ꆡ뗚26뻭뗚8웚춳볆퇐뺿,No182009쓪8퓂StatisticalResearchAꆡ쒣탍쟳뷢쯣램퇐뺿움쫶3샮샶ꆡ돂톸ꆡ짛뇸볒ꆡꆡ쓚죝쳡튪:CGE쒣탍쟳뷢쯣램쫇쒣탍듓튻냣뻹뫢샭싛ퟟ쿲쪵볊펦폃뗄믹뒡,놾컄춨맽뛔쿖폐뗄쟳뷢쯣램뷸탐ퟛ쫶,냼삨뒫춳뗄Scarf늻뚯뗣쯣램ꆢ얣뛙뗼듺램ꆢTatonnement쯣램ꆢJohanson2Euler램ꆢ춶펰삭룱샊죕(projectedLagrange)쯣램,틔벰뷼웚탋웰뗄틅뒫(GA)쯣램뫍쒣쓢췋믰(SSA)쯣램,뛳튪쮵쏷쯼쏇뗄쟳뷢풭샭벰듦퓚뗄컊쳢,횸돶룷ퟔ뗄폅좱뗣늢ퟷ쇋쿪뺡뗄뇈뷏럖컶폫첽쳖,뛔폚훂솦폚췆뷸CGE붨쒣폫춻웆럂헦쟳뷢벼쫵욿뺱뗄퇐뺿헟쏇뻟폐훘튪뗄닎뾼틢틥ꆣ맘볼듊:CGE쒣탍;쟳뷢쯣램;움쫶훐춼럖샠뫅:F224ꆡꆡꆡ컄쿗뇪쪶싫:Aꆡꆡꆡ컄헂뇠뫅:1002-4565(2009)08-0089-06ReviewofCGEModelꆯsAlgorithmsLiLiꆡChenXunꆡShaoBingjiaAbstract:AlgorithmsisthefoundationofCGEmodelfromgeneralequilibriumtheorytoitspracticalapplication,,suchasScarffixedpointmethod,Newton2Raphsonmethod,Tatonnementmethod,Johanson2Eulermethod,projectedLagrangemethod,geneticalgorithmandsimulatedannealingalgorithm,thispaperexpoundeachalgorithmpisprincipleandmainproblems,pointedouttheirrespectivestrengthsandweaknesses,:CGEModel;Algorithms;Reviewꆡꆡ튻ꆢ틽퇔쳢ꆣퟔW쯦ퟅ볆쯣믺벼쫵량쯙랢햹,헫뛔뿉볆쯣튻냣뻹alrasian튻냣뻹뫢뷡릹평돩쿳뗄뺭볃쏨쫶뇤캪쪵폃뗄뺭볃럖컶릤뻟틔살,평폚웤랽돌뗄럇뫢(CGE)쒣탍붨쒣쟳뷢뗄탂볆쯣샭싛폫돌탲늻뛏돶쿟탔탔ꆢ쯹짦벰뇤솿쫽솿ꆢ뷏듳랽돌ퟩ맦쒣틔벰랽돌놾짭뗄뢴퓓돌뛈,뛔볆쯣쳡돶쇋뫜룟튪쟳,쒣탍쟳뷢3맺볒짧믡뿆톧믹뷰쿮쒿(08BTQ031);훘쟬쫐짧믡뿆톧믹뷰쿮쯣램컊쳢튻횱쫇퇐뺿헟쏇얬솦볓틔뷢뻶뫍룄짆뗄컊쒿(20072ZH05);훘쟬쫐뿆캯ퟔ좻뿆톧믹뷰훺(CSTC,2008BB2042)ꆣ[16]Gao,T.,2005.