therealwagewillincrease c) What is the impact of opening trade on the real rental on capital? Thelowerlabor/capitalratioimpliesthatthemarginalproductofcapitaldecreasessothat therealrentaloncapitalfalls. d) Whichgroup(capitalownerorlabor)wouldsupportpoliciestolimitfreetrade?Briefly explain. § Thecapitalownerssufferalossduetothedecreaseintherelativepriceof automobiles § Theywillsupportpoliciestolimitfreetrade Question2 Consideracountry,callitHome,thatproducescomputers(C)andfood(F)usingcapital(K)and labor(L).ThetechniquesofproductionineachindustryareLeontief,andhenceunitfactor requirementsarefixedandgivenby:aKC=3;aKF=1;aLC=2andaLF=4.Note:aijisthenumberof unitsoffactorirequiredtoproduceaunitofgoodj. a) Whichindustryiscapitalintensive?Howdoesthecapital-laborratioineachindustry dependontherelativewageR/K? Thecomputerindustryiscapitalintensive: a KC 3 a KF 1 = > = a LC 2 a KF 4 BecausewehaveLeontiefproductionfunctiontheratioisindependent b) Supposethattheworldpriceofcomputersis$16andtheworldpriceoffoodis$12.Assume thattheHomecountryproducesbothgoods.WhatarethefreetradefactorpricelevelsW andR? Underperfectcompetition,themarginalrevenue(price)ofeachproducthastobesetequal totheitsmarginalcost: PC = R × a KC + W × a LC Û 16 = 3R + 2 W PF = R × a KF + W × a LF Û 12 = R + 4 W Wecansolve2linearequationsin2unknowns: W = 2, and R = 4 c) Whatistheshareofrevenuegoingtolaborineachindustry? § Underperfectcompetition: § Thereisnoprofit,sorevenue=factorincome § Shareofrevenue=shareofproductioncosts § K’sshareofrevenue(laborreceivestherest): Computers: Food: R ⋅ aKC 4(3) 3 = = R ⋅ aKC + W ⋅ aLC 4(3) + 2(2) 4 R ⋅ aKF 4(1) 1 = = R ⋅ aKF + W ⋅ aLF 4(1) + 2(4) 3 d) Similarto(b)andfindW=1andR=8 e) Similarto(c)andfind12/13forComputersand2/3forFood, f) Supposethatithasanaggregateendowmentof100unitsofcapitaland150workers.How manycomputersandunitsoffoodwilltheeconomyproduce? Here,weusethemarketclearingconditions Labor : L = a LC × C + a LF × F Û Capital : K = a KC × C + a KF × F Û Thesolutiontothissystemofequationsis C = 25, and F = 25 g) Similar to (f) and find F = 40 and C = 20 150 = 2C + 4F 100 = 3C + F Question3 a)Aswesawinproblemset1,therelativedemandfortheCobb-Douglasutilityis C C æ PC ö =ç ÷ C F è PF ø -1 b)Wehaveshowninquestion1thatwhentheendowmentsofcapitalandlaborare100and150, theoutputsofeachindustryarethesameQC=QF=25.Itfollowsthatinautarky,relativesupplyis: QC =1 Q F -1 Q C P æP ö RS = RD Û C = 1 = C = ç C ÷ Þ C = 1 QF C F è PF ø PF c)Inequilibrium,becauseofperfectcompetition,thepriceofeachgoodequalsitsmarginal cost.Itfollowsthat: PC = 3R + 2 W, and PF = R + 4 W Takingtheratioofbothequation,usingthefactthattherelativepriceis1,weobtain: 1= PC 3R + 2 W = PF R + 4W Û 3R + 2 W = R + 4 W Û W =1 R d)IfintheForeigncountrypreferencesarethesameasintheHomecountry,relativedemandwill notchange. Thesupplycanbeobtainbysolvingthefollowingsystemofequations: 3C + F = 100, and 2C + 4F = 200 Wefindthat: Q*C = 20 and Q*F = 40 Thereforetherelativesupplyis: Q*C 1 = * QF 2 and 1 Q*C C*C æ PC* ö RS = RD Û = * = * = çç * ÷÷ 2 Q F C F è PF ø * * -1 Þ UsingthesameargumentasforHome: * C * F Question4 P 3R + 2 W 2= = R + 4W P Û 3R + 2 W = 2R + 8W Û PC* =2 PF* W* 1 = R* 6 a)TheclosedeconomyequilibriuminForeignequilibriumisrepresentedbypointslabeledAand theassociatecurves. b)ForForeignwehaveanincreaseintherelativepriceofshoes.So,movefromAtoB.Higher relativewagesandcapital/laborratio. c)Realwagesareequaltomarginalproductsoflaborineachsector(i.e.,W/Pc=PcMPLc/Pc= MPLcandW/Ps=PsMPLs/Ps=MPLs).Similarly,realrentalsareequaltomarginalproductof capital(R/Pc=MPKcandR/Ps=MPKs) Frompart(b)above,changesinfactorintensitiesreflectanincreasedintensityintheabundant factorwhichimpliesanincreaseinthemarginalproductoftheabundantfactor(labor)anda decreaseinthemarginalproductofthescarcefactor(capital). d)ForHome,therelativepriceofcarsincreasesand,asaresult,thecarisovaluecurveshiftsdown. Thenewrelativewage(W/R)andcapital/laborratioarenowlower.Asaresult,Capitalisbetteroff andlaborisworstoff.