뗚7뻭ꆡ뗚3웚ꆡꆡꆡꆡꆡꆡꆡꆡ퓋ꆡ돯ꆡ폫ꆡ맜ꆡ샭ꆡꆡꆡꆡꆡꆡꆡꆡ,쓪9퓂ꆡꆡOPERATIONSRESEARCHANDMANAGEMENTSCIENCEꆡꆡꆡSept.,1998웫듎짺닺몯쫽쳵볾쿂뎤웚돉놾몯쫽뗄좷뚨랽램3쳆킡컒(뗧ퟓ뿆벼듳톧맜샭톧풺,쯄뒨,돉뚼,610054)햪ꆡ튪ꆡ컄헂퇐뺿튻냣탔웫듎짺닺몯쫽쳵볾쿂뎤웚돉놾몯쫽뗄좷뚨랽램,횤쏷쇋뎤웚돉놾몯쫽쫇맘폚닺솿뗄쏝몯쫽,늢횸돶쇋뎤웚뇟볊돉놾몯쫽뫍뎤웚욽뻹돉놾몯쫽횮볤뗄쳘쫢맘쾵ꆣ맘볼듊ꆡ웫듎짺닺몯쫽;뎤웚돉놾몯쫽;뎤웚뇟볊돉놾몯쫽;뎤웚욽뻹돉놾몯쫽훐춼램럖샠뫅ꆡF22415AMethodforDeterminingtheLongRunCostFunctionundertheConditionofHomogeneousProductionFunctionTangXiaowo(ManagementSchool,UniversityofElectronicScienceTechnologyofChina,Chengdu,Sichuan,610054,China)Abstractꆡ,ꆡhomogeneousproductionfunction;longruncostfunction;longrunmarginalcostfunction;longrunaveragecostfunction0ꆡ틽퇔ꆡꆡ뿂늼ꆪ뗀룱삭쮹짺닺몯쫽쫇튻훖퓚쫽솿뺭볃럖컶뫍벼쫵뺭볃럖컶뗈랽쏦뫜폐폃뗄몯쫽ꆣ컄쿗\[1\룸]돶쇋뛠훖짺닺튪쯘뿂늼ꆪ뗀룱삭쮹짺닺몯쫽쳵볾쿂뗄뎤웚돉놾몯쫽뗄좷뚨랽램,늢횤쏷쇋뎤웚돉놾몯쫽쫇닺솿Q뗄쏝몯쫽ꆣ뿂늼ꆪ뗀룱삭쮹짺닺몯쫽쫇웫듎짺닺몯쫽뗄튻훖쳘쫢쟩탎,컒쏇ퟔ좻믡솪쿫,튻냣뗄웫듎짺닺몯쫽쳵볾쿂뗄뎤웚돉놾몯쫽쫇럱튲쫇닺솿Q뗄쏝ꆡꆡ3놾컄뗃떽맺볒뷜돶쟠쓪뿆톧믹뷰(뇠뫅:79270052),맺볒뷌캯뿧쫀볍폅탣죋닅엠퇸볆뮮믹뷰(뇠뫅:뷌벼쳼\[1997\]2뫅뫍맺볒뷌캯룟킣늩쪿쿮믹뷰(뇠뫅:뷌벼랢훐탄\[1996\]50뫅)훺쫕룥죕웚:1998206230쳆킡컒,쓐,1955쓪3퓂돶짺,늩쪿,뷌쫚,쿖죎뗧ퟓ뿆벼듳톧맜샭톧풺뢱풺뎤ꆣꆶ풤닢ꆷ퓓횾뫍ꆶ쾵춳릤돌샭싛랽램펦폃ꆷ퓓횾뇠캯ꆢ훐맺쾵춳릤돌톧믡샭쫂ꆣ' 1995-2004 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
