Download PS4 - Solutions

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.