ꆰLaborqualityandthelocationofforeigndirectefficiencyꆱ,[J].AppliedEconomics,27,:EvidencefromChina,ꆱ[J].ChinaEconomicReview16,274-292.ퟷ헟볲뷩[17]Gholami,R.,Lee,.,Heshmati,A.,2006.ꆰTheCausal샮탓,얮,1971쓪짺,몺,붭쯕엦쿘죋ꆣ쓏뺩닆뺭듳톧뢱RelationshipBetweenInformationandCommunicationTechnologyand뷌쫚,쮶쪿짺떼쪦ꆣ퇐뺿랽쿲:맺볊춶,쫀뷧뺭볃뫍뫪맛뺭ForeignDirectInvestment,ꆱTheWorldEconomy,[J].UnitedNations볃ꆣ(돂췲뮪),볓쓃듳싳뿋십쮹쳘듳톧[18]Hansen,H.,Rand,J.,2006.ꆰOntheCausalLinksBetweenFDIandGrowthinD뢱킣뎤,짌톧풺뷌쫚ꆣ퇐뺿랽쿲:볆솿뺭볃,뫪맛뺭볃ꆣevelopingCountries,UnitedNationsUniversity.[19]Head,K.,Mayer,T.,2004.ꆰMarketpotentialandthelocationofJapaneseinvestmentintheEuropeanUnion,ꆱ[J].TheReviewof(퓰죎뇠벭:탭틠욵)EconomicsandStatistics86(4):959-972.[20]Kholdy,S.,1995.ꆰCausalitybetweenforeigninvestmentandspillover
ꆡꆤ9ꆡ0ꆤ춳볆퇐뺿2009쓪8퓂ꆡ쿖,죧춨폃쫽톧붨쒣쾵춳(GAMS)ꆢ튻냣뻹뫢붨쒣릤뗄떼쫽뻘헳살좷뚨ꆣ뚨틥뻘헳:뻟냼(GEMPACK)뫍튻냣뻹뫢쫽톧뇠돌쾵춳Dij=5f(iΠ5pji=1,ꆭ,n;j=1,ꆭ,n)(3)(MPSGE)ꆣ쯦뫳,퓚GAMS믹뒡짏폖돶쿖MPSΠGE뫍벴Jacobian뻘헳ꆣ붫f(iP)폃첩샕햹뾪:Hercules뗈ꆣ샻폃헢킩죭볾믲룹뻝탨튪뛔쯼쏇뷸탐f(P)ꇖ(f(Pk))+D(k)((P)(P-Pk))(4)룄퓬,뿉쏢돽믲듳럹복짙돌탲짨볆뗄릤ퟷ솿ꆣ쇮(f(iP)=0,P=Pk+1),뗃떽:쿖뷱(,뺡맜CGE쒣탍쟳뷢틑늻쫇ퟨ낭웤펦폃뗄Pk+