龚六堂高级宏观04

....Lucas.1.:Cagan.)(sttestpEp++=(4.1.1pestp+tst+tE.t,.1=s(4.1.1)111++++=tettepp(4.1.2)..1te+(4.1.2):.....1.CaganCagan)(tpmαπ−=−(4.1.3)(πγπ−=p(4.1.4lnmM=MlnpP=Pπ...(4.1.4.(4.1.3/pPP=π/dMMdαπ=.(4.1.3(4.1.4.(4.1.3πα=p(4.1.5(4.1.3(4.1.4(4.1.5(1pmγαγ)p=−−(4.1.61αγ.88Cagan..(4.1.4∞→γp=π(4.1.711()()pptmtαα−=−(4.1.8.(4.1.8/(01()()tttptAemsedsαα−=−∫)/sα(4.1.9).AA0)0(pp=0pA=mm=./0()()()tptmtpmeα=+−(4.1.10)mp≠0...A...(4.1.9A/01()[()]ttpteAmsedsαα−=−∫/sα(4.1.11/0011lim()()tst/sAmsedsmsedsααα∞−→∞==∫∫α−(4.1.12/1()()ttptemsedsαα∞−=∫/sα(4.1.13..(4.1.13()/lim()0tssmseα−→∞=(4.1.14.mm=.µαµ/1(4.1.14..0m//1()tstptemedsmααα∞−==∫(4.1.15)..4.1.1oP.890Tm0,0(),sTmsmsT≤≤⎧=⎨≥⎩(4.1.16)TT.(4.1.16(4.1.13()/,0(),sTmmesTpsmsT−⎧≤≤=⎨≥⎩(4.1.17)(4.1.17.1-1.α/Tem−OA.Tm1-1ABB.m.0T.,0()0,msmssTT≤≤⎧=⎨≥⎩(4.1.19(4.1.19(4.1.13()/[1],0()0,sTmmesTpssT−⎧−≤≤=⎨≥⎩(4.1.20))1(/αTem−−1-1OR.]1[/)(mTsem−−T0.4.1.1RSS.µ()mssµ=0≥s//()tstptesedsααµα∞−=∫()()pttµα=+90pµ=µαmtp=)(0≥t/0()(),0(),tmtpmetTptmtα⎧T+−≤=⎨⎩≤.0p0pT.T....0.lnttmM=tMttlnttpP=tP1etp+t1t+.1(ettttmpppα+−=−)α1(ettttppppγ+−=−1)−γ1()ttttmpppαγ−−=−L[(1)]ttLpmαγαγ+−=1[1]11tLpmαγαγαγ−=++t0111111itttiipmαγαγαγ∞−=⎛⎞⎛⎞=+⎜⎟⎜⎟+++⎝⎠⎝⎠∑c1{}Lttx∞=−∞1ttLxx−=91cttitm−tmmt=11αγαγ+11++=tetpp111(1)tLpmαααt−−−=0α1/)1(−αα11111(1)tttpmLααααα−−−⎛⎞−⎛⎞=+⎜⎟⎜−−⎝⎠⎝⎠c⎟01111itttiipmcααααα∞+=−⎛⎞⎛=+⎜⎟⎜−−⎝⎠⎝∑⎞⎟⎠0α1)1/(0−αα01111iiααα∞=⎛⎞=⎜⎟−−⎝⎠∑xαα/)1(1−≤≤x||ttmKxK.0=c.3.CaganCagan.12MPYPαα−=−(4.1.34(1)YcLθ=+−(4.1.35WPaLθ−=−(4.1.36(WLLγ)=−(4.1.3710α20α01θ0γ.YLLPMW.(4.1.34Cagan(4.1.35Cobb-Douglasθ(4.1.36(4.1.37.92(4.1.34--(4.1.371112121222aabWWaabPP⎛⎞⎛⎞⎛⎛⎞=⎜⎟⎜⎟⎜⎜⎟⎝⎠⎝⎠⎝⎝⎠⎞+⎟⎠(4.1.38)110aγθ=−120aγθ=121210aαθαθ−⎛⎞=−⎜⎟⎝⎠12222110aαθααθ−⎛⎞=+⎜⎟⎝⎠1()abLγθ=−12221()Mbcaαθαθα−=+−.M2M(4.1.38112221122/0aaaaγθα−=−(4.1.381λ2λ10λ20λ..M2M()aWPLγγγθθθ−++−=0111222211110MWPcaαααθθθαθααθαθα⎡⎤−−−⎡⎤2−++++−=⎢⎥⎢⎥⎣⎦⎣⎦1dPdWdMdM==..:Tt≤≤01212()ttWtWAeAeλλ=++12111211121212()ttaaPtPAeAeaaλλλλ−−=++Tt≥11()tWtWdMAeλ′=++1111112()taPtPdMAeaλλ−′=++1A2A'1A120AA+=12112()TTAAeAedMλλ′−+=0=t21212(0)PPaλλ−=+A2A21112121212(1)/TaAdaaλλλλ−−−=−Me211112(0)(1)TaPPedaλλ−−=+−M2PPdM=[phone](0){(1)1}TaPPedaλλ−−=+−−M..W0=P0=11012|1WadPdWa==−=21022|PadPdWa==−W.P0=0=XX1112112122()(aaPPλλ−−=−=−−).1()PPPλ=−1()λ=−YY2112112222()()aaPPλλ−−=−=−−.2()PPλ=−P2()WW.Wλ=−.0=TBBXX′′.......LL.BQQ.T.CCDDDXX′′94.......LL.BQQ.2.—TobinmrwyGmd==),,(LMm/=pympkLMpKLWw+=+==/)(/)/()(ppEkfr+−′=δ01,021GG03GGttpmx/=),),((),/,/(rxkkfGrpwpyGx+==(.,.)g(.,.)