.
.
521600
2004
,
330(075.8)
65.012.2 73
83
„
_
. .,
. .
.
:
2004. — 400 . — (
. . .
. —
.:
,
).
ISBN 5 16 001864 6
«
»
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—
«
»
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65.012.2 73
ISBN 5 16 001864 6
©
.
©
. .
.
, 2004
, 2004
250
.
. .
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.
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V «
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VI
—
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«
»
.
; . . .
. .
—
. .
,
. .
,
. .
;
. .
.
,
I
.
.
.
([1], [2]).
, . .
.
,
.
,
.
,
.
1
.
,
.
,
.
2
,
.
3
.
.
1
(
):
,
,
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,
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,
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,
,
. .
.
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—
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,
,
.
11
1.1.
.
,
.
.
.
:
.
+ I + G + NX,
=
Y—
—
/—
G —
NX —
(1.1)
;
;
;
;
.
( )
(V = F(K, L) = Y),
,
F—
, L—
.
( = f{Y
),
®</{
) < 0'
°
(G = G, T = T),
(/ = /( *)).
(NX = NX(er),
NX'Zr <0)'.
1
,
12
.
S — Y— — G —
(S— I)
,
,
.
.
NX{zr) = {S I).
(1.2)
.
,
,
,
.
,
.
(1.1)
(1.2)
,
(
. 1.1).
NX
S /(r*)
. 1.1.
,
.
,
.
1.1.1.
,
,
,
,
13
.
,
,
.
:|
,
. 1.2).
| = \ANX\ (
,
.
.
NX]
NX2
NX
. 1.2.
AT
AT,
—
.
,
AT (
S I
AT
NX2
. 1.3.
14
NX[
NX
. 1.3).
.
1.1.2.
,
,
, . .
.
,
(
,
).
,
,
,
.
,
.
: | /| = | ANX\
,
(
. 1.4).
S I
NX2
. 1.4.
.
15
1.1.3.
,
,
,
.
,
,
,
.
,
.
,
: | /| = |
/ (| (
S I
NX2
. 1.5.
1.1.4.
.
,
(
. 1.6).
,
.
,
.
16
. 1.5).
.1.6.
,
,
,
.
,
,
.
,
,
.
1.2.
—
.
IS—LM
,
,
,
,
( = *,
*—
)|
].
,
.
:
17
1)
= f (Y T )
2)
0<
3)
(1.3)
4)
= NX(e r ) NX'Zr < 0;
M
6)
,; < 0;
— = L(r, Y), Ly > 0,
7) r = r*.
5)
1—5 (1,3)
/S); 6 —
(
—
;
—
(
,
; L(r, Y) —
LM).
,
,
.
7 (1.3)
.
.
,
,
.
. 1.7.
,
LM
. 1.7.
—
18
, . .
,
Y—r
(1.3)
IS
.
,
,
,
,
IS
,
IS,
.
,
.
. 1.7
,
.
,
,
,
,
,
,
IS
,
,
(
. 1.8).
. 1.8.
,
,
,
,
,
.
IS
,
(
. 1.9).
(
)
,
,
.
,
,
19
.
).
(
,
Y— .
IS
—
«
» (Y,
),
(
,
,
).
LM
. 1.9.
,
,
,
,
,
.
,
,
,
.
.
(
(1.3)
)
,
Y—
.
IS,
1
2—5
.
d
NX
Y
*r
=
20
,
,
IS
der
l fr
<0.
.
,
,
.
— er L M
,
,
.
—
Y—
. 1.10.
LM
0
. 1.10.
—
.
—
,
.
,
,
.
—
.
.
—
.
21
1.2.1.
,
IS
,
(
. 1.11).
LM
. 1.11.
(
).
,
,
.
,
.
,
,
.
,
.
,
22
(
)
.
LM
(
. 1.12).
. 1.12.
,
,
.
,
,
,
,
.
,
,
.
,
,
,
LM
,
( . .
.
).
,
,
,
.
,
,
.
23
.
,
,
.
?
(
. 1.13).
LM
51,
—
*
. 1.13.
,
.
,
(. .
).
,
,
.
1.2.2.
.
,
.
,
,
.
.
,
.
.
24
IS
,
.
,
.
(
. 1.14).
. 1.14.
.
,
,
,
,
, . .
LM
;
,
,
. 1.14).
(
,
.
, . .
.
25
,
.
—
—
.
, LM
(
. 1.15).
{
. 1.15.
).
(
, LM
,
.
.
,
,
.
.
,
,
.
,
,
.
26
,
IS
, LM
.
(
. 1.16).
LM {
. 1.16.
.
, LM
,
(
,
),
.
.
,
,
.
.
,
,
,
.
—
,
.
27
,
,
.
,
,
.
,
.
.
,
.
*
,
.
1.
,
,
,
,
:
)
;
)
;
)
.
2.
,
?
?
3.
,
,
,
.
:
)
?
)
)
?
28
?
)
?
)
?
4.
Y = Kl/2L[/2,
; = 225, L = 1600.
L —
2.
,
50, 140
180.
0,7,
— 10,
— 50.
100,
50.
,
:
)
,
,
,
,
,
,
,
;
)
50.
,
« »,
.
?
)
« »
.
5.
Y = Kl/4Li/A,
L—
= 10 000, L = 256.
;
3.
:
= 50 + 0,6( — 7);
/ = 150 —
;
NX = 60 — 5 .
,
140.
29
)
,
,
,
,
,
;
)
10.
,
« »,
;
)
5.
,
« »,
;
)
20.
,
« »,
;
)
«»
«»
(NX, S — I; er).
6.
.
,
,
,
:
)
)
7.
;
?
.
,
:
)
)
8.
;
?
:
)
)
;
;
)
.
9.
,
,
30
:
.
:
)
)
10.
;
?
.
,
:
)
)
;
?
2
(
):
,
,
.
,
,
.
(
):
,
,
.
,
,
.
,
.
:
•
;
•
,
;
•
,
.
,
32
—
.
,
.
,
,
.
.
,
.
2.1.
(
)
{Net Foreign Investment,
,
,
NFI),
,
[6].
,
,
,
.
,
.
,
NFI'r<Q (
. 2.1).
N F I = N F J (r );
NFI>0,
;
NFI < ,
.
NFI — ,
(
,
. 2.2).
,
.
= *,
,,
NFI
NFI
. 2.1.
. 2.2.
•
,
,
.
,
,
.
,
(
. 2.3).
,,
NFI
. 2.3.
2.1.1.
1,
:
.
,
34
S
+ NFI:
S = I + NFI,
(2.1)
G.
S=
(L)
,
( )
Y.
,
C = f(Y T)
0</(V D<1.
/ = 1( ),
< 0; NFI = NFI(r),
NFI' < 0.
= ; G=G.
,
Y f(Y T) G=I(r)+NFI(r)
(
(2.2)
. 2.4).
(S — I)
,
,
, . .
,
= NX(er); NX't <o).
S = I + NFI
( . 2.5).
.
NX = S — I
NX(er) = NFI{r)
,
NFI
/(/ ) + NFI(r)
NX(er)
S,I + NFI
. 2.4.
. 2.5.
35
,
.
,
[7].
(2.3)—(2.9)
. 2.6.
Y =C+I+G+ NX
F = F(K, L) =Y
= f(Y T )
I = /(/•), NFI =
(2.7)
(2..3)
(2.•4)
(2.5)
(2.8)
NX(Er) = NFI(r)
(2.9)
NFI{r) (2. 6)
S
NFI{r*)
. 2.6.
f,
,
NF/(r*), . .
,
.
*
.
36
,
. 2.6
,
/ + NFI,
,
.
.
,
,
,
,
(7.
AG.
,
f
.
,
.
,
(
. 2.7).
NF I
NFI{r\) NFI(r*)
. 2.7.
37
,
(
. 2.7)
: \AG\ = | / + ANX\.
\AG\ == | /|,
—
,
: \AG\ =\ANX\.
,
.
,
(
,
. 2.8).
NFI(r\) NF/(r*)
. 2.8.
,
(/ + NFI)
"
.
,
.
,
/•,* > *.
,
38
.
| /| = \ANX\ (
.
. 2.8).
,
.
.
,
,
,
,
,
.
(
)
.
,
,
,
.
,
,
.
.
(
. 2.9).
,
,
*.
,
,
,
,
NFI(t*).
,
]
*,
.
,
\AJ\ = \ANX\.
39
NFI(rx) NFI(r*) NX
. 2.9.
,
.
.
,
(
. 2.10).
,
ej*.
,
.
,
.
,
,
,
.
40
NFI(r*)
. 2.10.
. 2.1
,
, . .
.
.
2.1
= iiv= const
I
Cf
(=
)
1
Const
NX
i
=
| /| = |
|
|
| = | <7|
| /+
|=1 <?|
41
. 2.1
r=rw\
1
w
G\
1
\
NX
\
t
\
1
| /| = |
|
/| =|
|
!
NX
Const
Const
Imp
J
J
E xp
1
1
|
|=|
1 | AImp | = |
\
2.2.
(
:
)
,
:
.
IS,
(2.10)
Yd
42
C=f{Y T)=f{Yd).
(2.11)
1 = 1( ) .
(2.12)
NX=NX(er).
(2.13)
NX(er) = NFI(r).
(2.14)
:
.
= , G = C.
(2.11)—(2.15)
Y=f(Y
(2.15)
IS
(2.10),
:
) + 1{ ) + G + NFI(r).
(2.16)
LM
)
=
L (r , ) —
(2.17)
,
Y
;
/
— —
.
,
,
(2.16), (2.17)
,
,
. .
.
.
.
(
, ,
(2.14).
,
,
,
. 2.11).
43
NX(r)
NFl
. 2.11.
:
,
,
,
?
.
,
,
IS
,
( , ).
.
:
1)
,
;
2)
,
.
44
2.2.1.
(
. 2.12).
G.
,
,
,
.
.
,
.
1
. 2.12
,
.
,
,
,
.
,
(
. 2.126
2.12 ).
,
,
,
.
,
.
)
LM
2
. 2.12.
45
,
.
.
,
,
,
LM
.
,
.
,
,
,
.
,
:
rLfi>r2>r1; e r > e > e ;
^1=^/1+^*1.
,
.
,
,
,
.
,
.
,
.
,
,
LM
.
46
.
.
,
,
. 2.13
77, NFI2
NF f
• NX(er)
NX
. 2.13.
,
, LM
,
,
(. .
).
,
.
.
,
.
,
,
,
.
,
,
.
,
,
,
.
47
,
,
,
.
,
.
,
,
.
,
,
.
.
(
. 2.14).
77*
NF I
NX' { t r )
NX*
. 2.14.
,
,
.
,
.
,
, . .
.
48
2.2.2.
,
.
.
,
(2.14)—(2.17),
,
—
.
.
,
,
.
,
(
.
. 2.15).
*
NFI*
NFI
NX*
NX
. 2.15.
49
,
.
,
.
,
,
.
.
,
,
,
LM
,
.
,
,
,
.
,
:
,
.
,
.
,
,
,
.
,
.
, . .
.
(
).
.
,
50
.
,
.
,
,
(
. 2.16).
NF I
NX(elr)
. 2.16.
,
,
, LM
,
( . .
).
,
.
.
,
,
:
,
,
.
,
,
.
,
—
.
51
(
,
)
,
,
.
,
.
.
,
.
(
. 2.17).
NF I
NFIX NFI2
NX,NFI
. 2.17.
,
,
.
,
.
.
,
, . .
52
.
,
, LM
,
,
.
,
.
,
,
.
.
,
.
,
.
.
.
1.
= Kl/2Li/2,
= 2500, L = 400.
L—
;
(NFI),
:
(Q,
(/),
(NX)
= 60 + 0,8(
7);
/ = 150
30/ ;
NFI= 50 20/ ;
NX= 19
3e r .
,
)
,
,
,
,
200.
,
,
,
,
.
53
)
20.
,
« »,
.
?
)
,
,
(
« »)?
« »)?
)
15.
,
« »,
.
)
,
10.
,
« »,
.
)
6.
,
« »,
.
)
« — ».
2.
,
.
,
,
,
,
,
,
,
.
3.
1980
.
.
)
)
)
)
54
:
;
;
;
?
.
:
)
)
)
)
4.
;
;
;
?
1971 .
,
,
.
,
,
.
)
,
—
,
,
,
,
,
.
)
,
—
,
,
,
,
,
.
5.
,
,
,
,
,
:
)
;
)
,
;
,
)
;
)
,
;
)
;
)
.
.
.
55
6.
,
—
.
,
,
,
:
)
,
;
)
.
.
7.
,
.
)
.
.
)
,
?
.
.
8.
,
.
,
,
,
,
)
)
;
?
.
9.
= 125 + 0,75(
;
/ = 200
NX= 150
50 ,;
NFI = 100
20/ ;
d
(M/P) = 0 , 5
G =
= 100;
= 500;
= 1.