1)((=Pk)-D-1f(Pk))(5)훷튪삧쓑,떫죋쏇튻횱쎻폐럅웺톰헒룼볲뇣폐킧뗄헢튲돆캪Jacobian쯣램,랽쿲쿲솿캪d=탂쯣램,떱잰탋웰뗄폃볆쯣믺쒣쓢짺컯뷧뷸뮯맽돌-D-1f,늽뎤캪a=1ꆣ헢훖쯣램뗄뷡맻뛔떼쫽뻘뗄틅뒫쯣램[1]벰뷨본춳볆솦톧훐컯훊췋믰랽램뛸쳡헳(Jacobian뻘헳)뗄탐쇐쪽뷏쏴룐ꆣ돶뗄쒣쓢췋믰쯣램[2]뻍쫇뗤탍듺뇭ꆣ본폚듋,놾컄(죽)Tatonnement쯣램춨맽움쫶벸훖뺭뗤쯣램(냼삨뒫춳쯣램벰쿖듺폅뮯룃쯣램훐랽쿲쿲솿평f(P)뗄럻뫅좷뚨,늽뎤쯣램)뗄쟳뷢풭샭벰듦퓚뗄컊쳢,횸돶룷ퟔ뗄폅좱뗣퓲평쪹폃헟뛔쳘뚨쒣탍뷸탐뗷헻,쫇뾼싇쟳뷢쿲솿늢ퟷ뇈뷏럖컶폫첽쳖,뛔훂솦폚췆뷸CGE붨쒣폫럂f뎤뛈랽돌뗄ퟮ킡뮯컊쳢ꆣ짨:헦쟳뷢벼쫵욿뺱춻웆뗄퇐뺿헟쏇뻟폐훘튪뗄닎뾼틢<(P)=틥ꆣꇆ2[f(P)]=[f(P)]ꇤf(P)(6)떱f(P)=0쪱,<(P)ퟮ킡,뛸평<(P)ퟮ킡닺ꆡꆡ뛾ꆢCGE쒣탍쟳뷢쯣램믘맋짺f(P)=0ꆣ튪쪹f(P)ퟮ킡,벴튪헒튻룶랽쿲,쪹PCGE쒣탍쟳뷢랽램훷튪럖캪솽듳샠:럇쿟탔맦쿂붵ퟮ뿬ꆣ뾼싇<(P+d)뗄첩샕햹뾪:뮮램뫍떼쫽램ꆣ룹뻝쿠맘컄쿗,놾컄훷튪뷩짜벸훖<(P+d)-<(P)ꇖdꇤ<(7)뺫솷뗄뎣맦쯣램벰뷼웚탋웰뗄뗤탍쯣램:ꋙ늻뚯뗣d캪늽뎤,<=5<Π5P,힢틢떽:램[3];ꋚ얣뛙뗼듺램[4];ꋛTatonnement쯣램[5];ꋜ춶dꇤ<=ꆬdꆬꆬ<ꆬcosꛈ(8)펰삭룱샊죕쯣램[6];ꋝJohanson2Euler램;ꋞ틅뒫쯣헢샯ꆬdꆬ뫍ꆬ<ꆬ뇭쪾쿲솿얷쫏랶쫽,ꛈ쫇램;ꋟ쒣쓢췋믰쯣램ꆣ웤볐뷇ꆣ죴튪쿂붵ퟮ뿬,뇘탫ꛈ=-1,벴d=-<ꆣ(튻)늻뚯뗣쯣램(Scarf쯣램)뛔<쟳떼뿉뗃:늻뚯뗣쯣램,평Scarf늻뚯뗣샭싛퇝뮯뛸살,훷<=2Dꇤf(9)튪늽훨쫇뛔뇪ힼ떥뒿탎뷸탐죽뷇럖룮,퓋폃뇪뫅뚨폚쫇뗃떽뗼듺릫쪽:샭뛔뇪ힼ떥뒿탎뚥뗣뷸탐뇪뫅,쯹폐뗄뚥뗣뚼뢳폨((Pk+1)(=Pk)-2ꛁ(k)D-1k)f(P)(10)뇪뫅뫳(돆캪좫뇪뫅떥뒿탎),벴믱뗃튻뷼쯆뗄뺺헹헢퇹훰듎뗾듺,횱훁쫕솲ꆣ뻹뫢뗣ꆣ퓚좫뇪뫅떥뒿탎훐톡퓱죎튻뗣볆쯣뎬뛮탨(쯄)쿟탔뛠늽램(Johanson2Euler쯣램)쟳,떱뎬뛮탨쟳돤럖킡쪱,좫뇪뫅떥뒿탎훐뇘듦퓚튻놾컄쿈쏨쫶튻볲떥CGE쒣탍,냼몬m룶랽돌,늻뚯뗣,벴쒣탍욽뫢뷢ꆣ죧맻뎬맽컳닮랶캧,뿉훘탂n룶뇤솿,춨뎣m<nꆣ싺ퟣ쿟탔랽돌ퟩ:톡퓱뇪ힼ떥뒿탎뷸탐룼쾸뗄죽뷇럖룮,횱훁믱뗃좫Q(X)=0(11)뇪뫅떥뒿탎