龚六堂高级宏观05

RamseySolow—Swan..Solow.RomeLucas1968Kurz.LucasRomer.1.AKSolowRamseyInada...SolowRamsey.1.SolowSolow()()()ktsfknkt=−)0(ksnAkkf=)(AAkf=′)(()()kktsAnktγ==−nsAAkkfy==)()()1(kfsc−=nsAcyk−===γγγ....()/()()/kktktsfkknγ==−li()fkm()/kfkk→∞snkkfk//)(lim∞→118snkfk/)(lim′∞→αBkAkkf+=)(BA,10α1)(−+=′ααBkAkfABkAkfk=+=′−∞→1)(limααsnA/nsAcyk−===γγγβββαα1])1([),(−−−−+=LKLKF10α1−≥β0=β0ββααβ1)]1([)(−−−+==kkfyβαααββ1)]1([)(1−−−−−+=′kkkfβα/1)(lim−∞→=′kfkns−βα/1nscyk−===−βαγγγ/1N1jjjYAKLαα−=01αA011()NjjAAKNη==∑η1jL≡10NYANKααη−−+=1αη+=Akkf=)(Akf=′)(119∫∞−=0))((maxdteetcuUtntρ0)0(aa=)()()()()()(tnatctatrtwta−−+=0]}))((exp[)({lim0≥−−∫∞→ttdvnvrta.()()()ccucrcuccγρ′==−−′′0lim{()exp[(())]}0ttatrvndv→∞−−=∫Akkf=)(δ−=Ar0=wka=()kAnkδc=−−−()/[()cucccAucc]γρδ′==−−−′′0lim)(=−−−∞→tnAtkeδ11()1cucθθ−−=−0θtAectc)(/1)0()(ρδθ−−=)0(c1()AAθnρδδρθ−+−−++δ1/()()()()(0)AtktAnktceθρδδ−−=−−−()1/(()(constant)(0)/AntAtktece)δθρδϕ−−−−=+()(1)//Anϕδθθρθ=−−+−(0)lim{constant}0ttceϕϕ→∞+=)0()0(kcϕ=()()ctktϕ=1201()kcAγγδρθ==−−Aky=)(/1ρδθγγγ−−===Acky(1)()/(1/)()kAnsKKYAnAρθθδγδθ−++−=+=++=δ0Aρδ+A1/()ykcAγγγθδρ===−−lim/kckϕ→∞=()(1)//Anϕδθθρθ=−−+−()//kfkkcknγδ=−−−1(())cfkγρδθ′=−−lim[()]lim()kttfknδγ→∞→∞′−+*lim0kktγγ→∞=∞=∞→ktlim*lim()0ktfknnγδδ→∞′+++lim()0tfkA→∞′=nA+δ0*kγ0)(lim=′∞→Akft)(1*ρδθγ−−=Acρδ+AnρnA+δ**ckγγ=*lim/kkAcknγδ→∞=−−−**ckγγ∞=∞→kck/lim−∞=*kγ0*kγ**ckγγ0/lim=∞→kckδγ−−=nAk*δγ++′∞→nkfkt*)(lim**ckγγ=*k*cγγ=lim/kckϕ→∞=()(1)//Anϕδθθρθ=−−+−121),(),(LKAKLKFYΩ+==AΩAρδ+A*1()cAγδρθ=−−Ω1(,)YFKLAKBKLαα−==+0,0AB01α11/(1/[]kcABkcknABkαα)γδγθαδρ−−=+−−+=+−−δρ+A][/1*ρδθγ−−=Akkfz/)(=kc/=χ(1)()()zzAznαχδ=−−−−−−[()()]zAθαχχχϕθ−=−−−()(1)//Anϕδθθρθ=−−+−),(**χz0==χzAz=*ϕχ=*χ,z0=χ(zAθαχϕθ−=+−)θαθ−αθαθ0=zAz=δχ++=nz0=z0=χ),(**χz———((0),(0))zχ——1220=z0=z0=χ)0(χϕχ=*ϕ=*z)0(zz110iiYLAxdiαα−=∫ixiiALix/iiixKA=iKiiAixi11iiipAxLααα−−=()()()iiCxrKrAxiiδβδβ=+−=+−rδβLix1max{()}iiiiiAxxrAxαiαδβπ−−+−=i//iiKAxKAk===1100,iiKKdiAAdi==∫∫k21krααδβ−=+−iiAmaxmaxjjAA=nλλnmaxA1ψ−max/AλVrnπλ=+1maxmaxmax{()}()(1)iiiiiAxxrAxAkAkααπαδβπαα−=−+−==−()1krnπψλλ−=+maxAmaxmaxAngAλσ==0σ12310iiYLRAxdiηνα=∫R1αην++=/xKA=1YAKLRααην−=maxmaxAAngAAλσ===11()1cucθθ−−=−111()(()cYARcKKαν)ρδαρδθθ−∂=−−=−−∂q/RRq=−0g/AAnλσ=0//KKccg==10ln((/))(1)()0dtdAKRngqαναλσν−=−−−=λσ*n,βψ1()ARKαν−YAKRν=SSR=−101max1tcedtθρθ−∞−−−∫KYc=−SR=−()()HucAKRcRνλξ=+−−,λξHKλρλ∂=−∂0Hc∂=∂ξρξ=1AKRνλνξ−=/1/(ccARν)θρ=−ξρ∞0R→KH),(HKFY=(,)(/)YFKHKfHK==1240(.)′fHRKR,max(,)KHKHFKHRKRH−−/(/)/(/)/(/)KHRYKfHKHKfHKRYHfHK′=∂∂=−′=∂∂=HHRδ−KKRδ−(/)(1/)(/)KHfHKHKfHKδδ′−+=−i—KH/KH/(,)(/)(constant)YFKHKfHKK===i(,)iiiYFKAL=iAiiiLLiAK=[(,)()]iiiLfkKrkwδ−+−fkKFKKLL=r(,)(,)/iiiiδ+w11//iiiiiykfrYLfkfwδ∂∂==+∂∂=−=ikk=KkL=(,)/(/)()iiifkKkfKkfL==1(,)()()ifkKfLLfL′=−111[(,)][()()]cifkKfLLfLγδρδρθθ′=−−=−−−(1)()()[()()]fLLfLfLLfLθδρδρδθ−′′−+−−−+1[()()]fLLfLγδρθ′=−−−125()kfLkckδ=−−0max(())tUucteρ∞−=∫dt1ˆ[()]cfLγρδθ=−−()()fLLfL′−()fLKH(,)YFKH=KHHKII,(,)KHYFKHCII==++,KHKIKHIHδδ=−=−HRKR/(/)/(/)/(/)KHRYKfHKHKfHKRYHfHK′=∂∂=−′=∂∂=HHRδ−KKRδ−(/)(1/)(/)KHfHKHKfHKδδ′−+=−KH/KH/KKHKfHKFY)constant()/(),(===δδδ==KHαα−=1//HKδαααα−−=−1)1(Ar])1([/11*δρααθγαα−−−=−AKHαα−=1//HK126αα−1/)0(/)0(HK0=HIteHtHδ−=)0()(0=HI)),(()(KCHKFCuHδν−−+=HK/αα−=1//HK0=HI])1([/11*δρααθγαα−−−=−Aαα−1/)0(/)0(HK0=KIteKtKδ−=)0()(0=KI)),(()(KCHKFCuHδν−−+=HK/αα−=1//HK0=KI*11/[(1)]Aααγθααρδ−=−−−4..CESσσγ−=−1)(),(1iizciizcu.zγ.0=γ.1=γ—..10≤γ.γσ−≥11..Aky=i.∫∞−0),(maxdtezcutiiβiiickAk−−=)(δ.)0(ik1)(iizcz−=ρ127.c2)(iiizcz−=ρ.Hamiltoniz1(,)(())iiiiHuczAkcπδ=+−−πHamilton..Hamiltoniz2(,)(())()iiiiiiHuczAkcczψδλρ=+−−+−,ψλHamilton.4.1cuπ=()Aππβδ=+−iikkπβπ+iczicczucu+=π1((iiiiczAczδβγσσ=−−+−1))cci=1((1)(ccAczδβγσσ1))=−−+−−—zc/(/)[(1dczcccdtzczρ)]=−−—zc/(/)0dczdt=—zc/1111(1)cAzcβδcργσσρ−−=+=+−+(1)cAcβδγσσ−−=−+.ρ.ρ—.zc/ρ—..zc/4.2cuψρλ=−()zuλρβλ=+−()Aψβδψ=+−lim0,0ttekβψψ−→∞=≥lim0,0ttezβλλ−→∞=≤.128()()ccuuzuψρβψρ=++−−()()()cczAuuuβδψρβψρ+−=++−−(/)[(1)]cccczzczρ=−−222(/)(/)(22(1))((1)1)(/)2(1)((1)(21)1(2)){()()(1)[((1)1)(22)]}dcccccAdtccccczczzAAAσβρδγρσργργγσγρσργσσσβρσβδρββδργσσργσβρδ=+++−−−−−++−+−−++−+−+++−+−×−+−++−)/,/zccc0)/(=dtccd.0)/(=zc0)/(=dtccd.—...0)/(=zcc(c/=zc0)/0)/(=dtccdzc/0)/(=dtccd—zk/(/)kkzkzzzz=−(/)[(1)]kckzAzzδρcz=−−−−—1((1))()[]()(1)(1)kAzAργσσδβρδσγβ−++−−=−−−+(zk/0)/=zkzk/129)(/11δρ−+ACarrollCompellSunderasonConstainides.3..Uzawa-Lucas.1.Rebelo(1991).KHKHuv,1()()YCKKAvKuHααδ−=++=1((1))((1))HHAvKuHηηδ−+=−−YA01Bα≤≤01η≤≤vu11()[()()][((1))((1))]tJuceAvKuHCKAvKuHHβααηηνδµδ−−−=+−−+−−−νµ,JJKHνµ∂∂=−=−∂∂(1)1[(/)CAvKuHα]γαδβσ−−=−−(1)(/)AvKuHααδ−−−1111vuvuηαηα=−−−−1=u1=v0=u0=v/pµν=1//(/)[(1)/(1)](/)pABvKuHηηαµναηαηη−−==−−1[(1)][(1)]QYpBvKuHηη−=+−−νµ/=p/()1/()(1)/()/()[(1pAppαηααηαηαηαηγφαφα−−−−=−)]−−1/(/)[(1)/(1)]ABηηφαηαη−=−−/pµν=pαη≠p/vKuH/vKuH2.Uzawa—Lucas21Uzawa-Lucas0=η.1=v1301()YCKKAKuHααδ−=++=(1)HHBuHδ+=−1(1)()//(1)//tuCeABuAuBβαααανµναωνναωµµδ−−−−′==−δ=−+=−+νµ/,/KHCKωχ==1(1)KAuααγωχδ−−−=−−(1)HBuγδ=−−/KHω=χωγααω−−−=−−−)1()1(1uBAu1(1)11()[CrAuαα]γβαωβδσσ−−−=−=−−/CKχ=1(1)1[(1)]Auααχασγω