56
7);
40 ;
,
IS
)
)
LM
.
,
,
,
,
,
.
)
100.
.
)
100,
100.
.
3
.
.
,
.
:
,
.
.
.
,
.
,
.
.
,
,
,
58
.
,
,
.
,
, . .
.
.
3.1.
,
,
.
.
.
,
.
,
2,
,
,
,
—
.
:
Y = f(G,T,M,P) fS>0, //<0,/^>0, /;<0.
,
.
,
.
,
.
,
(
,
.
2)
.
,
,
59
,
—
.
:
Y = f(G,T,P)
fa>0, /7'<0,
/;<0.
.
3.2.
.
,
,
—
dG
— ,
dT
dM
.
(
. (2.16)
(2.17)
,
:
2)
/ ; ; dT + f'rdr +dG+ NFI'rdr
(3.1)
M\ dM
dr=
dY = ftdY
60
d Y
L'r
+
;
PL ' r
,
:
(dT = dM = 0)
;)if
(dG = dM = 0):
~
TF
{dG = dT= 0),
4*
:
&
+ :
. (3.4)
^3
,
,
(3.4)
= 1.
,
(3.2)
, (3.3) —
,
(3.4) —
.
f yd —
,
(0; 1).
l'r, NFI'r, L'r < 0; Ly > 0,
—
,
;
.
,
(3.2)
(3.3)
dG
>0;
,
,
dT
<0;
dM
>0.
61
;
—
(3.4)
.
,
;
,
—
.
(3.2)—(3.4)
.
,
[NFI'r —»°°).
_
dY
dG
. dY . dY
1
= 0;
= 0;
= —,
dT
dM
. .
L'Y
.
,
,
,
,
.
dr = 0, dzr = 0,
dY
1
dG — 1 ,
(3.1)
ft,
dY
dT
1
,
,
.
62
,
3.3.
,
.
,
.
,
,
.
,
NX = NX(er, Y);
NX'tr < 0; NX'Y < 0.
,
NX(en Y) = NFI{r).
(3.5)
LM
IS
.
,
:
Y = f (Y
) + I (r ) + G + N F I (r );
NX{er, Y)=NFI(r).
:
•
IS
(Y, );
•
.
.
,
,
.
63
.
dtJdG, der/dT, der/dM.
1)
2)
:
;
,
,
.
(3.6)
,
f'yt dT + I'rdr + dG + NFI'rdr;
dY = f'yt dY
= L'rdr + LYdY;
—
(3.7)
NX'trdtr + NX'YdY = NFi;.dr.
,
dY
I
=
dG
c ,
,
, t i
dY_
/; + NFI'r
dY
d —
.
,
,
,
(3.1)
r
64
~
;
(3.8)
dr =
dM{\ fy\
Yd
\
\
LYdG + L'Y/Y, dT
^ — .
{)
dz,Nx
{
[L;(I fYd)+LY
Zr
(3.9)
)
(/;
dM[NFI'r(\ fyj) NXy(rr
=
dG(LyNFI'r + NX'YL'r) + fYjdT(LYNFI'r
(3.10)
+ L'rNX'Y).
,
dG
[N F I ' (l
der
f
r <)
+
(
NFI
'r)\
(
1 )
,
: —^ <0, . .
dM
—
,
.
,
.
,
.
,
.
,
.
.
(3.6)
,
( 3 1 2 )
d G
NX'tr [ (\
fYd) + L'Y (/; + NFl'r)\'
65
fYil{LyNFl'r
,
(3.12)
.
(3.12)
,
,
.
,
LYNFI'r + L'rNXY<0.
^ > 0 ,
dG
,
(3.13)
—
,
>
(3.13)
( . )
.
NF I ' r
(3.14)
LM
,
(Y, ) — = —Y—.
L*r
a i
(3.14)
,
(Y, )
dr
dY
NX'y
NFI'r
,
,
,
.
,
,
LM
.
,
,
,
(NX(er, Y)> NFI(r))
L'Y <
U~
de L
— <0,
dG
NX'Y
(
5)
'
. .
.
66
.
,
LM
(Y, )
,
),
(
(NX(er, Y)< NFI(r))
,
,
.
— — = NXy—,
L'r
NFI'r
dr
—
dY
. .
,
,
,
— = 0.
dG
LMv\
,
,
:
•
L'Y = 0
NFI'r = ~.
•
NFI'r = °°.
L'r = «>
•
L'r = °°
NX'Y=0.
•
Ly = 0 NX'y = 0.
,
.
,
:
«
»,
.
LM
(
( , ).
).
67
,
LM
.
,
,
,
,
,
.
,
.
,
(
)
.
,
(3.10),
,
,
(3.7).
dG> 0
,
dT = 0
*
(3.16)
,
(3.13)
,
(3.14) , . .
0,
•
> 0.
.
(3.16)
,
dG
de
— rL > 0 ,
dG
,
.
(3.14)
,
,
68
.
(3.15),
0,
< 0.
. .
(3.16)
,
dG
dtr
^< ,
.
.
(3.8)
(3.16):
(3.17)
j
,
V
dG
>0.
,
,
.
,
,
,
.
,
.
,
.
,
.
.
:
NX = N +
( , Y),
N—
,
(
,
—
N,
(3.18)
,
. .
);
69
NX(zr, Y) —
,
.
,
':
'£
=NX^ <0.
,
^:
'
(3.7)
= NXY<0.
(3.18)
, dT + I'rdr + dG + NFI'rdr
d Y = , dY
d\—
=
= Lrdr + LYdY
(3.19)
dN + NX'zdzr + NX'ydY = NFI'rdr.
dY/dN
(dG = dT= 0)
(der = 0).
(3.20)
NFI'r
NX ' Y
,
(3.20)
.
>0.
dN
,
,
—
.
,
dY/dN
(
(
,
NF I ' r )
/V),
.
,
.
(3.20)
70
(3.17)
,
dY
dY
>—.
dN dG
,
,
:
1.
,
,
,
,
.
,
.
,
.
.
2.
,
.
,
.
,
,
.
3.4.
,
.
,
—
,
.
71
,
,
.
,
,
,
.
,
.
,
,
3.3
[3].
1996—2000
.
1996 .
,
,
, . .
,
,
.
1998 .
,
.
.
,
,
,
.
(
[3]
)
,
.
.
.
.
,
.
,
.
.
72
:
NX = a,
,, ...,
—
4
8 —
;
.
:
NX = 8,409
/
.
0,047
+ 3,257
0,062
(2,632) (0,03)
(0,028)
(0,288)
3,195
2,197
11,292.
13,861
;
1
( .
—
R2 = 0,872,
/
.),
.
DW = 1,129.
.
0,97,
3
.
,
/
.
.
In NX(t)
,+
2
In er(t 1) +
3
In Y(t
1) +
4
In poil(t
1) + 5
:
In NX {t) = 41,299 2,054 lne r (/ l) 7,782 In Y{t 1) + 1,828 In
(8,718) (0,177)
/
.
4,737
11,605
(1,875)
(0,226)
4,128
8,089
poil{t \),
R1 = 0,761, DW= 1,436.
0,99.
,
.
73
3.4.2.
,
,
.
,
,
,
,
,
.
,
,
.
.
1999 .
2001 . [4]
:
—
AD —
;
;
ccj,
—
5 —
;
2
.
:
= 0,126
(0,269)
0,0298
(0,0102),
.
^
0,99
(t = —2,89)
2
,
.
.
74
R2 = 0,25
,
,
.
DW= 1,578
.
1999—
—
,
2001
.
,
.
,
.
,
.
,
1
,
.
.
.
3.4.3.
,
.
,
[3], [4].
1999—2000
.
.
:
AY = al+a2AOPEN
AY —
AOPEN —
,, 2 —
5 —
'
,
,
+ 8,
;
;
;
.
,
.
75
:
AY= 2,771
(5,218)
0,531
.
\9943,SAOPEN
(5228,854),
3,814,
,
—
/
.
0,99.
2
.
—
DW = 2,364
.
R2 = 0,398,
,
.
,
, . .
.
.
.
1.
d
= + (
7); / =
dr; NX = g — kzr; (M/P) =
, , d, g, , <?,/> 0, 0 < b < 1.
:
/,
.
2.
= 125 + 0,75(
7); / = 200
10/ ; NX = 150
50 ;
(M/P)d = 0 , 5
40/ ;
G = = 100; /= 500; = 1;
= 5.
)
(Y, )
/Sn LM
.
)
,
,
.
76
,
)
)
.
.
)
100.
.
.
)
100,
100.
.
.
)
?
3.
:
/, (M/P)d = eY fr;
= + b(Y 7); / =
dr; NX = g
, , d,g, , e,f> 0, 0 < b< 1.
.
4.
= 125 + 0,75(
7); / = 200
; NX = 150
(M/P)d = 0 , 5
40 ;
G=T=
100; = 1;
. = 5; £ = 2; /> . = 1.
(Y, )
)
50 ;
LM
IS
.
)
,
,
,
.
,
)
)
)
.
.
100.
.
.
)
100,
100.
.
.
)
?
77
5.
:
/, NFl = I
= + (
); I =
dr; NX = g
d
(M/P) = eY fr;
a, c, d, g, k, I, m, e,f> 0, 0 < b < 1.
mr ;
.
6.
= 125 + 0,75(
7); / = 200
\0r; NX = 150
50 ;
NFI = 100
20 ;
( / )'1 = 0,5
40/ ; G = = 100;
= 500;
=\.
)
.
)
.
)
100.
.
«»
9
2.
)
100,
100.
.
«»
9
2.
)
,
,
,
,
?
I
.,
1.
2
.
.,
, 1997.
2.
.
.:
.
.
, 1998.
.
.
.:
, 1997;
3.
/
.
78
. .
. .
.
.:
, 2000.
4.
/
. . .
. .
. .:
, 2001.
5. Blanchard ., Fischer S. Lectures on Macroeconomics. The MIT
Press, 1990.
6. Branson W. Macroeconomic Theory and Policy. New York: Harper
& Row, 1989.
7. Devereux M.B. Real Exchange Rates and Macroeconomics: Evidence
and Theory//Canadian Journal of Economics, 1997 November.
8. Edwards S. Interest Rates, Contagion and Capital Controls // NBER
Working Paper 7801, 2000.
9. Engel Ch. Real Exchange Rates and Relative Prices: an Empirical
Investigation//Journal of Monetary Economics, 1993, 32.
10. FrenkelJ. International Capital Mobility and Crowding out in the
US Economy: Imperfect Integration of Financial Markets or of
Goods Markets? «How Open is the US Economy?» ed. R.Hafer.
Lexington Mass: Lexington Books, 1986.
11. Frenkel J., Razin A. The Mundell—Fleming Model. A Quarter
Century Later //NBER Working Paper 2321, 1987.
12. Grilli V., Roubini N. Financial Integration, Liquidity and Exchange
Rates // NBER Working Paper 3088, 1989.
13. Krugman P. Pricing to Market when the Exchange Rate Changes
// NBER Working Paper 1926, 1986.
14. Romer D. Advanced Macroeconomics. McGrow Hill, 1996.
15. Taylor A. International Capital Mobility in History: PPP in the
Long Run// NBER Working Paper 5742, 1996.
II
.
,
.
.
,
,
.
4
.
.
5
,
.
.
,
6
,
.
4
.
,
.
.
.
.
,
,
.
.
.
,
.
.
.
/.
,
.
,
,
.
,
,
.
5
7
2.
III.
.
.
.
.
3.
.
,
83
(
),
. .
,
.
.
1992—1995
.
.
4.
.
,
,
(
)
.
,
,
,
.
.
.
,
(
),
.
,
,
(
).
.
:
,
.
.
4.1.
[13].
.
84
,
—
.
IS— LM
.
.
,
,
,
,
,
,
.
IS
,
(
).
.
.
.
,
.
(
. 4.1).
NF I
. 4.1.
,
,
85
,
,
,
,
.
.
,
:
,
(
,
. 4.2).
S
NF I
. 4.2.
,
,
,
(
.
9
IV)
.
.
,
—
.
86
,
.
—
,
,
.
4.2.
.
,
,
,
.
.
,
,
,
.
.
,
(
—
).
At.2 .
.
.
,
.
.
,
—
.
.
.
.
,
:
1)
,
2)
,
;
;
3)
,
.
.
.
,
,
,
,
,
.
,
87
, . .
,
.
,
,
,
.
,
.
,
,
.
4.2.2.
,
,
,
:
1)
,
;
2)
;
3)
,
,
{lump sum)
.
,
,—
.
.
.
.
.
,
,
,
.
,
=
,—
88
{
,
2
),
/ (U'c. >0, £/£' <0)-
D
,
.
(/•)
Gj
.
Tt; —
/,
D = G{ —
.
:
2
2
.
= (1 + r)D + G2.
= (1 + )(<7,
{
(4.1)
) + G2
(4.2)
(4.3)
,
,
.
,
,
:
^
(4.2)
(
1
1
)+ 2 ^ .