훐뗄늻뚯뗣ꆣ웤훐Q쫇m캬쿲솿,Q=(q1,ꆭT,qm),X캪n(뛾)얣뛙쯣램캬쿲솿T,X=(x1,ꆭ,xn)ꆣ뻟쳥탎쪽죧쿂:짨럇쿟탔랽돌ퟩP=(p1,p2,ꆭ,pn)(벴뎬뛮q1(X)=q1(x1,ꆭ,xn)=0탨쟳몯쫽),뇭쪾캪튻룶쪹N룶뎬뛮탨쟳몯쫽캪쇣q2(X)=q2(x1,ꆭ,xn)=0뗄컊쳢,벴쪹뗃뎬뛮탨쟳쿲솿몯쫽:ꆭ(12)f(qiP)=0ꆡ(i=1,ꆭ,n)(1)m(X)=qm(x1,ꆭ,xn)=0쟳뷢헢룶랽돌ퟩ뗄뗼듺컊쳢뿉킴캪:웤폐m룶쓚짺뇤솿,n-m룶췢짺뇤솿ꆣ튻떩톡(Pk+1)(=Pk)((+k)k)ad(2)퓱췢짺뇤솿뫳풭랽돌뮯캪:헢샯짏뇪뇭쪾뗼듺듎쫽(k),d캪뗼듺랽쿲쿲AX1=-DX2(13)솿(k),a캪랽쿲(k)d뗄늽뎤ꆣ랽쿲쿲솿평몯쫽f(P)웤훐,X1,X2럖뇰뇭쪾쓚짺뇤솿뫍췢짺뇤솿ퟩꚤꚤꚤꚤꚤꚤꚤ
뗚26뻭뗚8웚샮샶뗈:CGE쒣탍쟳뷢쯣램퇐뺿움쫶ꆤ9ꆡ1ꆤꆡ돉뗄쿲솿,A쫇mꇁm뷗뻘헳,D쫇mꇁ(n-m)뷗샊죕돋ퟓ뗄맀볆횵ꆣ붫쪽(16)훐뗄럇쿟탔몯쫽f(x)뻘헳ꆣ뷸탐죧쿂뷼쯆:f(x,xk)=f(xk)+J(xk)(x-xk)(18)웤훐J(xk)쫇퇅뿉뇈뻘헳ꆣ뗚k듎톭뮷뗄쿟탔풼쫸ퟓ컊쳢벴캪:F(x)+Tcx+Tdy-ꛋTk(f(xk)-f(xk))min1x,y+ꛑT(f(xk)-f(xk))(f(xk)-f(xk))2(19)(x)+A1y=b1(20)A2x+A3y=b2(21)lꇜxꇜu(22)y웤풼쫸쳵볾늻뇤,ꛑ캪돍랣틲ퟓ,좻뫳폃쳝뛈램뷢듋쿟탔풼쫸컊쳢ꆣ떱{xk,ꛋk}훰붥쫕솲,벴믱뗃럇쿟탔풼쫸컊쳢뗄뷢ꆣ춼1ꆡJohansen뷢폫Euler뛠늽쟳뷢쪾틢춼(쇹)쒣쓢췋믰(SAA)쯣램ꆡ캪랽뇣쮵쏷,볙짨뷶폐튻룶췢짺뇤솿x뫍튻룶쿈뾼싇튻룶솽튪쯘뛠늿쏅뗄CGE쒣탍,듓짺닺쓚짺뇤솿y,싺ퟣq(x,y)=0,췢짺뇤솿평X0뇤뮯랽쏦싺ퟣ샻죳ퟮ듳뮯쳵볾,탨쟳랽쏦싺ퟣ킧폃ퟮ듳떽X뮯쳵볾,뇭듯죧쿂:1,쿠펦뗄,쓚짺뇤솿평Y0뇤뮯떽Y1ꆣ죴붫쒣탍q(x,y)=0퓚xmaxU(jX1j,X2j,ꆭ,X)(ij23)0뒦ퟷ튻뷗떼쫽쿟탔뮯,뗃횵YJ,듋벴Johansen뷢쯹캽뗄쿟탔튻늽램,쯼폫쪵볊횵Y1쿠.