뗚3웚ꆡꆡꆡ쳆킡컒:웫듎짺닺몯쫽쳵볾쿂뎤웚돉놾몯쫽뗄좷뚨랽램9몯쫽ꆣ놾컄붫횤쏷죎틢폐쿞뛠훖짺닺튪쯘웫듎짺닺몯쫽쳵볾쿂뗄뎤웚돉놾몯쫽뗄좷튲쫇닺솿Q뗄쏝몯쫽,늢룸돶튻킩쳘쫢웫듎짺닺몯쫽쳵볾쿂뎤웚돉놾몯쫽뗄뻟쳥뇭듯쪽ꆣ1ꆡ뎤웚돉놾몯쫽뗄좷뚨짨뛠훖짺닺튪쯘뗄짺닺몯쫽Q=f(X1,X2,ꆭ,Xn)캪m듎웫듎몯쫽,웤훐Xi뇭쪾뗚i훖짺닺튪쯘뗄춶죫솿,Q캪닺솿,m캪쒳튻헽뎣쫽ꆣ짨뗚i훖짺닺튪쯘뗄볛룱캪Pi,퓲PiXi뇭쪾릺싲뗚i훖짺닺튪쯘뗄럑폃ꆣퟜ돉놾뻍쫇릺싲쯹폐짺닺튪쯘뗄럑폃횮뫍ꆣ볇ퟜ돉놾캪TC,퓲TC=ꇆnPiXiꆣ죧맻쯹폐뗄짺닺튪쯘뗄춶죫솿뚼뿉틔뇤뚯,퓲TC뇭쪾뎤웚돉놾몯쫽ꆣi=1퓚췆떼뎤웚돉놾TC맘폚Q뗄쫽톧뇭듯쪽틔잰,컒쏇쿈룸돶솽룶틽샭ꆣ틽샭1ꆡ짨몯쫽f=f(X1,X2,ꆭ,Xn)뿉캢,퓲f(X1,X2,ꆭ,Xn)캪m듎웫듎몯쫽뗄돤럖뇘튪쳵볾캪5f5f5fX1+X2+ꆭ+X=mf(1)Xn5X1525Xnꆡꆡ쿖뷶뻍뇘튪쳵볾볲떥횤쏷죧쿂ꆣ틲f(X1,X2,ꆭ,Xn)쫇m듎웫듎몯쫽,맊폐f(tX1,tX2,ꆭ,tXmn)=tf(X1,X2,ꆭ,Xn)(2)ꆡꆡ뛔(2)쪽뗈뫅솽뛋맘폚t쟳떼쫽,평뢴뫏몯쫽쟳떼랽램퓲폐X1fꇤX(tX11,tX2,ꆭ,tXn)+ꆭ+XnfꇤX(Xn1,X2,ꆭ,Xn)=mm21tf(X1,X2,ꆭ,Xn)(3)ꆡꆡ퓚(3)쪽훐쇮t=1뿉뗃떽X1fꇤX(XX11,X2,ꆭ,n)+X2fꇤX(X21,X2,ꆭ,Xn)+ꆭ+XnfꇤXnꆡꆡ(X1,X2,ꆭ5f5f,Xn)=mf(X1,X2,ꆭ,Xn),벴5fX1+X5X2+ꆭ+Xn=mfꆣ15X25Xnꆡꆡ볇Fi=Fi(X1,X2,ꆭ5f,Xn)=,i=1,2,ꆭ,n,퓲틽샭1훐뗄(1)쪽튲뿉틔뇭쪾캪5XiX1F1+X2F2+ꆭ+XnFn=mf(4)ꆡꆡ틽샭2ꆡ짨몯쫽f=f(X1,X2,ꆭ,Xn)쫇뛾듎뿉캢뗄m듎웫듎몯쫽5f,퓲Fi=쫇215Xmi듎웫듎몯쫽ꆣ횤쏷ꆡ틲f=f(X1,X2,ꆭ,Xn)뛾듎뿉캢,퓲f(X1,X2,ꆭ,Xn)듦퓚뛾뷗욫떼쫽,쟒믬뫏욫떼쫽폫쟳떼뗄쮳탲컞맘f52f5Fj,벴52=,벴5Fi=ꆣ5Xi5Xj5