^ ^^
^
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f
(k
t)
=
^
F
(Kt
/
AtLt ,1)
7
217 218 219 220 221 222
7 LYKKYL
8
Yt
^
Kt = f '(k)
Yt = [(Lf t
f (0) = 0 f '(0) = f '( ) = 0 Inada
^
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k t) k tf '(k t)]e©t
L
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) c e(〉n)
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n)u
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n)t
26e(〉n)t = ∝ / u '(c) 29 27 29
.
r = 〉 [u ''(c)c](c ) u '(c) c
u ''(c)c u '(c)
n>0 t = 0 1t L(t) = ent
A(t) = egt
Y (t) = F(K (t), A(t)L(t))
.
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)
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(K
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),
A(t
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™
K
(t )

C (t )
c(t) = C(t)
k(t) = K (t) c (t) =
L(t )
L(t )
(1.1)
(1.2) C(t ) e A(t)L(t)
^
f '(kt) = ™ + 〉 +⎝©
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kt
)

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.
kt
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kt
=
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t
t
225 226 229
.
^
kt
= w e©t t
+
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n

^
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k
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f '(kt) = rt + ™ 216TVC
复旦大学博士生宏观经济学讲义（一）
1
Frank Plumpton Ramsey
Frank Plumpton Ramsey (1903-1930), British mathematician and philosopher, best known for his work on the foundations of mathematics. But Ramsey also made remarkable contributions to epistemology, semantics, logic, philosophy of science, mathematics, statistics, probability and decision theory, economics and metaphysics.
(1.17)
(1.18) (1.19) (1.20) (1.21) (1.22) (1.23)
4
ce B ce' ce0 c0''
.
ce = 0
DD
.
ke = 0
ke0
ke*
k gold e
12
ke**
ke
g
c(t) , k(t)
1 Nt n Lt 1
Ct t c(t) = C(t) / L(t)
(1.12) (1.13)
(1.14)
(1.15)
cs / ct
⌠
=
[ u
'(
cs / cs)
ct /u
'(
ct
)
d[u
'(cs ) d (cs
/ /
u '(ct ct )
)]
]
1
(1.16)
3
s t ⌠ = u '(c) cu ''(c)
1.15
.
⎟
c(t )
= ce (t) = ce (t )
lim ertte(n+© )t kt = Blanchard Fischer1989
t
2Blanchard Fischer1989
e (ne+© )tkt
2DD
.
230k t
=
f
^
(k t)

(©
+
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t

ct
^
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t
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.
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e
1.14
.
ce
(t
)
c
(et)U ''(ce=(t))c U '(ce (t))
(t)[ ef
'(k
(t)) (n + ™e + g + © )]
⎝
=
c e(t)U ''(ce (t))⌠ = 1/⎝ U '(ce (t))
(1.6) (1.7) (1.8)
(1.9) (1.10)
(1.11)
Blanchard Fischer1989Barro Sala-I-Martin1995Zilibotti Dirk,kruger .
Ramsey (1928)Cass1965Koopmas1965
1
k (t) =
k (t )
e
A(t)
.
k e (t) = f (ke (t)) ce (t) (n + ™ + g)ke (t)
∠t
^
=
L
t[
F
(
Kt
^
,
L
t
)

^
Rt
k
t

wt
e©
t
]
^
Rt Rt = rt + ™ L t
225 224
6 1c = ce© t ^
^
f '(kt) = rt + ™
[
f
^
(k
t)

^
k
tf
^
'(k t
)]e© t
= wt
2at = kt
.
^
(ct )
/(ct )
^
=
.
ct
/
ct

©
=
f
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334 k * < k gold
〉 e = 〉 + ⎝© > n + ©
^
f '(k t) = © + n + ™
^
^
8©
10
. ^
k =0
^
^
k **
k
334 335
〉 + ⎝© 〉 ⎝
^
^
c' 0 232 c 0
^
c'' 0 TVC
^
1DD c'' 0 k ,
n+©
e e rtt (n+© )t rt
.
c=
r〉
c⎝
27
∝ (t) = ∝(0)et(rtn) ∝ (0) > 0
28
6=
〉r ct +=1[ ct
(1+ r) ]⎝ ⎝1 = 1/ ⌠ (1 + 〉 )
7
29 210
211
212 213 214 215 u '(ct) 1+ r u '(ct + 1) 1+ 〉
lim[atet(rtn) ] = 0
''(c
(t)) c
(t)
© e©tU
'(c
.