(4.4)
,
AT,
2
= AT,
= (1 + ) AT = (1 + ) .
(4.4)
:
V
\ +r
'
l+r
,
(
,
. 4.3).
,
89
7 2 ( l + r)AT
Y2
. 4.3.
,
)
(
(
').
{ {,
—
,
,
,
.
.
.
.
/?,_!•
.
t
,
,
.
F [t, F\
,
.
(4.5)
90
,
/
,
,
.
[/, F]
_
|
:
,(
>
\
^
^
\ ^
\
^
••• 1
,
:
(4.7)
,
.
,
.
,
.
,
,
.
,
,
91
(
)
,
.
,
,
.
,_1
(4.6)
[t, F]
(4.7),
:
^ .
(4.8)
,
(
)
.
,
,
,
.
,
.
4.2.3.
.
.
,
,
,
[35].
—
.
,
,
.
,
,
92
,
,
.
,
,
—
.
,
,
.
,
,
.
.
,
.
,
,
.
,
,
.
.
,
,
,
.
,
,
,
,
.
,
,
,
,
,
.
[42J.
,
—
,
.
, . .
.
.
,
,
.
,
93
.
. 4.4.
'.
,
,
,
_
.
(1+ )
. 4.4.
,
,
,
,
.
,
—
.
,
,
.
,
.
,
.
,
.
94
,
,
,
,
,
.
:
,
,
,
.
,
,
,,
,
.
,
.
,
—
.
,
.
,
—
.
4
1.
'
'
,
,
.
,
.
?
.
.
F
2.
.
(
)
?
.
3.
,
,
,
,
.
)
?
95
)
,
?
4.
.
?
5.
.
,
.
?
?
6.
?
7.
.
,
,
{
{
=
2
).
,
,
D2.
Yl = 200, Y2 = 110,
,
{ = 40,
(7, = 50, G2 —
= 0,1.
2
= 55,
)
.
?
,
?
?
)
)
, = 50
,
1
,
2
= 44,
2?
,
.
?
?
,
1
2?
?
)
8.
71, = 30,
« »,
2
= 44?
,
.
Y2
96
,.
.
,
:
/•=0,
/.
( 2) = Y x .
tl
.
U = U(C{) + EU(C2),
t2.
,—
)
.
)
,
U(C2) = (C 2 ) 2
.
,,
)
,
,
.
(, . .
)
.
U(C2) = (C2)2
?
)
tx
t2
,
U" ' > 0
,
?
5
:
;
.
—
,
:
,
.
.
.
: «
«
»
»
,
.
.
,
.
5.1.
,
.
,
,
.
,
:
1)
;
98
2)
,
,
,
;
3)
,
,
;
4)
,
.
5.1.1.
,
.
.
,
,
.
,
.
,
.
,
,
—
.
.
,
,
,
,
.
,
.
.
1994
[34]
1996 .
,
.
,
,
.
5.1.2.
(
)
,
,
.
99
,
,
.
,
,
,
[37].
.
,
.
,
.
,
,
,
,
,
.
,
,
,
,
,
.
,
,
,
.
[37].
1118
.
1175
1984 .,
.
57,9
.
,
.
,
,
,
—
,
,
,
.
,
.
100
.
,
.
,
.
1997 .
6%
,
0,7%
.
.
5.1.3.
—
.
.
,
,
.
—
,
,
,
,
[37, 4].
,
,
,
,
.
,
,
(
,
,
).
,
,
.
.
.
,
,
,
.
,
,
101
.
.
,
.
.
.
.
5.1.4.
.
:
—
,
.
—
:
.
,
.
.
«
»
.
,
,
.
,
,
,
,
,
.
.
,
,
,
.
102
.
,
,
,
,
.
,
,
:
•
,
;
•
.
,
;
•
,
,
.
,
.
,
,
.
1980
.
,
,
,
1982—1984
.
.
,
.
.
5.1.5.
:
,
(
,
)
,
.
,
1993 .
3,59
3,59
.
.
103
12,81
9,4
.
.
1993 .
2
1,3
.
[6].
,
1995 .
,
.
1998 .
.
.
1970
.,
,
,
,
.
,
.
.
.
[37].
.
|18]
1997—2000
.
5.1
1997 2000
.
(
(%
1997
1998
1999
2000
194,2
282,4
547,6
540,1
111
184,4
136
103,4
86,4
(3,5)
67,5
(2,7)
86,5
(3,2)
141,7
( 5,3)
52,9
(1,2)
86,7
( 2,0)
173,5
( 2,5)
273,3
( 3,9)
)
( %
)
( %
)
:
. 1998.
.
, 1999.
104
)
4; 2001.
.
2. .
. I. M.
1997—2000
.
,
,
1998 .
,
,
2000
.
1998, 1999
,
.
.
,
,
.
,
.
(
. 5.2).
5.2
,
1997
1998
1999
2000
18,9
227,2
171,9
99,8
11,2
110,8
52,2
57,2
59,3
48,8
30,3
57,3
.
,
.
,%
. 5.2,
1997—1999
.
,
,
.
.
,
,
.
105
5.2.
,
.
,
,
.
.
.
,
.
,
.
,
,
,
,
,
.
,
,
.
.
,
.
,
,
,
.
,
.
—
.
5.2.1.
/(
106
,
,
,
), — ,.
,—
t;
S, = Tt— G,—
),
(
,
.
t
:
, = (1 +
_, 5,
(5.1)
t.
t
(—S,).
/
,
(r,Bt_{).
ABt:
Z?,_,
ABl=Bl Bt_l=r,B,_i St.
(5.2)
(5.2)
,
,
,
7,
, =
(G, — , = 0).
_„
(5.3)
,
—
.
,
,
,
,
.
,
BF
/
F
.
,
(5.2)
t—\,
/.
,
107
F — 1,
,
,
F — 2,
_
f
,
i
f
,
/!
=
,
5f+5
f
0+'> ,
S
S
H]
B
F
F
,
t, . .
,
(5.2)
[t; F].
^
l + r
j=t
(5.5),
t,
7
(5 5)
l
J
+r
,
,
F,
(
^
),
(
).
,
, . . BF= 0.
(
Game Condition —
F—> °°),
(No Ponzi
NPG):
0,
F —» ° .
F
108
,
,
,
,
.
.
(5.6)
(5.5)
:
(5.7)
.
.
,
.
,
,
.
1998 .
,
.
,
70%
70%
—
?
[15]
,
1999 .
93 94%.
,
.
,
.
.
,
,
1993—1998
.
(5.7),
.
,
,
,
,
,
.
,
:
109
,
.
,
,
,
.
.
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,
,
,
.
— g,\
,
„
/,
Y, = (1 +g,)Y,_l.
(5.8)
t , =— —
,
s, = — —
.
V.
(5.1)
, _(\ + rl)B,_]
,
s, =
,
+ //)*, !
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Ab, =bl b,_i=\7—^
(5.10)
110
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1+
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).
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,
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(5.23)
—
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115
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8
GAP =
LR
O
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(5.25)
)
,
— Myopic Solvency
Gap (MGAP).
{ r
~
g ) b {
0+ £/.*)
a
l +
s
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) .
(5.26)
.
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—
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1.
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2.
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?
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3.
1996 .
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32
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.
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.
4.
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—
,
» 40%.
( %
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117
5.
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60%.
,
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6.
100%,
.
— 5%.
?
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—
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?
7.
60%.
3
:
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.
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,
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40%?
,
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2%.
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6
.
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119
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120
6.1.
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t D,
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(6.1)
;
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t.
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(
6
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2
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,
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t
(—NX').
,
t
[i*DlAy
D,_i
= D, /),_, = /,*/),_,
NX'.
AD,:
(6.3)
121
:
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(6.3)
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J =
122
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lim DFT[—
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:
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.
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123
6.2.
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(6.8)
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(6.12)
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,
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(6.9)
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\lAzLd
+
nx
~ , .* "F \ +
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l +'
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j=F \
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k= F \
125
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(
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(6.15)
(6.7), . .
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,
126
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[23],
,
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.
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6.2.1.
(6.7)
(6.15)
.
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NX
,
,
127
,
.
(6.7)
:
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:
(6. )
j=t V 1 + i
)
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(6.7')
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> £:
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(6.15')
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128
(6.11).
).
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)
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,
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.
< g°,
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:
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,
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(P Y E ).
,
,
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,
,
129
,
:
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1.
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(6.1 )
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(6 17)
,
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130
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.
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6.17)
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(6.15)
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(6 19)
,
nx = [r
g
) </,_,.
(6.20)
131
6.2.3.
(
)
(6.18)
«
(5.22),
» «
—
—
»
.
,
,
,
.
,
—
,
80%,
2,2.
»
«
,
.
,
.
.
,
,
1992 .
:
300%
,
60%,
3%.
,
,
(
100%).
,
,
,
.
(HIPC).
,
,
40
,
1991 .
600%.
,
,
200—250%,
,
.
.
,
,
.
132
20%
,
.
.
6.3.
,
[11],
,
,
.
,
1999 .
,
.
.
1995
2002 . (
,
,
)
,
,
,
.
,
,
,
.
,
,
.
,
1998 .,
.
,
,
.
133
.
,
,
.
.
,
2002 2003
.
5,5%
.
.
2001 .
.
6.4.
,
,
.
(6.15)
.
,
,
,
.
,
,
G.
S =
.
,
,
[24, 25].
(6.21)
t,
,
,
.
134
(i +
e,P,Y,
/
l
; )
+
( i
(
/)
Ad,=
+
r
, )
V
'U,P,Y,
' ; Y,
Y,
l + r, ,
,
Y,
P,Y,
,
(6.22)
1
Ab, = b,
/>,_,.
,
(
(6.22))
,
g
(
,
,
,
),
t.
,
,
1, gt)d, i +{r, * , ) * , _ , Ab, s,
4 =(
,.
(6.23)
,
/
,
,
,
.
,
,
[25, 10].
,
,
,
135
,
,
,
.
,
,
,
,
,
.
,
,
.
,
,
,
,
,
.
1.
10
.
.
)
,
,
9%?
)
2.
75
,
12%?
— 80
.,
= 500
.,
—
.
?
12%,
8% (
).
3.
«
Z
»
50%?
(
80%.
)
3
(
): 3, 4
8%.
,
3%
136
;
4, 2 1%
: —5, —2, 3%
5%.
;
.
.
60%?
,
4.
?
3
,
,
,
(NX)
( ):
In (NX) = 2,4
3
5.
0,81n(er).
,
,
,
,
(
)
6.
,
3%
.
2003 .
.
,
,
:
NX = 2 ;1>8 ?
.
\n(NX) = —0,61 ( )?
,
7.
,
.
,
.
8.
,
.
.
9.
.
10.
,
World Bank Statistics on External Debt
(www 1 .oecd.org/dac/debt/htm/debto.htm).
137
)
.
)
.
.
.
)
,
.
II
.,
1.
2
.
.
.
:
.,
2.
.
, 1998.
.
:
//
. 2001.
3.
.
2.
:
.
., 2001.
. .
4.
.
.
5.
6.
7.
8.
.:
. .,
,
, 1998.
. .
EERC
99/08.
. .
//
1997. . 33.
. 3.
.,
.
, 1997.
. .
//
. 6.
. 1997.
.
.
.
.:
,
,
^
.
2.
9.
.
.
.
10.
. .
, 2000.
11.
.
.
. .
.:
.
,
//
138
., 2001.
//
/
:
.:
2001.
, 2001.
.
12.
.
//
/
. .
. .
. .
. .
13.
14.
.:
.
.
.:
, 2001.
.:
, 1994.
.
, 2000.
15.
.
.
., 1999.
16.
.
.
17.
.
18.
. .,
.:
. .
//
. .
, 1998.
/
.:
., 2000.
2.
.
. .
—
. .
, 2000
.
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140
III
.
,
(
),
,
(
,
).
,
14.
,
.
7
.
«
.
»
8
,
.
,
.
.
,
.
,
,
,
.
,
,
,
.
,
—
.
,
,
.
,
.
142
—
,
.
,
7
:
.
.
.
«
.
.
»
.
.
«
»
.
7.1.
,
—
.
.
:
(
)
;
,
.
—
,
, . .
.
.
143
,
,
,
.
,
IS LM.
([1]—[91).
1992 .,
.
,
.
,
,
.
,
.
[3]:
1)
,
,
,
. .;
,
2)
,
.
,
,
.
(
)
,
,
,
.
:
,
,
,
,
,
,
,
144
.
|6].
,
.
,
.
1992 .
.
—
(1992 1995
.);
—
—
(1995 . —
1998 .);
1998 .),
;
—
( 1999 .
) —
.
(
—
,
[7].
,
.
,
.
(. .
)
.
,
.
,
I.
.
—
.
,
,
.
.
145
7.2.
,
,
.
,
,
.
.
.
,
,
,
.
.
.
t•
—
.
,
/—
,
.
