索洛模型详细推导

Solow·SolowYKLA()((),()())YtFKtAtLt=(,)F⋅⋅(,)F⋅⋅λ0(,)(,FKALFKAL)λλλ=1Euler(,)(,)(,)FKLFKLFKLKLKL∂∂=+∂∂00lim(,),lim(,)lim(,)0lim(,)0KLKLKLKLFKLFKLFKLFKL→→→∞→∞=∞=∞==Douglas()()()()YtAtKtLtαβ=0,1αβ11(,1)(,)KFFKALYALALAL==KkAL=YyAL=(,1)()yFkfk==sδLnL=&SolowModel1AgA=&KsYKδ=−&sY2()()()()[()()()()]()()[()()]()()()()()()()()()()()()()KKtKtALktAtLtLtAttAtLtAtLtKtKtLtKtAtAtLtAtLtLtAtLtAt∂==−+∂=−−&&&&&&&()()()()()()()sYtKtktktnktgAtLtδ−=−⋅−&⋅()()()()ktsytngktδ=−++&0k=&**(())()()sfktngktδ=++k*k()sfk()ngkδ++1kRamseykk1sngSolowModel2***max()()()()()scsfksfkfkngk*δ=−=−++ks**k**()[()()]cskfkngssδ∂∂′=−++∂∂k****()()fkngδ′=++k()fk**k()ngkδ++()sfk2SolowModel3