ꇆpiXij=wLj+rK(ji=1,ꆭ,N,j=1,닮뷏듳i(죧춼1)ꆣEuler랽램퓚쎿튻늽뗄틆뚯랽쿲좡ꆭ,M)(24)뻶폚쟺쿟짏쿠펦뗄뗣뗄쟐쿟랽쿲,벴늻뛏뗷헻웤틆웤훐,U쫇쿻럑헟뗄킧폃몯쫽;Xij쫇뗚j룶쿻럑뚯랽쿲ꆣ쯼뗃떽뗄횵YE2룼뷓뷼쪵볊횵Y1ꆣ죧듋닉헟뛔뗚i룶닺욷뗄탨쟳;pi쫇닺욷볛룱;w샍뚯솦볛폃룼뛠늽훨,뷡맻룼뷓뷼럇쿟탔뷢ꆣ룱;r쫇놾볛룱ꆣ(컥)춶펰삭룱샊죕쯣램뛔CGE쒣탍뛸퇔,쟳뷢컊쳢죧쿂짺닺몯쫽(CES탍)Qi캪i닺욷닺돶솿::Q)i=Q(iLi,Ki=A[ꛁꛑiLi+1Πꛑ(1-ꛁ)iKꛑi]minFT(x)+cx+Tdy(14)x,y(25)(x)+A1y=b1(15)룹뻝샻죳ퟮ듳뮯램퓲뗃튪쯘탨쟳몯쫽:A2x+A3y=b2(16)Li=L(ir,w,Q)iꆡ(i=1,ꆭ,N)(26)Ki=K(ir,w,Q)lꇜxꇜu(17)iy웤훐췟뛻삭쮹뻹뫢쳵볾쫇닺욷뫍튪쯘뗄뎬뛮탨쟳킡c,d,b1,b2,l,u캪뎣쿲솿,A1,A2,A3쫇뎣폚뗈폚0,벴:쾵쫽뻘헳,F(x)캪튻맢뮬뗄뒿솿몯쫽,f(x)캪튻맢뮬뗄몯쫽쿲솿,쯼랴펳쒣탍훐뗄럇쿟탔늿럖뗄랽돌ꆣꇆꇆX(ijp1,p2,ꆭpn,r,w)-Qiꇜ0jix캪럇쿟탔늿럖뇤솿,y캪쿟탔늿럖뇤솿ꆣ짨m,n럖뇰캪헻룶풼쫸뫍뇤솿쫽쒿ꇆL(iw,r,Q)i-ꇆLjꇜ0ij,m1뫍n1럖뇰캪럇쿟탔풼쫸뫍럇쿟탔늿럖뇤솿쫽쒿,퓲A3뻟ꇆK(iw,r,Q)i-ꇆKjꇜ0ij폐m-m1탐뫍n-n1쇐ꆣ짨뗚k듎톭뮷훐,xk쫇럇ꆡꆡꆡꆡ(i=1,ꆭ,N;j=1,ꆭ,M)(27)쿟탔뇤솿뗄뗚k듎맀볆횵,ꛋk쫇럇쿟탔풼쫸뗄삭룱쓇쎴,쒣탍뷢뿕볤캪좷뚨N룶닺욷뗄볛룱믲튪
ꆡꆤ9ꆡ2ꆤ춳볆퇐뺿2009쓪8퓂ꆡ쯘볛룱S={p1,p2,ꆭ,pn,r,w},i=1,ꆭ,Nꆣ(웟)틅뒫(GA)쯣램쿂쏦컒쏇틔짺닺튪쯘볛룱w폫r캪샽,룸돶죔틽폃SAA훐쏨쫶뗄CGE쒣탍,웤뷢뿕볤캪좷CGE쒣탍쒣쓢췋믰쯣램쏨쫶:뚨N룶닺욷뗄볛룱믲튪쯘볛룱S={p1,p2,ꆭ,pn,뗚튻,뚨틥뷢뿕볤,좷뚨쒿뇪몯쫽,뚨틥샤좴뷸r,w}(i=1,ꆭ,N),죔틔짺닺튪쯘볛룱캪샽,폃GA뛈뇭,룸돶돵쪼뷢ꆣ폯퇔쏨쫶웤늽훨:(1)뷢뿕볤:S={r,w}(28)(1)훖좺뗄릹퓬ꆣ짨훖좺쫽캪Gꆣ붫G룶놸톡돵(2)쒿뇪몯쫽:짺닺튪쯘뎬뛮탨쟳벴쒿뇪몯쫽,쪼뷢훐뗄쎿튻룶뇠싫캪튻룶쿲솿x,헢룶쿲솿놻돆볇캪:캪좾즫쳥(chromosome),쿲솿뗄룷럖솿돆캪믹틲ꆣ평E(r,w)=|El(r,w)|+|Ek(r,w)|(29)폚탨쟳몯쫽뗄쇣듎웫듎탔,r뫍w뚼뿉좡쿠뛔볛룱,E쇮r+w=1,퓲뛔r뷸탐뇠싫벴뿉,좻뫳뷸탐뷢싫뫍l(r,w)=ꇆL(iw,r,Q)i-ꇆLjꇜ0맦랶뮯쪹0<r<1ꆣEk(r,w)=ꇆK(iw,r,Q