,
,
,
.
.
,
= / ( 0 . //<0
:
,
.
,
,
,
,
,
,
,
.
(f)
,
.
,
,
*,
,
f
,
.
1982 . (
146
.
. 7.1).
,
. 7.1.
,
.
,
.
,
,
II,
.
.
,
,
.
«
»
.
,
,
.
,
?
.
,
,
,
.
(. .
(dM/dt)),
( ).
|
=const
147
„_
•
RS
1
M
=— —
/
z=
;
—
.
,
,
.
.
.
,
—
,
:
IT =
L/=const
(7.3)
P
*• • •'
,
d M
( /p)\
dP
Pl
|/W=consi
dt
—
dt
P
(z)
.
,
( )
,
= ,
.
,
,
,
RS = IT—
,
.
,
,
.
,
,
( *),
.
«
.
»
.
,
( *),
,
148
(
. 7.2).
RS
n*
n
. 7.2.
,
,
1971 .
.
[20].
7.2.1.
1.
(7.5)
—
'—
;
, fy >0, /^, <0.
,
f(y,
—
/),
, /—
,
,
( = const).
/= +
,
,
(/)
( )
/( ,
').
/( , /)
,
,
.
149
2.
.
,
,
(
3.
.,
: [21]).
,
.
,
(
)
.
( )
( ):
71 = .
(7.6)
(7.5)
,
° = NPf(y, ),
N—
(7.5')
.
,
.
MD = NPf(y,
s
M —
—
) = M = M,
s
(7.7)
.
(7.8)
;
.
,
NPf{y,
ln/V + \
) =
+ In/Cy, ) = 1
.
(7.9)
N
1 df . 1 df . M
— +— +
— +
— =— .
N
f
dy
f
dn
._ ...
(7.10)
M
(7.10)
:
df
"
df
= (df/dn)(n/f) —
;
150
gn=—
=
—
;
(4f/dy)(y/f) —
;
g =— —
.
=m,
N
=— —
(7.11)
.
JV
,
( . . # = 0),
=
+
+ r \ / yg.
(7.12)
RS
(7.2).
,
:
RS = mz^> max;
(7.13)
JC
(7.14)
(7.14)
—— = Nf(y, n)\ l + g—r1
\ + N[n + K + ri/yg\—K
, . .g =
^ = 0.
(7.15)
= 0,
(7.15)
,
,
(—1).
,
151
,
,
(—1).
(g
.
/
)
,
,
,
.
(7.15)
{dr\jy/dn = 0),
,
> 0, g > 0 (
(7.5)).
r\j
)
:
y
> 0, / ' <0 (
(7.18)
.
(7.16)
,
(7.18),
,
(7.18).
,
(7.16). (
> *,
%*,
| < — 1.)
(dx\j y/dn < 0).
,
,
.
,
,
.
.
,
;
,
,
.
152
7.3.
«
»
,
[10, 11].
1.
1995—1997
,
,
2. 1999—2000 . (
z
z=
/
= f(Y,
:
. (
).
).
~ ',
) =Y
—
Y —
(7.19)
;
,
> 0,
> 0,
> 0.
1995—1997
.
:
^ f
, = const.
,
(
)
0,09,
3,57.
1999—2003 .
:
Z,
,
0,015,
.
*
(7.20)
—
| —
g —
;
;
.
153
1995—1997
.
8—20%
,
.
,
.
1999 2003
.
,
,
0,5—2,6%
,
.
,
,
.
.
,
.
1.
.
2.
.
3.
1992 .
4.
\^
(
= ~6 .
—
,«
»
,
.
5.
Fcnpoc
:
d
—
.
,
.
154
100
6.
,
,
: —
=
y/ 3 e
1Olt
.
,
3%
,
8%
?
7.
.
,
,
: —
= ^
.
,
2%
?
,
9%
.
8
1
.
:
,
.
.
.
.
.
.
.
.
.
.
.
.
.
,
,
.
[191.
156
8.1.
.
.
, . .
.
1.
(8.1)
[—
\ )
—
;
' —
—
;
,
,
> 0.
,
an'.
2.
,
— = m=6=const.
(8.2)
3.
^
. .
= '=$(
),
,
>0,
(8.3)
.
( )
,
( ')>
— "< 0, . . < ',
<0.
>0,
,
,
,
.
157
:
TJ T
=1
/ 1 />.
,
'=9
(8.3)
.
(8.5)
,
=
(3(
).
(8.6)
(8 7)
W
,
(8.5),
:
(0 = + ( (0) ) '
n(t) —> G
,
( ),
,
(0) > 8.
t —> .
( )
= = 9.
> I,
7i(t) —>
, . .
(8.9)
,
,
.
(8.9)
,
,
, . .
t > °°.
,
.
158
,
< 1,
,
,
.
,
.
—
,
.
,
.
.
[18],
.
,
.
8.2.
.
,
,
,
.
.
,
80
1980
1984 .
.,
(
4
.
20,6
133
445%),
16,9%.
—
[18].
:
1.
:
\
~
0
,
(8.10)
,
(
,
).
,
.
159
2.
,
.
:
£ 7 L_ ; *-'-«-•
d —
,
,
.
(8.11)
,
( ,
,
)
.
3.
:
_
Y
Y
_
const.
4.
(8.12)
:
ie= (
,
4
> .
(8.13)
:
_ ^
\d ( M Y
1 ={~ 7)
KPY,
=
P Y~
(8 14)
•
(8.14)
:
an'.
(8.15)
(8.11)
=
=
PY
M
=d.
(8.16)
YP
m = dem'.
(8.13)
(8.17)
(8.15),
(8.18), . . ',
=0.
> * 1,
160
> 0,
=0
,
~ 0.
,
(8.16),
if = dem' p.
(8.19)
, . .
=
7ie = deaK — (
. 8.1).
. 8.1.
d »
(8.19)
—
, . .
= .
= deaK — p
,
,
.
,
( ,
,
)
,
.
.
> d, . .
,
—
.
d > p,
.
,
,
,
,
,
. 8.2
—
.
,
.
161
. 8.2.
—
.
(3 < 1,
dn'/dt
(
.
(8.19)),
,
,
,
,
,
,
, ,
,
,
,
,
,
.
,
—
,
,
—
.
,
,( )
,
)
.
(3 > 1
.
,
,
,
.
(
,
d),
,
,
,
.
162
' = de"* — .
dx < d0
,
1
,
>
7
1
7
1
71°
>
(
. 8.3).
"
"•
. 8.3.
—
.
,
(
.
. 8.3).
(
)
,
,
.
.
(
),
,
.
,
),
).
(
—
(
.
—
,
,
,
—
,
> 1,
163
.
(
,
,
,
)
,
.
:
,
.
,
.
8.3.
.
,
,
,
,
G T
.
I ,
.
:
^ + B rB = G T=dY,
—
—
d —
(8.20)
;
;
.
V—
(
)
,
:
/ , V=
— \ =ve
+
164
= /—
v
+
),
/ ; v = V / Y.
(8.21)
.
,
:
+ G.
Y =
(8.22)
,
.
.
,
=^
{ ,
[
(8.24)
>0,
,>0.
(8.22)
,
(8.23)
(8.23)]:
(
)
t = T / Yn
% = G / Y.
v = (l + c,/ $)r* = v(r, $, /),
—
,
,
(8.25)
> 0.
(8.20)
Qz + i> + nb = d + rb,
—
,
;
z —
b = B / Y.
;
= 0, 0 = + «,
(8.26),
(8.26)
,
b = v —z (
(n + r)z = d + (r n)v.
' = .
v),
(8.27)
( , )
165
dr
,
b + aiz
(8.28)
>(1/ ) — .
(8.28)
dy
r
<(1 / )
.
( < *,
(8.28)
(8.28)
( > *),
,
* = r(b + aiz)/d),
. 8.4.
* —
,
. 8.5.
*
*
. 8.4.
—
( < *)
,
. 8.4
*.
8.5.
,
,
*,
. 8.4
.
8.5
= *.
.
,
0*,
166
,,
*
. 8.5.
—
( > *)
.
= G* — .
.
,
£"(
(
.
. 8.4),
— E w Z.
. 8.5)
?
,
.
GG
GGl (
. 8.4
. 8.5).
,
,
,
.
> *
,
,
,
Z.
167
.
,
,
(8.13)
(3 —
,
,
> 0.
(8.27)
d + (r n)b = Qz v z,
z,
,
(8.27')
(8.21).
,
.
,
.
(8.13)
(8.27')
(8.21)
,
:
)I
rjyv
r/r = |
(1
)+ (
1 ) ^ 1 | {(1 aP)[rf + (r n)v zr]
> ,
,
(
).
,
,
.
,
(
),
168
,
.
,
—
,
,
,
< 1.
,
—
:
(
,
)
,
.
,
,
,
,
,
,
,
. .,
.
,
(
),
,
.
8.4.
,
.
.
—
:
= 7^ (>«
).
(8.18)
(
[11])
. 8.1.
1995—1997
,
( — — ),
,
> 1,
,
.
,
.
169
8.1
< (3
«
1995 1997
1
DW
Krlj
/
0,17
5,65
1999
.
0,49
2003 .
( —
1,59
— ).
. 8.2'.
8.2
1999 2003
1
/
0,35
,
< 1.
1995 1997
2,43
.
Radj
DW
0,3
2,66
1999 2003
.,
,
,
.
,
,
.
,
,
.
.
,
,
,
.
,
[24],
.
/
( .,
1997.
170
).
(
. 264).
:
2
,
.
.
.:
,
8.5.
[22, 24]
,
,
.
,
.
,
.
,
.
:
(Y)
1.
(TV)
—
:
Yt+x={\+n)Y,
(8.29)
N,+l={\+n)Nr
,
(8.30)
,
,
.
2.
:
>
.
(8.31)
,
,
.
.
3.
.
df Y
il/r= ^7 y=const.
(8.32)
,
.
1—3
,
.
.
Dx, D2, ..., /),, ...,
D, —
171
t, . .
(
)
(
).
,
, ...,
Mt —
...,
2
,
, D2, ..., Dp ...
.
,
,
.
:
= 1,2,...
,—
,—
(8.33)
/;
t;
,_, —
/— 1.
,
.
(8.33)
t
/V, —
,
,
N,
1+
,
9
,~\
N._,
D,
N,
, ,_
/
N,P,
,
br(Q).
.
,
, = (1 + 6) /,_,, 1= 2, ...,
.
(8.35)
,
.
172
.
0
£>1, D2, ..., D,, ...,
t= 1
,
6
.
, . .
.
(
)
.
MtV— PtNty,
)
,
(
—
/
.
1
/>= ± ^
(8.36)
t = 2, ...,
,
(8.36)
^
= >,
>0.
(8.35)
,
Pt/Pt_l = (1 + 6)/(1 + ).
8
,
.
—
.
(8.34),
(
,
I
/ 1
• [bbj[ifr
,
1
t> T
br(Q),
,
:
~;
"» '
/>r
LJ
t
<SJ7)
2) rr_, — « > 0.
^ J < 1,
(8.37)
(8.36)
(8.37)
,
.
bT(Q),
173
,
,/ ,_]
P,_x/Pt,
,
.
,
,
,
,
9,
br(Q).
(8.34)
/=1
,( ),
(\ + 0)
1
/ {,
,
(8.38)
—
/=0.
0
1,
8
1.
)=^
(8.39)
~,—L^i + ^ 2 ~
\+
174
4—^
(
(8.36)
/),, Nu
,
+
(8.34)
— ,
\+ J
/
/
£|(6) =
{
\( . .
0
(8.36),
8.39)
£ 2 (6),
1).
($), ..., br(Q).
(8.39')
3 <t<
(8 40),
(l + ,
1+
( 0
,1
0+i)0
# 2)
0+«)
2
1 +2
*
1 +
1+
0
\i+e
N
i2 h\~x + 0 ,
1+/
J
"2
+
3
0
2
1+
1+0
0
1+ 0'
[. ,+,
~[/=1(1+ )
f, i
^
/
0+1/)
;
0+«
=2
i \
1+ 9 •
(1 +
. + „)
. »
(8.41)
( 1
,
(8.41)
,
t>
,
(! + >/) = 1,
= t.
,
0,
,
.
,
0,
bj(Q).
,
,
,
.
(
.
(8.34)).
,
.
,
.
,
,
(8.42)
,,
2
> 0.
175
iii —
,
'I
; , —
;
—
2
.
(8.42)
,
.
(8.42)
1+]
,
1
a,
,
2
,
,
(8.43),
J
w
j
^
,
,
.
,
,
.
(8.44)
. .
2,
,
,
.
—
,
,
.
,
,
,
: 1)
,
,
; 2)
176
,
,
.
.
—
.
,
.
—
.
,
,
,
.
,
.
.
,
, . .
,
.
.
.
,
,
.
.
1.
D
.
(
Y
: \~^\
= ~
.
D
( )
_ ,
: — \ ~ 1
177
D
,
2
.