Xj5Xi5Xj5Xi틲f(X1,X2,ꆭ,Xn)캪m듎웫듎몯쫽,룹뻝틽샭1뿉뗃(4)쪽ꆣ(4)쪽솽뛋뛔Xi쟳욫떼쫽뿉뗃:5F15F25X1+X+ꆭFi5Fn+(X+Fi)+ꆭ+Xn=mF5Xi5Xi5X2i5Xiii벴5Fi5FiX1+X+ꆭ5Fi5Fn+(Xi+Fi)+ꆭ+Xn=mFi5X215X25Xi5Xi벴' 1995-2004 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
10ꆡꆡꆡ퓋ꆡ돯ꆡ폫ꆡ맜ꆡ샭ꆡꆡꆡꆡꆡꆡꆡ1998쓪뗚7뻭5Fi5Fi5FiiX1+X2+ꆭ+X+ꆭ5F+Xn=(m21)Fi5X15Xi25Xi5Xiꆡꆡ평틽샭1뗄돤럖탔뿉횪5f,Fi=Fi(X1,X2,ꆭ,Xn)=쫇21듎웫듎몯쫽ꆣ5Xmi룹뻝틽샭1뫍틽샭2컒쏇뿉틔췆떼돶뎤웚돉놾몯쫽TC맘폚닺솿Q뗄쫽톧뇭듯쪽ꆣ컒쏇폐죧쿂뷡싛ꆣ뚨샭1ꆡ짨짺닺몯쫽Q=f(X1,X2,ꆭ,Xn)캪뛾듎뿉캢뗄m듎웫듎몯쫽,퓲뎤웚돉놾몯쫽TC(Q)캪죧쿂탎쪽뗄1m듎쏝몯쫽1TC(Q)=TC(1)Qm(5)쪽훐,TC(1)뇭쪾닺솿캪1쪱뗄돉놾ꆣ횤쏷ꆡTC=ꇆnPiXiꆣ쟳뎤웚돉놾TC맘폚닺솿Q뗄쫽톧뇭듯쪽,맩뷡캪쟳죧쿂풼쫸벫i=1킡뮯컊쳢:minTC=ꇆnPiXii=1(6)s1t1Q=f(X1,X2,ꆭ,Xn)ꆡꆡ룃컊쳢뗄쟳뷢맽돌죧쿂ꆣퟷ삭룱샊죕몯쫽죧쿂:Z=ꇆnPiXi+Κ(Q-f(X1,X2,ꆭ,Xn))(7)i=1ꆡꆡTC좡벫킡횵뗄뇘튪쳵볾캪5Z=0,벴P-Κ5f=0,벴5Xii5XiPi=Κ5f=ΚFi,i=1,2,ꆭ,n(8)5Xiꆡꆡ(8)쪽튲뿉틔뇭쪾캪:PjFj=FPiꆡꆡi,j=1,2,ꆭ,n(9)iꆡꆡ(9)쪽벴캪뛔폚죎틢룸뚨뗄닺솿Q(>0),캪쪹TC듯떽벫킡,룷짺닺튪쯘춶죫솿Xi뇘탫싺ퟣ뗄쳵볾ꆣXi뮹뇘탫싺ퟣ죧쿂풼쫸쳵볾:Q=f(X1,X2,ꆭ,Xn)(10)ꆡꆡ솪솢쟳뷢쪽(9)쪽뫍(10)쪽벴뿉쟳돶Xiꆣ쿔좻Xi틀삵폚Q뗄좡횵,듓뛸Xi쫇Q뗄몯쫽ꆣ짨Xi폫Q뗄몯쫽맘쾵캪Xi=gi(Q),i=1,2,ꆭ,n,퓲뿉틔뗃떽:5f=Fꆭ,Xn)=Fi(g1(Q),g2(Q),ꆭ,gn(Q))5Xi=Fi(X1,X2,=Fi(Q)ꆡi=1,2,ꆭ,ni(11)ꆡꆡ평(9)쪽뿉뗃:PjFj(Q)=F(Q)ꆡꆡj=1,2,ꆭ,n(Pi12)iꆡꆡ틲Q=f(X1,X2,ꆭ,Xn)쫇m듎웫듎몯쫽,평틽샭1떼돶뗄(4)쪽뿉뗃:X1F1+X2F2+ꆭ+XnFn=mf=mQ(13)' 