φ),(rkgx=),(xkrφ=0,021gg0,021φφmrwpkGmd==),,(01,021GG03G(.,.)g(.,.)g95)(),1(/rrgkxA==0(.)′A)/(pKM),(rymm=my0,021mm)(/1),1()(//rvrmkpfmym===),()(LKpFrMv=0(.)′v0),(==xkrφ0r0r0),(==xkrφ),(rkgx=kppppE/)/(=δφδ+′−=+′−=)(),()(/kfxkkfrpp))(1()()()),()((nxxsksnksfkxxknkfx+−−+−=−−−+′=δφδθsθnδpMKW/+=dtpMdKLKFY/)/(),(+−=δKKCLKF++=δ),(CWY+=ssYW=YsC)1(−=)/(pLMx=)/()(ppnppLLMMxx−−=−−=θ96xxknkfx)),()((φδθ−−−+′=dtpMdKsLKsFK/)/(),(++=δ))(1()()(nxxsksnksfk+−−+−=δ**,xk0==kx0)),()((****=−−−+′xxknkfφδθ0)),()()(1()()(******=−−+′−−+−xxkkfsksnksfφδθδrnkfknkf−−−+′=−−−+′δθφδθ)()0,()(******0,()()0xsfknskδ=−+=0x0=x(,)()(,)0Hkxfknkxθδφ′=+−−−=0−=xxHφ0),(=xkH))(,()(nkfkgkhx−−+′==δθ(.)h0(.)′h0x)0,()(knkfφδθ−−+′k)0,()(knkfφδθ=−−+′0=x0xkk))(,()(nkfkgkhx−−+′==δθk)0,()(knkfφδθ=−−+′0,0()|()()(1)(,())xxkksfknsksngkfknϕδ=′==−+−−+−−θδε**0kk≤ε0)()(+−ksnksfδk0))(,(=−−+′δθnkfkg**kk()0kϕ(.)ϕ**()0kϕ**lim()0kkkϕ→],[***kkk∈0)(*=kϕ0)(=kh0)(′kh****lim(,())()0kkgkfknhkθδ→′+−−=****lim()(1)()0kkknshkϕ→=−−()0()|0kkϕϕ=′97)(khx=∞kk1)(/)(′khkhk()()()()/(1)()(1)sfknskkksnhsnδϕ−+Γ=−=−−k()()()(1)sfknskksnδγ−+=−()0kϕ=()0kΓ=**0kk()()/kkkγγ′0)(=Γk)()(khk=γ()()/()/()kkkhkkhkγγ′′=0)()(|)(0)(′−′=Γ′=Γkhkkkγ0|)(0)(′=kkϕϕ0=x0x)(khx=∞kk∞kk1)(/)(′khkhk)0,0(),(**kx****(,)(,)0xxkkxk==)0,0(),(**kx))(1()()()),()((nxxsksnksfkxxknkfx+−−+−=−−−+′=δφδθ⎟⎟⎠⎞⎜⎜⎝⎛−−=⎟⎟⎠⎞⎜⎜⎝⎛**kkxxJkxJ00)(0))(1())(1()(22211211−=−′′=−−=′′+−−−+−′=xJxfJnxsJxfssnfsJxkxkφφφφδ0)()1()]([21122211−′′−++−′−=−kxfnxssnfsxJJJJφδφJ1λ2λ02112221121−=JJJJλλ1λ2λ),(**kx0=x0=k),(**kx0=x0=k*)0(kk98),(**kx*)0(kk),(**kx*****()()()(1)(,())0ksfknsksngkfknϕδθ′=−+−−+−−=δ***2(,)12(1)|0()(1)()kxsngdkdsfnssnggfθδ−=′′−+−−+′***()dxdkhkddθθ′=*(,)0dxdθ=*(,)kk=k()()0sfknsδ′−+=()0kγ′=pnpθ=−(/)/1dppdθ=——()()0sfknsδ′−+=()0kγ′=—k~kk~*(,)nθ=—(,)ucm991211220,0,0,0uuuut()Ktt()rtt()rKt()wt()Lt()(Lt)wtt()()()()rtKtwtLt+t()Ct()()()()()()()MKtwtLtrtKtCtXpt+=+−+1()pt/()MptXt()()/()ktKtLt=()()/()ctCtLt=nt/()mMpL=/ppπ=1kmwrkmnmcnkπχ+=+−−+−−/XLχ=0max(,)tucmedtβ∞−∫kmwrkmnmcnkπχ+=+−−+−−00(0),(0)kkm==m(,)cucmλ=(,)()mucmrλπ=+(rnλβλλ)=−−lim()0ttkmeβλ−→∞+=λ(,)(,)()mcucmucmrπ=+()rfk′=()()wfkfkk′=−MMθ=(,,),(..)cckmkmλππλ==1230,0,0ccc1230,0,0πππ100k0klf/()()dMdtMMmPLMPLχθ===MmmnmPLπ=++((,,))mkmnmσπλ=−−()(,,)kfknkckmλ=−−()(,,)kfknkckmλ=−−((,,))mkmnmσπλ=−−(())fknλβλλ′=−−),,(***mkλ0===mkλ*****()(,,)0fknkckmλ−−=0****((,,))kmnmσπλ−−=***(())0fknβλλ′−−=***(,,)kmλ**1333*123/00fkccckkmmmλλλπδππππ⎛⎞′′⎛⎞−−⎛⎞⎜⎟⎜⎟⎜⎟=−−−−⎜⎟⎜⎟⎜⎟⎜⎟⎜⎟