.,
1 . .
3%.
,
.
)
?
?
)
?
,
.
2.
.
5%.
3%.
(
)
(MY
\ =
. ,,'
• .
:
•
3
. .,
1,5
. .,
1 . .;
•
1 . .
,
?
,
,
.
—
3.
.
—
(
)
,
Tf = dean
=
(
.
. 8.1).
,
.
?
?
?
178
4.
—
(
)
:
(9) —
(7ic)
.
.
5.
—
.
,
.
?
.
6.
—
,
,
?
.
III
.,
//
1.
.
. 1995.
.
2.
3.
//
.
.
. 1995.
. .
5.
2.
//
:
3.
. 1995.
4.
3.
. 1996.
//
3.
//
.
.
V
. 2.
, 1998.
. .,
6.
. .
//
. .
7.
8.
.
.:
, 2001.
/
. 1.
. .
,
.
. .
,
. .
//
, 2001.
.
.
. 2.
.
//
. .
. 1999.
.
.:
2.
179
.,
9.
. .,
. .
//
:
1995.
.
5.
. .
10.
. .
.
.
11.
.:
//
/
. 2.
, 2000.
.
. .
,
. .
//
/
. 3.
, 2001.
.
//
12.
.
. .
,
. .
. 1991 — 1997.
.:
, 1998.
1998
/ . .
14.
,
. .
,
.
. .
.:
.
, 1999.
15.
.
,
. .
,
.
16.
18.
19.
20.
21.
22.
180
.:
. .
, 2000.
1999
.
/
2000
/ . .
. .
.
. .:
, 2001.
Blanchard . and, Fisher S. Lectures on Macroeconomics. Ch. 4.
The MIT Press, 1990.
Bruno M. and Fischer S. Seigniorage, operating rules, and the
high inflation trap//Quarterly Journal of Economics. 1990. Vol. 105.
Cagan P. The monetary dynamics of hyperinflation//Studies in
the quantity theory of money. Ed. Friedman. Chicago, 1956.
Friedman M. Government revenue from inflation//Journal of
Political Economy. 1971. Vol. 79.
4.
Mundell R. Inflation and real interest//Journal of Political Economy.
1963. Vol. 71.
3.
Sargent T. and Wallace N. Inflation and the government budget
constraint//Economic policy in theory and practice. Ed. Razin,
Sadka. L., 1987.
,
17.
.:
:
1.
. 1998.
.
13.
.
. .
,
23. Sargent T. and Wallace N. Rational Expectations and the Dynamics
of Hyperinflation//International Economic Revue. 1973. Vol. 14.
24. Sargent. T. and Wallace N. Some Unpleasant Monertarist Arithme
tic//Federal Reserve Bank of Minneapolis. Quarterly Review 5.
1981.
1 17.
25. Taylor M.P. The Hyperinflation Model of Money Demand
Revisited//Journal of Money, Credit and Banking. 1991. Vol. 23.
3.
IV
,
,
),
.
,
(
.
—
.
—
,
, . .
.
(
2 3%)
.
,
,
,
,
XX
.
,
,
,
.
—
,
,
,
.
.
,
.
.
9
.
(
)
.
.
.
.
.
.
.
.
.
.
.
,
.
.
,
.
,
Y
Y,
.
:
—
L
«
:
, L,
»,
.
,
«
Y= F(KE, L),
).
, Y = EF(K, L),
».
(
,
,
.
185
L,
(
)
t
:
,
Yt= F(K,, LtE^.
(£,£,).
,
,
.
,
. .
,
:
])
§>«•££<« £ > * £ < *
»••>
,
2)
;
3)
F(XK,X(LE)) = XF(K,LE).
(9.2)
,
,
,
4)
:
(
;
,
)
;
(
)
,
\im(FK)= lim (F,) = °°;
* _>ov Kl
/, >ov L>
(9.3)
lim(/v)= lim(/V) = 0.
(9.4)
,
F(K, 0) = F(0, LE) = 0
.
—
:
186
IS
=
LE
Y
;
=
—
LE
.
=f(k).
,
1
.
.
,
,—
F(K, LE) = Ka(LE)l~a;
0<
<1.
9.1.
,
,
,
=
+ /,
,
i—
.
,
,
, . .
.
.
.
s
.
(0 < s < 1).
«
»
«
, / = sy = sf(k).
»
.
1
,
.
LE
187
5.
sY
8 ",
. . K = sY 8K.
5/
LE
{L E )
L_
_ _
L E ' L ~ L E ' ~E ~
sf(k) {n +
n=
;
g=
.
,
= sf(k) (n + g
(9.5)
(9.5)
.
,
—
,
sf(k),
,
,
)
. 9.1.
188
,
g
5 (
(9.5)).
,
,
,
,
s (f(k)) > ( + g + ) .
,
= 0,
,
(
sf(k*) = ( + g+
= ,
.
. 9.1),
=0
. .
,
) *.
.
*
=
,
Y = y{ L E )
:*).
( + g),
g,
—=
Li
—=
Li
LI
. 9.1,
,
.
(. .
)
,
,
,
.
,
,
,
.
,
,
,
,
.
189
9.1
> 0, g > 0 n > 0, g = 0 n = 0,g=0
0
0
0
g
0
0
n+g
n
0
0
0
0
8
0
0
n+g
n
0
* = *
LE
±kt
L
— k(LE)
= y(LE)
,
.
9.2.
,
,
st.
£,*
s2
^,
;,*
,
(
190
. 9.2).
\
\ —*• \
. 9.2.
— = Ef(k)
.
g.
\,
:
g.
,
.
,
.
9.3.
.
,
s
.
*
,
.
*
:
?
,
max [
191
\k{s)} = (\ s)y = f [k(sj\ {n + g + 8) k(s).
s
.
,
f'(k)
(n + g+b).
,
,
,
( + g+ 5).
,
( + g + 5),
,
,
,
,
.
( + g+ 5),
,
,
f'(k) — ( + g+ 5),
.
,
.
,
,
,
.
s,
.
,
( + g+ 5)
** (
f(k)
. 9.3).
,
,
:
(9.6)
192
(9.7)
sf(k) = (n + g+8)k;
(9.6)
f'(k)
(9.7)
= (n + g+S).
,
sf(k)=/'(k)k.
*)
*
. 9.3.
,
s = f'(k)—
, .
.
,
,
**.
= AKaLl~a,
—
(0< <1),
, s = a.
,
,
,
,
,
.
1.
.
,
,
.
,
.
/
.
193
,
/
,
,
.
,
,
.
.
,
,
,
(
,
. 9.4).
(
)
.
.
( )
( )
(
. 9.4.
2.
,
.
,
,
.
.
,
.
,
,
(
194
. 9.5).
( )
( )
(/)
. 9.5.
,
,
,
,
(
.
,
).
.
9.4.
.
1957 . .
Y= AF(K, L),
.
.
195
, L, :
Y = MPKK + MPL L + F{K, L)A,
(9.8)
, MPL —
.
(9.8)
:
MPLL
Y _
LA
+
—
+
j y—
(9.9)
L
,
« »
A
:
,
;
,
;
.
MPLL
„
,
.
Y= AKaLl~a,
:
—
(9.9)
(0< <1),
.
,
.
(9.10) (
):
<9 1)
i T 'T c 'f
,
,
(9.11)
,
196
,
(
,
).
9.5.
,
.
,
1
.
(9.5)
,
(9.12)
(9.12)
.
. 9.6
:
,
*—
1)
0;
2)
,
,
—
3)
,
—
;
DE ,
.
^ '
:
.»,
(9.13)
(
\
,1 )
\LE
)
,
,
(
Y = LE F \
0.
,
.
197
. 9.6.
k0
*
,
(9.13),
. .
—
. 9.6
.
,
< *
0
,
.
,
0
,
> *—
*.
:
_f'(k)k Jf'{k)k\
{/( ))
_
'
(9.14)
.
(9.12)
(9.14)
:
(9.15)
198
(9.15)
.
' "'
°
/ 2( )
\
f'(k)k)
(9.16)
,
0
1.
0.
,
< *
f"{k) < 0
.
(9.16)
.
0,
0
,
. .
> *
(9.16)
,
,
0,
(9.16),
.
,
( = (1 — s)y).
,
,
,
.
,
,
, . .
.
9.6.
(9.16)
,
s, n, g, 8
,
199
(
),
,
,
.
,
.
.
,
,
.
:
—
,
,
;
8—
.
,
,
, [6],
8
(
.,
1).
,
(
),
. .
.
,
,
,
.
(
.,
, [23]).
,
,
,
,
,
(9.12)
s ( + g + 5)
s
(9.12)
_
(9.17)
.
f(k)/k
l
/MA* J
(9.17)
,
.
,
200
,
.
. 9.7.
. 9.7.
. 9.7
,
2
1 ( 2(0) > &i(0)),
(NP> DE).
,
.
2
),
(PL >
,
,
1
,
,
.
.
.
,
,
,
.
.
,
,
= *,
(
. (9.5)),
= ( ).
:
201
(9.5)
{ )
(9.19)
^*)—
=
(9.18)
(9.19)
(**))(« + g + S)(k k').
= (1
x(t) = k(t)
(9.20)
*, ?i =
x(t) = Xx(t),
,
*.
(9.20)
) (&*))( + ,? + 5),
x(t) = (0) ~ '.
,
k{t) k*=e Xt(k{0) k*).
(9.21)
(9.21)
,
X.
,
— \%, g = 2%, 8 = 3%
,
(
),
4%.
*
18
( ~ ' =1/2,
/ = (in (l/2))/A = 0,69/0,04).
,
,
.1/3,
,
.
,
,
.
202
.
[7]
,
,
,
,
,
,
,
.
,
.
,
[15]
.
,
Summers and Heston (1991),
,
[23],
,
.
,
.
,
,
,
.
,
,
,
.
,
.
9
.
1.
.
)
.
)
?
)
,
.
,
?
)
.
203
2.
,
a
x
a
= K H {LE)^ ~
+ < 1.
, , X > 0,
,
—
sk,
sh.
5.
.
,
.
.
3.
,
—
=
l
a
a
K (LE) ~ .
4.
—
] 3
= K I (LE) .
1%
.
0,05.
2%
.
.
?
5.
,
,
,
.
6.
.
,
,
?
.
7.
,
,
.
N—
,
s,
— g,
.
204
> 0,
> 0, ( + ) < 1.
— ,
— 5.
)
,
,
.
)
.
)
,
.
8.
=
' 0' 4 /,0' 6.
,
,
,
2%
.
.
200
.
90%?
9.
—
X
Y = F(K, L) = A[bKV+(\ b)L?\*,
10.
50
2%,
.
?
1%,
Y=
0 3
' /,0'7.
A>0,
0<b<\,
< <1.
10
(
«
).
».
.
(R&D)
«
{ le arning by doing)
,
.
».
«
».
.
{ exp anding variety).
.
.
.
,
.
,
.
,
,«
».
,
, . .
.
«
».
.
.
,
,
,
,
.
.
206
—
1}
Y =
(0<
<1).
(10.1)
(
[1],
.,
:
4):
=
=
\—\
5.
,
,
Li
(10.2)
,
,
,
.
5
,
(10.1)
,
v
~
'
(*
"
~
>^
1950 .
.
;
~
,
.)
( / )
^
(10.2)
=5 ' /
,
,1
+5
/
+5
.
=
_^
4 ±
(10.3)
_
=
5
^
,
1
~ ( 6 )
[
]
(10.4)
5 .
6,5%,
< = 1/3, 8 = 0,1,
(10.4)
,
1950 .
400%.
,
.
,
.
,
,
.
207
.
—
,
.
)
,
(
1/3,
.
, . .
.
—
g
.
10.1.
,
,
,
.
[22].
—
:
, = « (/,//, ) ,
0 <
< 1;
—
,—
>0;
,
t( . .
,
).
,
,
,
(LH,).
.
,
,
.
/
(/*]
(//')
,
Y=
,
208
=/
,
+ I.
\
=Ih
:
.
.
,
,
. .
(10.5)
=^
(10.6)
(
.6)
:
(10.7)
Y = AK,
1
.
,
~
=
=
'
/(
'"
)
(10.7)
».
«
,
,
.
,
, . .
,
.
.
y=f(k)=Ak,
—
.
k = i bk = sAk bk,
f(k)
— = s—
8 = sA 8
,
.
(10.8)
,
.
209
. 10.1
—
sA
sA > 8,
5.
— >0
.
sA, 6f
sA
. 10.1.
^=
= (1 — s)y,
,
,
,
,
(10.9)
,
.
,
,
,
,
.
.
(10.7)
,
,
.
(10.9)
,
,
,
,
.
, . .
210
,
.
,
.
.
,
,
,
,
(sA — 8), . .
.
—
.
,
.
,
(
),
[21].
,
i sif b.
„0.0,
,
.
,
(10.10)
,
(
i mk4
*I>~
,
>
,
,
),
(
s
s
. )
, (10.11)
Hm /( ) =°°,
.