1995-2004 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
뗚3웚ꆡꆡꆡ쳆킡컒:웫듎짺닺몯쫽쳵볾쿂뎤웚돉놾몯쫽뗄좷뚨랽램11ꆡꆡ붫(12)쪽듺죫(13)쪽뿉뗃:P1P2PnX1[F(Q)\]=mQPi]+X2[FPi(Q)\]+ꆭ+Xn[F(Q)\iiPii벴11FPPi(Q)ꇆniXi=FiPi(Q)ꇆnPigi(Q)=mQ(14)ii=1i=1ꆡꆡ(14)쪽쫇맘폚Q뗄뫣뗈쪽ꆣ틲(14)쪽뗄폒뛋쫇Q뗄떥쿮쪽,맊(14)쪽뗄ퟳ뛋튲뇘탫쫇Q뗄떥쿮쪽ꆣ튪쪹(14)쪽뗄ퟳ뛋쫇Q뗄떥쿮쪽,Fi(Q)뫍ꇆnPigi(Q)뚼뇘탫쫇Q뗄떥쿮쪽ꆣ뛸튪i=1쪹ꇆnPigi(Q)캪Q뗄떥쿮쪽,g1(Q),g2(Q),ꆭ,gn(Q)뚼뇘탫쫇Q뗄떥쿮쪽,쟒캪춬샠쿮ꆣ듓i=1뛸뿉틔뾼싇짨Xi=gi(Q)=aiQΑ,쪽훐ai뫍Α캪듽뚨뎣쫽ꆣ룹뻝틽샭5f2,=F5Xi=Fi(X1,X2,ꆭ,Xn)쫇m21듎웫듎몯쫽,듓뛸폐iFi(X1,X2,ꆭ,Xn)=Fi(a1QΑ,a2QΑ,ꆭ,anQΑ)=(QΑm21)Fi(a1,a2,ꆭ,an)=QΑ(m21)Fi(a1,a2,ꆭ,an)벴Fi(Q)=QΑ(m21)Fi(a1,a2,ꆭ,an)(15)ꆡꆡ붫(15)쪽뫍gi(Q)=aiQΑ듺죫(14)쪽뿉뗃:1QΑ(m21)FPi(a1,a2,ꆭ,an)ꇆnPi(aiQΑ)=mQii=1벴1F21),aQΑ1)(Pi(a12,ꆭ,anꇆnPiai)QΑ(m=FPi(a1,a2,ꆭ,an)(ꇆnPiai)QΑm=mQ(16)iii=1i=1ꆡꆡ틲캪(16)쪽폒뛋캪Q뗄쿟탔몯쫽,맊뇘폐Αm=1,벴Α1=m,듓뛸폐1Xi=aiQm,i=1,2,ꆭ,nꆣ붫듋뷡맻듺죫TC=ꇆnPiXi뿉뗃:i=1TC=ꇆn11Pmi(aiQ)=(ꇆnPmiai)Q=TC(Q)(17)i=1i=1벴1TC(Q)=(ꇆnPiai)Qm(18)i=1ꆡꆡ평11(18)쪽뿉뗃TC(1)=(ꇆnPiai)1m=ꇆnPiai,듓뛸뿉뗃TC(Q)=TC(1)Qmꆣi=1i=1뚨샭1뗄(5)쪽뇭쏷,죧맻짺닺몯쫽캪뛾듎뿉캢m듎웫듎몯쫽,퓲뎤웚돉놾몯쫽쫇닺솿Q뗄쏝몯쫽,쏝듎헽뫃캪웫듎몯쫽듎쫽m뗄떹쫽ꆣ뎤웚돉놾몯쫽뇭듯쪽훐캨튻탨튪좷뚨뗄쫇TC(1)ꆣ틲듋,뎤웚돉놾몯쫽뗄좷뚨맩뷡캪쟳뷢쿂쫶컊쳢:' 1995-2004 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
12ꆡꆡꆡ퓋ꆡ돯ꆡ폫ꆡ맜ꆡ샭ꆡꆡꆡꆡꆡꆡꆡ1998쓪뗚7뻭minTC(1)=ꇆnPiXii=1(19)s1t1f(X1,X2,ꆭ,Xn)=1ꆡꆡ쿔좻,쟳뷢(19)쪽쯹좷뚨뗄풼쫸벫킡뮯컊쳢,뇈쟳뷢평(6)쪽쯹좷뚨뗄벫킡뮯컊쳢튪볲떥뗃뛠ꆣ2ꆡ뎤웚뇟볊돉놾뫍뎤웚욽뻹돉놾뗄맘쾵뛔폚튻냣탔짺닺몯쫽쳵볾쿂쯹좷뚨뗄뎤웚돉놾몯쫽TC(Q),뿉뷸튻늽떼돶뎤웚뇟볊돉놾몯쫽MC(Q)뫍뎤웚욽뻹돉놾몯쫽AC(Q)뗄맘쾵캪:MC(Q)=AC(Q)+QdAC(Q)dQ(20)ꆡꆡ듓(20)쪽컒쏇뿉틔뗃돶죧쿂뷡싛:뷡싛1ꆡMC(0)=AC(0),벴MC쟺쿟뫍AC쟺쿟쿠붻폚ퟝ훡짏쒳튻뗣ꆣ뷡싛2ꆡ짨Q3뇭쪾AC쟺쿟ퟮ뗍뗣쯹뛔펦뗄닺솿,퓲MC(Q3)=AC(Q3),벴MC쟺쿟뺭맽AC쟺쿟뗄ퟮ뗍뗣ꆣ뷡싛3ꆡ퓚뾪쟸볤(0,Q3)쓚,MC쟺쿟캻폚AC쟺쿟뗄쿂랽,퓚뾪쟸볤(Q3,+ꇞ)쓚,MC쟺쿟캻폚AC쟺쿟뗄짏랽ꆣ룹뻝뚨샭1,m듎웫듎짺닺몯쫽쳵볾쯹좷뚨뗄뎤웚돉놾몯쫽캪1TC(Q)=TC(1)Qm,평듋뿉쟳돶뎤웚뇟볊돉놾MC(Q)뫍뎤웚욽뻹돉놾AC(Q)죧쿂:MC(QdTC(Q)TC(1)12m)=Qm(21)dQ=mTC(12mACQ)(Q)=Q=TC(1)Qm(22)ꆡꆡ듓(21)쪽뫍(22)쪽뿉틔뾴돶,뛔폚죎틢뗄m>0,MC(Q)뫍AC(Q)뗄맘쾵캪:MC1(Q)=mAC(Q)(23)ꆡꆡ평(23)쪽뿉틔뗃돶죧쿂뷡싛:뷡싛14ꆡMC(0)=mAC(0),벴MC쟺쿟뫍AC쟺쿟튻냣늻쿠붻폚ퟝ훡짏쒳튻뗣,돽럇m=1ꆣ뷡싛5ꆡ죧맻m=1,퓲MC쟺쿟뫍AC쟺쿟췪좫훘뫏ꆣ뷡싛6ꆡ죧맻m<1,퓲퓚뾪쟸볤(0,+ꇞ)쓚,MC쟺쿟쪼훕캻폚AC쟺쿟뗄짏랽ꆣ뷡싛7ꆡ죧맻m>1,퓲퓚뾪쟸볤(0,+ꇞ)쓚,MC쟺쿟쪼훕캻폚AC쟺쿟뗄쿂랽ꆣ뷡싛4훁뷡싛7뷒쪾쇋웫듎짺닺몯쫽쳵볾쿂뎤웚뇟볊돉놾뫍뎤웚욽뻹돉놾횮볤뗄쳘쫢맘쾵ꆣ3ꆡ쯣샽샽1ꆡ짨짺닺몯쫽캪Q=XTEX,웤훐,X=[X1,X2,ꆭ,XTn]캪짺닺튪쯘춶죫쿲솿,E캪' 