)i-ꇆKjꇜ0폅뮯컊쳢뮯캪(2)쒿뇪몯쫽뗄좷뚨뫍뷢뗄쫊뫏뛈ꆣ짺닺튪쯘:뎬뛮탨쟳캪쒿뇪몯쫽,룃폅뮯컊쳢벴캪E(r,w)E1(r,w)=0,f(r,w)=[1+E(r,w-)]=1=0ꆣE(r,w)캪풭쪼쫊뫏뛈,f(r,w)캪톡퓱쫊뫏(30)뛈ꆣ(3)샤좴뷸뛈뇭:좷뚨뿘훆닎쫽돵횵t0,뿘훆닎쫽뗄훕횵t(f춣횹램퓲),쮥복닎쫽a좡횵랶캧(3)훖좺훐쎿튻룶좾즫쳥xk,k=1,2,ꆭ,G,뚼(015ꆫ놻뷢싫캪튻훖쫊틋폚뷸탐움볛뗄탎쪽rk뫍wk,좻뫳0199),십뛻뿆럲솴Lk=100nꆣ(4)돵쪼뷢뗄룸뚨:쯼쫇쯣램뾪쪼뗼듺뗄웰뗣룹뻝쒿뇪볆쯣돶쫊뫏뛈횵f(rk,wk)ꆣ,웤톡좡펦쪹뗃쯣램떼돶뷏뫃뗄ퟮ훕뷢ꆣ뿉죎틢횸뚨(4)뛔쎿튻좾즫쳥뚼럖엤튻룶퓙짺뗄룅싊pk,k튻돵쪼뷢=1,2,ꆭ,G,헢룶룅싊뗄좡횵쪹뗃쒳룶좾즫쳥쿠뛔(r0,w0)ꆣ뗚뛾,쒣쓢췋믰쯣램쟳뷢늽훨폚훖좺훐뗄웤쯻좾즫쳥살쮵,쯼놻톡퓱뗄뿉쓜탔헽:뇈폚쯼뗄럻뫏뛈ꆣ평쫊뫏뛈횵뿉뗃쎿튻좾즫쳥뗄퓙(1)룸뚨돵쪼컂뛈T0뫍돵쪼뷢f=(r0,w0),볆쯣룃뗣뗄몯쫽횵짺룅싊:fꆣf(rk,wk)(2)쯦믺닺짺죅뚯ꚤ,뗃떽탂뷢xꇤ=x+ꚤx,볆pk=Gꆡk=1,2,ꆭ,G(32)쯣탂뗣뗄쒿뇪몯쫽닮ꚤf=f(xꇤ)-f(x)ꆣꇆf(rk,wk)k=1(3)에뛏탂뷢쫇럱놻뷓쫜ꆣ에뛏뗄틀뻝쫇뷓쫜웤훐,G캪훖좺뗄ퟜ쫽,f(rk,wힼ퓲믲뷓쫜룅싊ꆣk)캪뗚k룶좾즫쳥뗄톡퓱쫊뫏뛈ꆣ1ꚤfꇜ0P=(5)룹뻝퓙짺룅싊pk,k=1,2,ꆭ,G,춨맽듓쿖exp(-ꚤ(31)fΠt)ꚤfꇝ0t캪뿘훆닎쫽,ꚤf캪탂뷢폫떱잰뷢횮볤뗄쒿뇪폐좾즫쳥훖좺훐쯦믺톡퓱뇠싫뒮살닺짺튻룶탂좾즫몯쫽닮쳥훖좺ꆣ놻톡퓱뗄좾즫쳥닉폃튻뚨틅뒫쯣ퟓ(붻뮻뫍;죴ꚤfꇜ0,뷓쫜탂뗣ퟷ캪쿂튻듎쒣쓢췋믰뗄돵쪼뗣;죴ꚤfꇝ0,퓲볆쯣탂뗣뷓쫜룅싊캻뇤틬)닺짺ퟓ듺ꆣ:p(ꚤf)=(6)죧맻헒떽xB쪹E(rB,wB)ꇜꛄ(ꛄ튻냣좡exp(-ꚤfΠ(K3T)),닺짺[0,1]쟸볤짏뻹퓈럖늿캱쯦믺쫽01001),믲헟듯떽쇋풤뚨뗄톭뮷볆쯣듎쫽,쓇쎴뷸뮯r,rꇊ[0,1]ꆣ죴pꇜr,뷓쫜탂뗣ퟷ캪쿂듎쒣쓢뗄돵쪼뗣;럱퓲죔좡풭살뗄뗣ퟷ캪쿂튻듎쒣쓢뗄맽돌뻍훕횹뷸탐ꆣ럱퓲,략믘늽훨3,닺짺탂뗄좾즫돵쪼뗣ꆣ쳥늢퓙뷸탐볆쯣톭뮷ꆣ(4)에뛏돩퇹ힼ퓲(십뛻뿉럲솴뎤)쫇럱싺ퟣ,ꆡꆡ죽ꆢ룷쯣램럖컶뇈뷏죴쫇퓲볌탸쿂늽훨,럱퓲략믘늽훨2ꆣCGE쒣탍뗄쫽횵쟳뷢,쫗쿈듓Johansen뾪쪼,웤(5)뷸탐췋컂닙ퟷ,tk+1=aꇁtk,쇮k=k+1ꆣ쟳뷢닟싔쫇쪹폃쿟탔뮯뫍뇆뷼벼쫵,냑CGE쒣탍뮯(6)에뛏쯣램훕횹ힼ퓲쫇럱싺ퟣ,죴쫇퓲뷡쫸쯑캪튻룶뛔쫽쿟탔랽돌ퟩ,춨맽뷡맻쾵쫽뻘헳ퟷ쟳쓦쯷늢뗃떽ퟮ뫳뗄뷢,럱퓲략믘늽훨2ꆣ퓋쯣,쫴ퟮ볲떥뗄쯣램ꆣ헽틲웤쯣램볲떥,쒣탍쏨쫶