Iim — ; — = lim /'( ),
.
(10.11)
,
:
li m / '(*) > > 0 .
. .
,
(10.12)
211
lim f'{k) = 0 .
(10.12)
,
.
,
(10.12),
Y = F{K, L) = AK + BKal} a,
> 0,
(10.13)
> 0, 0 < < 1.
(10.13)
lim F'K = A > 0, . .
,
.
(10.13)
.
(10.15)
(10.14)
,
,
.
(10.15)
(
)
f(k)
.
• •
(10.16)
£i-a
,
,
:
(sA — 5).
sA > 5,
, . .
.
.
,
212
D
( < kD).
-
\
/
. 10.2.
(sA — 5),
: sA + s
•
5 > sA + s
5.
,
,
.
sf(k)/k
. 10.2
,
sA,
—
DXD2
D.
,
.
,
.
10.2.
«
»
.
[26],
(R&D).
,
,
.
213
,
,
,
,
,
.
» {learning by doing).
(
«
),
,
,
.
,
,
,
(
—
)
.
,
:
? ,= ?
Y,
?, 0< <1,
,L —
>0,
(10.17)
,
/;
, —
,
.
,
,
.
.
.
,=
„
,—
t.
„
'
.
(
• = NK,,
L, = NL,
:
Y, = ? 1 } '
?,
0<
<1,
>0.
(10.18)
s
5
,
+ (1 — ) +
,
.
,
.
1
= (1 +
) > 1,
,
.
:
K = sY bK.
214
Y
— =s
Y
8
,
,
/
.
)
+(1
) .
£
— =—,
Y
£={\- )
(10.19)
(10.19)
,
0,
.
>0
=1
,
.
( + ) > 1,
,
,
lim — = s lim
Y
8 = s lim Yi — 5 =
,
,
.
,
=0
=1—
sK
L
.
K
Z
(10.20)
^
= jL
i «_5.
(
.20)
,
,
.
,
(10.20)
,
215
. .
,
.
=
( + (3) = 1 (10.18),
,
,
.
,
,
.
,
.
,
,
.
,
,
,
(
.,
,
: [6]).
,
[9].
[8]
.
,
,
,
,
R&D,
.
.
«
»
,
,
.
10.3.
,
«
216
».
—
?
, . .
,
,
,
.
,
(
2),
,
.
. [1],
,
,
,
.
,
—
.
10.3.1.
,
,
.
,
.
.
Y,=A \!(xj)adi [,' ",
__
x' t —
0<
<1,
(10.21)
/
/;
,—
/;
—
.
(10.21)
.
,
,
.
:
217
Ll~a
\
p'xidi wL
,
^ —
(10.22)
L
*' •
(
)
/;
w —
.
:
1} ' = \
})
(\ a)A
1
i;
,
(10.24)
L r a = w.
(10.23)
/
,
(10.23)
/
.
,
,
.
:
max (/>;*; *;).
L ] ax ' ,
x
'i
1
,
\
\
,
(10.23).
,
:
(10.25)
,
.
(10.25)
1,
218
\=
(10.23).
(10.26)
,
(10.26)
.
{10.21),
:
Yt =Am,L,
= *~ —
.
(10.27)
,
R&D).
(
s
,
,
/, = sY,;
={mt+\ mi)^
(10.29)
(10.28)
yxmr
+
(10.29)
,
(
)
(
(10.27)
).
,
Yl+l
Aml+]L
ml+l
Y,
Am,L
m,
.
(10.29) sY, = (ml+l mt)(p
(10.28)
+ yxmt,
sAm,L = <pml+l (<p yx)mr
.,,
JiL
(10.30)
,
=
sAL + tp yx
——.
(10.30)
(10.26)
,
1
I Y J
=
(10.27),
,
i
,
m
t\\
,
1+
t
J
2
),
219
s>
2
.
,
,
.
,
,
,
(
. (10.27)).
,
,
.
.
,
, —
L, . .
.
,
.
,
R&D.
,
,
,
,
.
,
,
(10.31)
[13].
,
,
.
,
,
,
.
,
,
.
[27]
,
,
.
,
,
,
,
( ,).
(
,
).
220
10.3.2.
.
.
,
. .
,
—
,
[4]
.
,
,
.
.
,
,
.
,
,
,
.
,
.
:
1
Yt=A
—
(10.32)
/
/.
/
,
.
,
/
:
\ ; ( ;) ] )1} .
\ =
(10.33)
Y
\ = =— .
,
,
X, (ktl = Xt),
:
,^,
,
,
(/„•),
1=
1
.
(10.34)
,
221
(< ).
:
./+1 = * , + — •
(10.35)
(10.35)
,
, . .
.
/, =sYt;
(10.36)
l,=llr+yc.
(10.37)
,
2l±L=^±L =
(10.38)
1+
,
/,
10.3.1,
iA(5_a2).
(
,0J8)
,
.
,
,
,
.
.
[3]
.
.
—
.
,
R&D ( )
.
.
,
,
,
.
,
,
.
,
,
222
.
,
,
,
.
10.3.3.
.
,
,
,
,
.
[17].
,
(10.21)
rl Ct
,
,
.
,
7 («/ * L~
a
p J x',di wL—> max.
(10.39)
I<
(10.39)
:
)1
=\ —
\
)
L.
(10.21),
:
Y,=Am,Lp ! ,
=
,
/ ( , °°).
,
,
.
,
,
,
m / + 1
/, —
,
"/"'+ p
(10.40)
.
223
I,=sYt
s,
(10.40)
,
,
.
,
,
.
.
[6],
.
,
,
.
,
.
[24|.
,
,
,
.
,
.
,
.
[12]
,
.
,
.
XIX
1974 .
.
,
,
.
,
.
,
,
"
,
.
.
,
,
,
.
224
1
.
.
.
,
.
,
.
,
,
.
,
,
.
,
,
.
—
,
,
,
,
.
1.
Y = F(K, L) = A[bKv+(l b)L<f]^,
Q<b<\,
0<
<1.
)
.
)
.
)
)
£-><*>
,
,
X
sA^ >( + ).
.
' Aghion P. Growth, Productivity and Interdependence.
«
10
19 21
.
.
»,
., 2002,
225
\ ,
)
sf(k)
.
2.
Y = F(K, L) = A[bK'f+(l b)L*]v,
Q<b<\,
<0.
)
.
)
&—»°°
.
)
,
(
)
,
k
J
.
3.
4.
2
?
?
,
5.
2%
.
16
6.
?
+ KI/2L>/2.
Y = F{K, L) —
.
0,4.
.
,
«
»
.
7.
?
?
,
,
?
8.
?
?
226
.
9.
Z
Y=
, ".
,
. 25%
.
20
.
,
.
.
11
.
.
.
.
.
.
.
.
(
)
.
.
.
.
.
.
.
.
.
.
—
—
,
([26],
[11], [20]).
,
,
,
.
,
.
11.1.
.
, . .
228
,
.
,
,
.
L
L.
1,
. . L , = "' .
,
(
)
:
(11.1)
,—
( > 0) —
/;
,
.
,
,
.
, . .
.
"( )<0
'( )>0;
:
()
—>0
;
— >~
()
.
, . .
.
.
,
.
.
—
.
,
.
,
,
,
,
.
229
t
,
,.
t
(
),
— w,,
, — ,,
(w, + , at).
,,
:
a = w + ra c na.
(11.2)
—
(
).
— ,
:
\\r(v) n\dV
\\mate °
>0.
(11.3)
,
(11.1)
(11.2)
(11.3).
.
= u(c)e"pl + X(w +
^
—
= '( )
=(
)
1
=
ra c na).
X,
'( ) ~ ' = .;
(11.4)
,
= (
(11.5)
) .
:
Y\mX,a, =0.
(11.6)
X
.
,
(11.5) —
,
.
—
230
.
.
.
(11.4)
.
££ = i £ £ L p.
.
)p/;
(11.5) —
( )
,
(11.8)
(11.7)
(11.7)
,
I—I
"\
— >0 ,
.
)
,
,
.
,
,
,
.
,
(11.8).
.
(/• — )
,
—.
,
(— )
,
—.
.
( — const,
— const),
.
231
( )=
,
) _,
1—0
1/0.
(11.8)
£ = 1(
/!
).
(11.8')
(11.6)
,
,
X
,
0.
,
,
.
.
(11.5),
:
(11.4)
.
,
—
= '( )> , . .
,
,
\\
j[r(v) n\ dv
, °
=0.
(11.6')
—
,
,
,
( ,< 0)
,
.
—
. .
,
r—
.
(
232
.
(11.3)).
,
11.2.
,
Y, = F(K,, LtEt)
,
,
9
.
g,
,
( £ 0 = 1), £ , = <•*'.
=
Y
,
*•
=
,
y = f(k).
Y = LEf(k),
,
( + 8) (
7) Y
— • = /'(&);
. [1],
?) Y
— = \f(k) kf'{k)
—
L
*1.
J
4).
P = F(K, LE) {r + b)K wL.
(11.9)
.
.
we* ]
= (LE) [/( ) ( + 5)
f'(k)
= r + d;
[f(k) kf'(k)jegl
(11.10)
(11.9')
(11.10)
=w.
< . )
(11.11),
(11.9),
,
, . .
0.
(
. [1],
2).
,
,
0.
233
11.3.
.
,
, . .
.
,
.
.
,
\ =— .
V
L)
:
k = kE = kes',
gl
=
, c = ce~s',
.
(
.
= —.
LJ CJ
9):
(11.12)
(11.12)
,
,
(
).
— = — g,
(11.8')
(11.12)
c\ \J
t) L
i
ev
\ ~)
\ '
(11.10)
"
v' ' • * J /
"°
"
J
(11.13)
0
,
.
= , k = kegl
(11.6')
(11.10).
:
Mm
234
,
•
.
(11.14)
(11.14)
,
,
,
f'(k) 8 g n>0,
, . .
,
+ g.
> 5 +
(11.15)
(11.15)
,
— 6)
(
(n + g).
(11.15)
.
(
. 13),
,
f'(k) = 8 + n + p,
.
( g ^ 0)
: f'(k) = b + n + p + Qg.
(11.15)
+ 6g > g.
,
0 > 0,
> g.
11.4.
.
,
,
.
,
, . .
,
,
.
:
U = ju(c,)e pla *
max.
235
:
= f{k) ce
0.
= (
gl
+ +g)k; c>0;
{
"" ( 5 + + g)k\.
' + *.[ / (*)
—
:
= u'(c)e
pl
Xe~gl =0;
(11.16)
)
(11.17)
\f()(
L v /
(11.16)
.
>0
g
J
,
( )
(11.17)
(11.18)
—
.
,
,
,
.
(11.18)
,
,
,
,
.
,
(11.18)
(11.13),
(11.14).
236
,
,
.
,
.
11.5.
—=0
— = 0.
,
—
g,
( + g).
.
(11.12)
(11.13)
,
0;
( .19)
0.
(11.20)
(11.19')
(11.20')
( , )
. 11.1
(11.19),
= *\
,
,
,
f'\k\ = b + n + g.
(11.20)
,
=
(f'(k) b)
,
(n + p + Qg).
.
,
(11.20)
.
*,
237
. 11.1.
(11.19),
*.
f'(k*)>
,
Hie**),
* < **,
.
,
.
,
, . .
,
,
0,
.
.
,
,
0 ,
(11.20)).
, ,
/'(/£*) (
,
, *, *
k = k*
,
,
.
,
k = k* (
=0
(11.20)).
5, , g
= *.
*, *.
238
,
. (11.19)
:= 0
*, *, *
.
*,
11.6.
0
(11.13).
.
(11.12)
,
= 0,
(11.20)
> *
= 0.
.
. 11.2
(11.20)),
< *
.
(
.
,
,
,
,
. 11.26
(11.19),
= 0.
( , ),
,
< 0.
,
,
(
).
(
).
11.2
.
,
,
11
IV
.
11.3
.
,
\)< *.
.
,
,
I
,
0.
d2k
dt1
,
,
=\ ( )
8
.
(11.12)
,
^ £<^
239
*
. 11.2.
. 11.3.
,
,
(11.13)
240
0.
.
0,
.
D
,
,
.
j/'IA] 8)<(/7 + g).
.
,
.
, —
,
(11.19), (11.20)
.
,
,
,
.
.
0
.
III
,
,
—
.
,
«
».
11.7.
(
. 11.3)
,
,
,
5 =—
,
.
,
,
.
,
,
.
.
f'(lc)
,
,
.
.
241
.
,
,
—
.
,
(
)
,
,
.
,
—
.
.
.
,
—
.
11.7.1.
.
—
,
—
Y = Ka(LEf'a, 0< <1.
(11.19) (11.20),
f'\k*\
.
.
=
(11.20) _ * ! _ =
2
,
(11.21),
°(8 + + ! )
5 + + + Qg
(11.20)
p + Qg>g,
242
s* < .
