Ramsey-Model之详细推导

·KrKwLC=+−&rKwLC(,)YFKLKδ=−(,)FKL(,)(,)(,)FKLFKLFKLKLrKwLKL∂∂=+=∂∂+−kngkcδ(,)KFKLKCδ=−&()()kfkngkcδ=−++−&0()max(())tctuctedtρ∞−∫s.t.kf()()=−++−&1Hamilton(())[()()]Huctfkngkcλδ=+−++−2()0()Hucuccλλ∂′′=−=⇒=∂[()()]Hfkngkλρλρλλδ∂′=−=−−++∂&lim()()0ttktλ→∞=kf()()kngkcδ=−++−&63ln()lnucλ′=()()uccucλλ′′=′&&RamseyModel1()[()()]()uccfkngucδρ′′=−−+++′′&0c=&***()(fkng)δρ′=+++ρkf′*****k()[()()]()()()uccfknguckfkngkcδρδ′⎧′=−−+++⎪′′⎨⎪=−++−⎩&&0=k&Dkk*k0c=&AkABD*cc1kABckc*Ak*()()Afkfk′′0Ac&AADk0D=&DAkk()()0fkngδρ′−+++()()()()AADDfkngkfkngkδρδρ−+++−+++0Ak&ARamseyModel2’FE0=k&kF’k0c=&cc2EE’FF’EE’SolowRamseyρHH’OJHH’0c=&OOJ0c=&0=k&0cˆ*kk*cH’c0c=&HE’Ec279RamseyModel3