뗚26뻭뗚8웚샮샶뗈:CGE쒣탍쟳뷢쯣램퇐뺿움쫶ꆤ9ꆡ3ꆤꆡ쫜떽쇋뛔쫽쿟탔탎쪽뗄쿞훆[7]ꆣ믹폚Johansen쮼쫊뫏폚헢훖쯣램,퓲쫇쿠떱폐킧뗄ꆣ떫튪쟳헢훖쯣쿫,Euler닉폃뛠뷗뛎쿟탔쒣쓢랽램뷼쯆뇆뷼쒣탍쪵램뛔쒣탍쫊뫏춬퇹믡닺짺컊쳢,틲캪헢훖쯣램뇘탫볊뷢,떮짺쇋룄뷸뫳뗄Johanson2Euler쯣램,벴붫튻쫇쪹폃헟뎹뗗샭뷢웤쒣탍쳘뗣ꆣ냣뗄럇쿟탔쒣탍뇤돉튻룶폃뇤솿뗄냙럖싊뇤뮯뇭쪾춶펰삭룱샊죕쯣램,쫇춨맽톭뮷쟳뷢쿟탔풼쫸뗄쿟탔쾵춳,냑쒣탍췢짺뇤솿뗄뇤뮯럖뷢돉뛠룶킡뗄ퟓ컊쳢살뇆뷼럇쿟탔풼쫸컊쳢뗄뷢ꆣ헢튻쯣램늢뗄뇤뮯,쪹쒣탍볆쯣뷡맻뷓뷼쪵볊횵ꆣ룃쯣램ퟮ듳늻쓜듓샭싛짏놣횤뷢뗄쫕솲,퓚쪵볊쟳뷢CGE쒣탍뗄뫃뒦쫇튻뚨폐뷢,듓뛸뿉쟳뷢튻킩맦쒣쿠떱듳뗄쪱,평폚뇤뮯뫳뗄췢짺뇤솿춨뎣늻믡폫돵쪼뻹뫢횵쒣탍ꆣ듓샭싛짏붲,쿟탔뮯놾짭믡뛔CGE쒣탍닺짺쿠닮첫듳,쯹틔튻냣뚼쓜릻쫕솲뗃떽뻹뫢뷢ꆣ컳닮,뛸뻝GEMPACK뗄퇐뺿헟뫍쪹폃헟뺭퇩뇭쏷,짏쫶뒫춳쯣램뚼쫇듓쯑쯷뿕볤뗄떥뗣돶랢,춨쿟탔뮯쒣탍쯹퓬돉뗄컳닮쫇뿉뫶싔뗄ꆣ맽쒳킩뮻맦퓲좷뚨쿂튻뗣ꆣ헢훖뗣떽뗣뗄쯑쯷랽쯦뫳,Scarf짨볆쇋튻룶뻟쳥쟳뷢CGE쒣탍뗄쯣램퓚뛠럥횵폅뮯컊쳢훐,헒떽뗄뿉쓜늻쫇좫뻖ퟮ폅램[2],벴톹쯵늻뚯뗣쯣램ꆣ쯼쫴폚뗚튻듺쯣램,뻟폐뷢,죝틗쿝죫뻖폲ퟮ폅뷢ꆣ뛔폚늻춬샠탍뗄폅뮯컊좷뚨뗄쫕솲탔훊,퓚폐쿞늽쓚뿉뗃떽좷뚨뷢ꆣ웤훷쳢,뒫춳랽램탨튪늻춬탎쪽뗄뢨훺탅쾢,쎻폐춨폃뗄튪폅뗣퓚폚:ꋙ쓜놣횤뻹뫢뷢뗄듦퓚탔;ꋚ돽싺ퟣ맦퓲쓜쫊뫏쯹폐컊쳢ꆣWalras풭샭췢,뛔쒣탍쎻폐웤쯻쿞훆;ꋛ쓜놣횤폐쿞ퟷ캪튻훖탂뗄폅뮯랽램,쒣쓢췋믰(SAA)쯣램늽퓋쯣쓚쫕솲떽뷼쯆뻹뫢뷢ꆣ쯤좻쓜놣횤쒣탍쫕ퟮ퓧쫇평Kirkpatrack뗈죋뷨본춳볆솦톧훐컯훊췋믰솲,떫웤좱뗣쫇쯦ퟅ뎬뛮탨쟳몯쫽뗄쫽쒿퓶볓,쯣램랽램쳡돶뗄[9]ꆣ쯼쫇믹폚MonteCarlo뗼듺쟳뷢닟싔쪵쿖뗄쓑뛈볓듳,볆쯣쪱볤돊횸쫽짏짽ꆣ뛸쟒퇏룱뗄튻훖쯦믺톰폅쯣램,쓜릻틔쯦믺쯑쯷벼쫵듓룅싊뗘쮵,늻뚯뗣쯣램뇘탫싺ퟣ늻뚯뗣뚨샭뗄볙짨,튲뻍뗄틢틥짏헒돶쒿뇪몯쫽뗄좫뻖ퟮ킡뗣ꆣSAA쫇뷡뫏쫇쮵쓇킩듦퓚ퟅ만뚨볛룱뗄쒣탍늻쓜쫊폃폚늻뚯뗣룅싊춻쳸쳘탔퓚뷢뿕볤훐쯦믺톰헒쒿뇪몯쫽뗄좫뻖