1995-2004 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
뗚3웚ꆡꆡꆡ쳆킡컒:웫듎짺닺몯쫽쳵볾쿂뎤웚돉놾몯쫽뗄좷뚨랽램13헽뚨뻘헳ꆣ퓙짨짺닺튪쯘볛룱쿲솿캪P=T[P1,P2,ꆭ,Pn],쫔좷뚨뎤웚돉놾몯쫽TC(Q)ꆣ뷢ꆡ1Q=XTEX캪뛾듎웫듎몯쫽ꆣ룹뻝뚨샭1뿉뗃TC(Q)=TC(1)Q2ꆣ쿂쏦살좷뚨TC(1)ꆣTC(1)=ꇆnPiXi=PTXꆣ릹퓬풼쫸벫킡뮯컊쳢죧쿂:i=1minTC(1)=PTX(24)s1t1XTEX=1ꆡꆡ쇮Z=PTX+Κ(XTEX21)ꆣTC(1)벫킡뮯뗄뇘튪쳵볾캪dZ=P+2ΚEX=0(25)dXꆡꆡ폃XTퟳ돋(25)쪽뗄솽뛋뿉뗃XTP+2ΚXTEX=XTP+2Κ=0,벴2Κ=2XTP(26)ꆡꆡ폃PTE21ퟳ돋(25)쪽뗄솽뛋뿉뗃:PTE21P+2ΚPTE21EX=PTE21P+2ΚPTX=PTE21P2(PTX2)=0(27)ꆡꆡ평(27)쪽뿉뗃PTX=PTE21P=TC(1)ꆣ듓뛸쯹쟳뎤웚돉놾몯쫽캪TC(Q)1=PTE21PQ2ꆣ컄쿗\[2\퓸]룸돶솽훖짺닺튪쯘쟩뿶쿂,튻훖쳘쫢뗄뛾듎웫듎짺닺몯쫽쳵볾쿂뗄뎤웚돉놾몯쫽ꆣ샽1뗄뷡맻췆맣쇋컄쿗\[2\뗄]뷡맻ꆣ샽2ꆡ짨짺닺몯쫽캪쿟탔웫듎몯쫽Q=ꇆnaiXi,웤훐ai>0,짺닺튪쯘볛룱캪Pi,쫔쟳뎤i=1웚돉놾몯쫽TC(Q)ꆣ뷢ꆡ쯹쟳뎤웚돉놾몯쫽캪PiTC(Q)=min{iQ}Qꆣi볆쯣맽돌싔ꆣ닎뾼컄쿗11ꆡ쳆킡컒1Cobb2Douglas짺닺몯쫽쳵볾쿂뗄샻죳ퟮ듳럖컶1쾵춳릤돌샭싛랽램펦폃11998,7(1):7ꆫ1121ꆡWilliamJ1Baumol1EconomicTheoryandOperationsAnalysis1Prentice2Hall,Inc1,1977' 1995-2004 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