( .22)
,
,
,
,
.
z ——,
=4— = —
Z
f £
/£
= —
4=4 «4. ( .23)
/
(11.20)
1"
_ •' \ )
9
5 + + + Qg
9
'
(11.19)
(11.24)
(11.22)
1
±^lM
(11.24)
(11.25)
( .25)
(11.23),
,
s
,
1
—.
.
.
* 1 _
1. 5 = —.
)
=0
:
z, =—£-;
243
7
9—1
)
/ z, >
)
/ z, <
« »
9
1
,
t — >0;
z
,
/ — <0.
z
«»
j
,
,
* 1
s =—,
9
,
z
_
2.
.
1
(1 _£) = _ .
1 _
>—.
9
/ s, > —.
' 9
, . 1
3. s < —.
9
1
a s, < — .
' 9
6-1
z, <
t,
0
.
.,
9 1
,
t z, >
,
(11.26)
(11.27)
,
,
,
/>—,
9
(11.27)
,
— <0 (
z
,
,
z< 0
).
,
s * < —,
9
,
, i>0.
i<0.
. 11.4.
1
,
,
,
244
9
K
s <—
0
. 11.4.
.
2
.
(11.22)
(1/9) < .
,
,
,
0>(1/
)
,
.
,
.
3
9 < (1/ ),
.
11.8.
.
,
,
. .
.
•
_
=
(*
:
(11.28)
245
,
(11.28)
(11.20)
0.
,
~—
(11.30)
(11.19)
= {p + Qg g)(k k*) (c c*).
=
P =p +9g g,
(11.31)
=
*,
*,
(11.30)
(11.31)
(11.32)
;
=•
=$
.
(11.33)
(11.32),
(11.33)
:
=
<
;
=
,
X.
;% = ( ^
*) *';
(
,
—
i
246
, *=
0
*) ' .
(11.19)
J•
X
(11 34)
,
,
9,
.
,
,
.
9,
—
,
(
2)
, . .
.
,
,
,
.
«=
,
,
(
)
,
.
= 0,75, . .
,
.
11.9.
,
247
G,.
.
,
,
, . .
.
, . .
G,.
(11.12)
k=f(it) c G (b
(11.35)
,
,
(11.2)
:
(11.36)
a — w + ra—G — c—na.
(11.5) ,
,
.
.
=0
,
G.
,
=0
G(
*
. 11.5.
248
. 11.5).
(11.20)
. 11.3
'
.
G.
,
,
.
,
:
b + nb = G T + rb,
b, G,
(11.37)
—
,
.
(11.5) —
d = w + ra T c na,
(11.38)
a,=k,+br
(11.37)
(11.38)
:
(11.37')
J c,R,dt =Ao + b0 + J wtR,dt
J TtRtdt,
0
(11.38')
0
j(r,. n)dv
Rt =
°
(11.37')
jc,R,dt =
(11.38'),
+j
0
0
vitRtdt \GtRtdt.
0
,
(11.36)
.
,
249
.
,
,
.
(
)
.
(
)
,
.
,
—
.
.
,
.
.
,
.
1.
,
,
.
.
2.
,
,
Y= /w°'3(Z,£)0'7,
— 1%
— 2%
— 0,02
,
,
,
3.
3.
.
.
)
)
?
,
—
.
)
250
?
4.
(
):
)
)
;
;
)
5.
.
,
.
6.
,
,
.
7.
(
)
?
.
.
12
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
—
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.
.
252
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,
,
[28]
(11]
».
«
12.1.
,
,
,
.
.
,
.
,
,
.
,
.
,
,
.
t
/
L,
.
, . . L,+I = (1 + n)Lt.
L,
. .
Lt_x
,
(L,_, = L,/(\ + «)).
.
(
)
,
.
,
:
, —
,
2
t.
,
,
.
,
, = F{Kt, LtE^),
,
g
.
,
5
/+1
= (1 + g)Et.
.
.
253
/
>„
— / ,.
,
(c w )
, w,Er
,
( ,),
w,E,= c , , + v
(12.2)
.
,
.
— cXt).
Lt{w,Et
/,
,
12.2.
.
.
2
», ,
,+ ,
„).
:
(12.3)
,
(12.1)
,
1
.
1+
(12.3).
io
,7 =
254
[ ' '
1
;
"
(1 2 . 4)
(12.4), (12.5)
.
(12.4) (12.5)
(12.3)
,
+ ..
(12.6)
(12.6)
(12.6)
(12.7)
.
(12.3),
1
„+
,
,
1
1
s,:
1
i
he'
p)e+(l+r f + 1 ) e
(12.9)
255
(12.8)
,
f
(s' w >0).
(12.9)
.
.
,
,
,
.
,
/
.
,
.
,
/
.
,
,
(12.9).
,
,
!,(/•)
,
,
0.
, . .
0 > 1,
,
0 = 1, . .
,
0 < 1,
.
.
,
st =
.
,
.
,
.
,
,
(
\
,
~
, =—'—.
,
.
256
/
w, = fikA kff'ik,
(
.
,=
I,
f'ikA
9).
,
*,,= [ ,) , [ ,\,
(12.10)
, =/'(*,) 8.
(12.11)
12.3.
,
,
:
Km
(12.8)
= s,Lr
(12.12)
(12.12)
1
Ll+lEl+l,
(12.13)
,
L, =
(1 + )
,
,=
(l + g)
(12.10)
(12.11),
,
1
(12.14)
257
(12.14)
,
,
1+1
.
,
.
.
[ ]
,
(12.14)
( .,
.
/
0
: [5]),
,
,
,
.
.
(12.14)
),
s(rl+l, *,) = -£- (
. (12.8));
s r
{ i+v wi) ~~
t.
(12.J0)
(12.11)
:
] } 02.15)
(12.15)
.
,
,
• •
258
(12.16)
s'w >0, f"(k)<0,
(12.16)
.
s' r .
,
.
,
,
,
,
,
,
,
,
.
^<0
,
.
(12.16)
.
s ' r >0 ,
kt+l
,
,
,
kt+l =k,.
.
.
,
(12.14)
.
kl+i
: kl+i = \ , ).
.
,
,
,
/
,
(12.17)
,
(12.17)
,
( )
lim 4 < Mm
^~
»
(12.18)
259
(12.18)
,
.
,
,
(12.18),
, —» °°
1+1
,
, = 0.
0
• .
0.
(12.14)
,
,
(12.14)
,
,
1+1
,
= ,
.
. 12.1
12.2.
"7 + 1 "
,
,
. 12.1.
.
. 12.2.
.
2
1
( '(0) > 1,
45*
0
(
.
. 12.1).
,
,
kl+i > ,,
,
1+1
,
—
,
,
—
(2
+ 1)
.
(
,
+ 1)
.
< '(0) < 1,
45*
( .
. 12.2).
,
,
260
,
tp'(O) > 1,
Jim
,
...
,
,
,
<
n)(\+
g
) s'rf"(k*)
,
(12.14)
(
.
1+]
,
. 12.1
12.2,
,
.
,
,
(
).
4^ > 0
, —> °°
,
,
,
.
,
,
.
,
.
.
,
,
,
.
261
12.4.
.
,
, . . 9 = 1.
—
Y = Kn(LE)l~a.
s, =
w, ~(1 ) "
2+
,
(12.14)
:
** • ( , + , . )( , + ' , )( , + , , ) < • • ')» •
< " • '»
1+]
= , = *,
1
. 12.3
.
—
.
lkQ<k*\,
kl+i —
> \.
= 1 :0) <
*\ = *,
{
\,
*
,,
< *.
,
,
. .
*.
262
. 12.3.
—
,
.
*—
,
0—
,
,
.
,
,
.
12.4.1.
*
:
1
=
.
kt+l
,
:
V+1
,
,=
=
7+1
, *, =*
,+1
,
( ,
*
,
* = X ' ( / CQ
1+]
*).
X.
,
X
(12.19)
(12.20).
1
1
1
1
= .
,
,
,
.
,
,
30
. .
.
,
,
.
12.4.2.
,
, . .
.
.
,
,
.
.
,
(12.20).
264
.
t 1
t
,
,
:
, = cuLt+ clt_KLt_K.
,
L +L
1 + n c<
2+ n
,
,
.
,
f ' ( k ) = n + g + 8.
f'(k*)<f'(kj,
.
* > **,
. .
,
.
,
1 oc4
(12.21)
/v
(12.21)
,
,
,
,
,
.
t0
,
**.
flk*) + (k* k**\ (n + g + S)k**.
f(k**\ (n +g + 5)k**.
.
* > **,
f(k*) + * > f(k**\ + **.
265
, f\k*\ + \h* k**\ {n +g + b)k**
f{k"\ (n
+ g + 5)k**,
,
. .
.
tQ
,
,
,
.
,
,
.
,
—
.
,
,
,
.
,
,
.
.
,
,
,
. .
,
.
,
,
,
(
. [2]).
12.4.3.
.
,
,
,
—
.
G, —
,
.
266
w, G, =(1
) ™ 6,,
(12.19)
1
(12.22)
,
,
.
. 12.4.
.
—
,
(12.21),
.
. 12.4.
*
,
,
.
,
,
,
.
,
,
,
, . .
,
,
.
,
267
.
,
.
,
,
—
.
12.5.
,
,
.
,
,
.
,
,
,
.
(
1
.,
1+
: [6]).
1
(i+p)(i+y)
Ut+l.
(1 + n)Ut+[
,+2
(12.23)
,
,
268
,
,
,
(12.23)
. .,
(12.23)
. .
, ,
Ul+2
..
,
Ul+]
,
.
,
(1 + ) < (1 + )(1 +
).
t
„
,
,
bl+l.
:
cu+s,=w,+bt;
(12.25)
c2l+]+(\ + n)bl+,=(\ + rl+l)Sl.
(12.26)
,
,
/ bt+j>0
. .
[31]).
[19]
(12.25)
ci,+ / =w/+, +*, + / • */ + / ;
(12.26)
1= 0 , 1 , 2 , . . .
2/+1+/ = 0 + /. +/)*/+, (! + )*/ + i+«;
(12.27)
dU,
,
(12.28)
(
(12.24)
s,
(1 2 . 2 7)
' = 0 , 1, 2, ...
bt+{.
(12.28)
:
.
(12.29)
(12.29), (12.30)
1+ i
,
:
1 + /7
/
269
(12.31)
1
f
,,
i+^i
V
£/,_,,
,
,
„
c2l
t
(*)
j_
LH = JLH = J±± \
L±]— .
(12.32)
(12.32)
,
. .
.
,
.
,
270
= ,
—
.
,
.
,
,
,
.
1.
Y — Ki/3(LE)2/:i.
.
1.
)
.
)
.
(
)
)
.
,
.
.
)
?
2.
1
.
« ».
,
.
3.
.
,
= \ (\ + ),
.
4.
j_
Y = A\bK^ +(1 6)/ ] .
271
.
1.
,
=0
.
5.
,
6.
,
< 0,
.
4,
> 0,
,
,
7.
,
.
4,
> 0,
,
.
8.
—
.
4
1.
2.
3.
4.
5.
6.
7.
8.
9.
272
. .,
. .
2.
.
. .:
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V
,
.
,
.
,
.
,
.
.
,
.
13
,
—
—
.
14
—
—
.
15
.
16
,
.
XIX
.
70
. XX
.
,
:
1.
,
(
5
2.
,
3.
,
2
4%.
,
—
(. .
),
276
,
8
).
—
—
).
(
,
.
4.
(
,
,
,
),
,
,
—
(
) —
(
5.
,
,
),
(
.
)
,
.
,
—
.
.
'
.
35
,
[7],
,
.
,
—
.
,
45%
1989 .
1945
26%.
:
.
,
.
,
«
.
1.
«
(
»
[1]:
40
60
,
23
.
(
»).
,
,
2.
15
,
3.
).
).
(
5—8
,
,
,
277
.
.
2 4
4.
,
.
,
,
.
,
,
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. (
,
.)
.
,
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,
,
—
,
,
.
.
,
.
.
,
,
.
13
:
.
.
.
.
.
.
.
.
.
.
.
.
.
,
, . .
,
,
.
—
.
,
Y f:
,
, = f{Yf\.
,
,
.
,
(
):
d
, = f[Yl _l).
279
:
,
—
.
,
(
).
—
—
[27],
[19].
.
.
,
.
,
,
.
,
,
(
,
,
,
),
,
,
,
.
,
,
,—
,
—
.
—
.
13.1.
,
, . .
.
,
,
^
.
,
,
280
,
.
.
,
,=
]
0
0
+ , • Y,,
—
—
,
0 < , <1;
0 > 0.
bQ (b0 > 0)
/, = V +
,
(Y,
,_|):
, .)
{
bi > 0.
,
(
Y, =
1
+
< 1).
, + I, + G, + NX,.
,
G
NX
0
Y, =
,(1
0
+
Y,+ bo+ b,(Yt
,
,) =
,
<0,
,
,
+
Yt_x) +
0
/>, •
.