쯣램,샽죧떱쒣탍늻싺ퟣ맽뛈탨쟳몯쫽쫇볛룱뗄쇣ퟮ폅뷢,벴퓚뻖늿ퟮ폅뷢쓜룅싊탔뗄쳸돶늢ퟮ훕쟷웫듎몯쫽쪱뇣쫇죧듋ꆣ틲듋,늻뚯뗣쯣램뛠냫뮹횻폚좫뻖ퟮ폅ꆣ웤훷튪폅뗣뻍쫇쓜틔튻뚨뗄룅싊뷓쫕쫊폚쟳뷢킡뗄믲훐뗈맦쒣뗄CGE쒣탍ꆣ샽죧,쒿뇪몯쫽횵늻첫뫃뗄ힴ첬ꆣ헢쪹뗃쯣램벴뇣실죫뻖Shoven2W[8]halley퓸닉폃늻뚯뗣쯣램살쟳뷢탂맅뗤튻늿ퟮ폅뗄쿝?훐,샭싛짏뺭맽ퟣ릻뎤뗄쪱볤뫳튲뿉냣뻹뫢뷡릹뗄CGE쒣탍ꆣ쳸돶살듓뛸쫕솲떽좫뻖ퟮ폅뷢ꆣSAA춨폃탔잿,뛔뾼달CGE쒣탍쟳뷢쮼슷,붫럇쿟탔쾵춳쿟탔뮯컊쳢탅쾢틀삵뷏짙,뛸쟒ퟮ훕뷢늢늻틀삵돵쪼뷢뗄쫇튻쳵훘튪랽램ꆣ퓚쪵볊펦폃훐,헢튲쫇뒦샭럇쿟톡좡,틲듋뿉뫶싔뛔돵쪼뷢톡좡뗄튪쟳뛸죎틢횸뚨탔쒣탍뗄뎣폃랽램ꆣ뺭뗤뗄쿟탔뮯랽램,쫇퓚욽뫢튻돵쪼뷢ꆣ떫SAA퓚펦폃훐캪톰쟳ퟮ폅뷢,탨랴뢴뗣뢽뷼ퟷ첩샕햹뾪,좻뫳좡쿟탔뷼쯆,돆캪뷼쯆쿟탔뗼듺퓋쯣,쳘뇰쫇떱컊쳢맦쒣퓶듳쪱,퓋쯣쪱볤뎤,뮯랽램,죧쒿잰뎣폃뗄얣뛙램뫍Tatonnement쯣램ꆣ맛달떽SAA뗄뷡맻뿉쓜믡닺짺늻뻹퓈탔ꆣ볲퇔횮,얣뛙램뗄쪵훊,쫇폃쟺쿟짏쒳튻뗣뒦뗄쟐쿟살SAA닉폃뒮탐폅뮯뷡릹,웤쯑쯷닟싔폐샻폚뇜쏢쯑듺쳦쟺쿟ꆣ틔첩샕햹뾪쿟탔뮯캪샽,쯼쫇폐컳닮뗄,쯷맽돌쿝죫뻖늿ퟮ폅,떫뛔헻룶쯑쯷뿕볤뗄ힴ뿶쇋늻싛쪹폃쟸폲뛠킡,튲늻쓜뎹뗗쿻쏰컳닮;쇭췢첩샕뷢늻뛠,늻뇣폚듳랶캧뗄쯑쯷ꆣ햹뾪쫇뻖늿뗄,쟸폲풽듳,컳닮풽듳,쯹틔늻쓜폃폚틅뒫(GA)쯣램쫇튻훖웴랢쪽쯑쯷쯣램,춨맽쳖싛풶샫욽뫢뗣캻훃뗄ힴ첬ꆣ헢튻랽램쯤늻쓜놣횤뛔떱잰좺쳥쪩볓톡퓱ꆢ붻닦ꆢ뇤틬뗈튻쾵쇐틅뒫닙뷢뗄쫕솲,떫쪵볊퓋폃훐좴뷏캪폐킧ꆣ쇭췢,듋쯣램ퟷ,닺짺탂튻듺뗄좺쳥,늢훰늽쪹좺쳥뷸뮯떽냼몬믲죴돵횵톡퓱늻쫊,퓚f(p)=0뗄낰뗣(럇ퟮ폅뷢)뢽뷓뷼ퟮ폅뷢뗄ힴ첬ꆣ폫뒫춳폅뮯쯣램뗄쟸뇰퓚폚:뷼믡춣횹뗼듺,틲듋탨튪뛔뇤솿뗄돵쪼횵랴뢴뎢쫔ꆣ뒫춳폅뮯쯣램듓떥룶돵쪼횵뗼듺쟳ퟮ폅뷢,죝틗컳Tatonnement쯣램퓲쫇볲떥뗘뛔늿쏅뗄볛룱뷸탐죫뻖늿ퟮ폅뷢;틅뒫쯣램듓뒮벯뾪쪼쯑쯷,뢲룇쏦뗷헻살뾼싇뛔늿쏅뎬뛮탨쟳뗄랴펳ꆣ헢룶벼쟉쪵볊듳,폐샻폚좫뻖퓱폅ꆣGA쯣램뗄돵쪼뒮벯놾짭뻍듸짏쫇Gauss2Seidel뗼듺램뗄쳘쫢탎쪽,튪쟳샻폃뎬뛮폐듳솿폫ퟮ폅뷢짵풶뗄탅쾢;춨맽톡퓱ꆢ붻닦ꆢ뇤틬탨쟳몯쫽뗄떼쫽탅쾢ꆣ룃랽램뷏볲떥,쟒튻떩쒣탍닙ퟷ쓜톸쯙업돽폫ퟮ폅뷢쿠닮벫듳뗄뒮;헢쫇튻룶
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