0
,_,.
/
t— 1
g'
+
, . .
= G +NX.
Y, = g(Yt_^),
1,
,
.
Y, = Yt_{ = Y.
,
281
_
+ Z)o + c 0
1 ,
(13.2)
1
(132)
,
,
,
.
.
AY, = Y, Y.
(13.3)
/— 1
bY,_x = Y,_x Y.
(13.3)
bx
1
(13.4)
(13.4) ,(13.1)
\
(13.2),
(13.5),
(13.1),
,
.
>0,
.
,
,
.
,
.
282
, . .
,
(
{
+2
{
< 1,
1
, 6,
. 13.1 ).
)
\
. 13.1.
•
,
1
+2
{
>1 ,
,
,
• > 1,
,
283
.
(
. 13.1 ).
, + 2/>, = 1,
(
. 13.16).
,
,
,
,
.
,
(
.
).
. 13.1
.
,
(
.
. 13.16),
,
.
—
.
,
13.2.
—
.
,=
0
/,=
Y, =
+ ,.
0
+
_,
+
0
_„
;
+
0
>
Y,_2),
+( , +
,
0 < , < 1.
bQ,b{>0.
,) ,_,
,_2.
,•
(13.6)
,
t— 2.
Yt=Y(_x =
,
,,
= ._2 = / ,
„
— 0+
Y =—
+
1 0,
284
0
_
.
.
,
,
Y,=AYt+Y.
(13.6)
) bx(Y+AYl_2).
)(V
AYl={ax+bx)AY,_x blAY,_2.
(13.8)
2
(13.7)
(13.8)
.
2
(13.8)
%2
[2,12]
X2
)\ + , = 0.
( , +
(13.9)
(13.9)
:
1)
, . . ( , +
,
)2 > 4
(
2)
3)
,
(
, =*,*,',+*2 /2.
,= +
,
2
—
1
.',+*2 ,'2,
+
)2 = 46,;
2
, . . ( + {) < \ .
(13.8)
)
(13.11)
(13.11')
,
.
285
(
]
=
X=
2
(13.8)
AY,=kft+k2tX'.
(13.12)
Y,=Y+k^+k2tXl.
(13.12')
,
(13.10)
1 2
= ± v/,
,+
=—
;
(13.11)
AY, =
1
\ + :2^'2 =*,(* +v/)' +A2(A v/)',
(13.13)
,.
(h±vi)' = R' (cos wt + i sin wt),
w—
(13.14)
[0, 2 ],
v
tgw = .
(13.13)
i
A Y, = b}[K] cos wt + K2 sin wt),
/ |,
2
—
,
.
Y, = Y + bf (K^oawt + K2sinwt).
286
(13.15)
.
,
, =0.
,
| ,| < 1 \
{ = ^|^2>
,
{
(13.16)
\<1
,
2
{
,
(13.16)
+ />, = \ + ,2,
:
0 < \ <1
0 < \< 1.
,
(13.17)
(13.17) { < 1.
(13.10)
(13.17)
+ < 2.
0 < , < 1,
{ <1
,
,
,
,
> 1,
.
.
,
(13.11)
(13.12).
, . .
—
(13.11),
,
.
,
,
t
—
(
. 13.2).
Y
<
IV, VII '
I, VI
t
t
. 13.2.
•
287
(13.15),
.
,
,
\ > 1,
(
< 1;
. 13.3).
t
. 13.3.
.13.4
.
•
,
,
. 13.1.
:
,
,
,
;
•
,
.
.
—
,
.
288
. 13.4.
—
13.1
—
. 13.4
1.
( , + />,)2 > 4 ,
2.
( , + ,)2 =
,
3.
( , + ,)2 < 46,
I
6, < I
IV
6, > I
VI
6,< 1
VII
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11
, <1
V
/,,= !
III
/>,> 1
,
,
,
,
—
,
.
,
(
),
.
289
1.
0,75,
0,3.
,
.
?
.
2.
0,75,
1,5.
,
.
?
.
3.
0,75,
0,1.
,
.
?
.
4.
0,5,
0,25.
,
.
?
.
5.
0,625,
0,125.
120
80.
— 150.
250,
)
.
)
,
(
1300,
)
1 — 1400.
.
2.
290
)
.
?
)
?
6.
(0 < < 1),
(3 (
> 0).
.
:
)
)
;
,
;
)
;
)
7.
,
« ».
,
,
.
,_\ — ( ,—C,_t).
:
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)
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;
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;
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« ».
14
.
—
.
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—
»
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,
.
.
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,
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,
292
,
,
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.
«
», . .
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.
—
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50
.
.
.
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.
.
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—
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.
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,
,
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.
293
.
,
,
—
.
.
«
—
».
.
14.1.
.
.
,
.
,
2.
,
.
:
)
F—
—
(14.1)
;
,
. > 0.
> 0,
71 —
" —
—
294
;
.
;
(14.1)
/*_,
P P_l = P' P_l+X(Y Y).
,
)
(
—
(14.2)
, . . =\ ,
.
(14.2),
dP = —,
,
,
_ ~dP =
_{= '.
(14.2)
(14.3)
K = K'+X(Y Y).
,
,
,
Y Y= b(u u"), 5>0.
(14.3)
(3 =
,
,
,
:
= _|,
(14.3)
:
F).
(Y,
)
(14.4)
. 14.1.
,
,
.
,
.
,
295
(
(
.
. 14.1).
Yt=Y)
.
SRAS(ne2)
SRASfc)
Y
. 14.1.
,
' =
.
.
Y, = Y
.
.
.
14.2.
LM,
.
296
,
/
—
)
= L \ i,
+
.
,
,
(14.5)
, 3 >0 —
.
,
.
, *,).
(14.6)
,
,
,.
,
,
„
,
;
,
,
,,
.
(14.5)
(14.6)
,
,
/
(/, = , +Ke,)
,
( . . Art= 0),
:
, =!(„,, ,) + | <.
297
= —, a V = 7T'
:
, =
(14.7)
, \|/ > 0.
(14.7)
,
,
,
,
.
:
,
,
,
,
,
.
' > 0,
,
,
,
.
An' =0, . .
,
, = y, i+
(14.8)
,
Y, = Yt_t,
, = ,.
,
( , )
. 14.2.
AD{m2)
AD(m{)
7
. 14.2.
298
(Y, )
,
.
,
,
.
(X, )
.
,
,
,
,
.
Am (
.
. 14.2).
14.2.1.
,
.
,
IS,
:
+ / + G + NX;
Y =
AY= &
) £,
(14.9)
—
(
(7;
,
;
,
/ 0;
,
yvo)
= <7 +
5, | —
,
0
+ / + AN0;
.
299
(14.8),
(LM),
=
(
).
(14.10)
,
= 0.
(14.9),
0 = AY = 5AA r]Aer,
=
(14.11)
.
(14.11)
,
.
.
LM(14.10)
,
.
14.2.2.
.
,
,
: <7=
AD:
,=
AS:
, = ,._,+ ( ,
,_, + < (/ ,
= 0.
,);
(14.12)
Y).
(14.13)
,
. 14.3
,
ADQ
AS0.
—
.
0
(14.12),
AD
,
—
300
(
£,.
{ —
0).
ADX
0
.
,
. 14.3.
{
(
) ,
,
> 0,
(14.13),
: AS
,
( ,
( ,>
(
( ,—
( ( — 0 ),
^.
AS2
,
)
(14.12)),
)
.
,
—
,
,
.
,
2
,
—
—
.
0
< / ,,
, 2>
2
> Yt,
,,
,
. < 1.
301
( —
)
(X —
).
.
:
2
1. Y2> Yb
2.
2
>
AD
ADy
;,,
AS
,
,
1. Yi<
AD
2. 7 3 >
AS
,
4,
1. 4<
2. 7 4<7
.
:
2,
,
2,
ADA.
,
AS4.
:
AD
3,
,
dS
3
14.4
.
.
,
(14.12),
. 14.5 —
,
(14.13).
. 14.6
,
,.
=
. 14.4.
302
. 14.5.
,
ASi.
Y
Y
. 14.6.
. 14.7.
,
. 14.7 —
.
,=
,
,
(14.13).
14.3.
=
.
,
. .
.
,
IS:
AY = 8AA r\Aer =
\
(14.14)
? ].
,
,
,
(14.14)
:
(14.15)
= ) > 0.
303
,
:
AY =
(7
(
*).
AD:
,=
/
_,+5
(
;*),
(14.16)
(14.13), AS:
,
n,=n^+X(Yl Y).
(14.16)
(14.17)
,
.
14.3.1.
(
,
.
. 14.8).
,
AD 0
,
—
AS0.
.
*:
0
= — ( — *),
/S
LM — AY= (/ — ).
,
AY=0,
,
=
=
*.
ADX.
,
—
£",.
|>
£|
(
)
,
0
(14.17),
(
AD
AS2).
—
,
:
,
,
,
,
—
(7= 0 ,
304
,
,
,
,
,
.
,
AD
AD2.
2,
,
:
1. Y2 < [,
2.
2
AD
ADy
> ,,
ASy
AS
,
1. Y3< Y2,
2. 3 < 2,
}
,
:
AD
AS
.
.
,
(
. 14.8).
. 14.9.
,
Y3 Y
Y2
,
. 14.8.
305
7
. 14.9.
{
.
,
.
,
. .
.
JE14
/
4: *
I.
:
, 400 200
/ =
;
3
3
NX= 200
100 ;
G = T = 100;
— =
/>
306
,= \ ;
— — 100/ .
2
=\;
*=1;
=2;
:
)
,
,
,
;
)
« »,
150?
)
)
)
;
;
"'
+
1200
(
1,
« »),
.
150.
.
)
,
,
.
2.
:
,
400
200
3
3
'
NX = 200
100£ ;
=G =
= 100;
= 1;
* =1;
— =100 + — 100 .
2
)
= 2;
,
,
.
)
150.
,
,
.
)
)
.
.
307
)
800 v
"'
(
«»
2)
.
150
.
.
,
,
.
,
15
:
—
.
.
.
.
.
.
.
.
IS LMc
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
309
15.1.
.
.
80
,
.
,
,
,
,
,
,
—
,
.
.
,
,
.
80
.,
,
[20]
.
,
,
,
,
,
.
,
.
?
,
,
,
:
Y, = g, +bY,_, +Zl,
g, —
(15.1)
,
;
, 0 < b < 1.
z, —
,
,
t
.
/,
.
310
,
tx
,
.
/
,
.
,
)
(
< b < 1.
,
,
(
. 15.1).
,
,
.
,
(15.2)
(random walk with drift),
:
Y, = g, + /,_, + zr
(15.2)
,
(
. 15.2).
+
. 15.1.
. 15.2.
,
.
tx,
,
,
.
«
Y,_x),
» (
,
.
311
.
(
)
,
.
,
,
,
,
.
,
,
,
,
.
.
,
,
.
—
.
15.2.
,
,
:
1.
.
2.
,
.
—
.
.
3.
.
312
4.
,
.
5.
.
,
.
6.
.
,
(
,
.,
: [II, 25, 29]).
.
,
,
.
—
.
,
,—
.
,
—
.
.
,
,
.
.
.
IS—LM
,
,
AD—AS.
—
15.2.1.
,
(
)
,
.
,
313
,
.
,
„
:
Y, = A,F(K,, L,E,).
,= 1,
, > 1.
, < 1.
. 15.3
( ,= 1)
( , * 1).
. 15.3.
(9.5)
k = sAf(k) (n +
,
,
,
314
.
,= 1
,
. 15.4.
&,*.
»vi
.1
. 15.4.
,
(
).
, . .
, > 1,
,
.
,
\.
,
(
).
.
,
,
.
. .
.
&,*,
,
,
,
,
,
.
, > ;,*,
,
.
,
315
(
.
. 15.1).
,
,
.
,
.
,
,
.
,
,
.
,
,
.
,
.
,
,
.
, . . — = + \,,
, X, >
,
; %, —
,
—
,
" ,< —
(9.5)
.
:
= sAf(k)
,
,
.
. 15.5
,
.
,
(
).
,
,
.
316
^
k*
. 15.5.
(
1
< )
,
,
,
—
.
,
,
.
,
(
).
—
.
15.2.2.
,
,
,
,
.
,
;
,
317
.
,
.
.
,
.
,
.
,
,
.
/
:
(15.3)
/
Wt,
,+1 —
t w /+1.
Wt
(15.3)
Wl+l
,
.
,
.
.
,
.
,
,> 1
. 15.4,
,
(>g).
,
,
.
(15.3)
.
,
.
.
,
,
.
318
,
,
,
15.3.
«
—
»
IS—LM.
,
,
,
:
Y = Y = F(K,
I),
, L —
F(K, L) —
;
,
.
IS—
,
(
Y
IS:
f
{
)
()
.
()
NX(zr) = NFI(r)
(15.4)
LM: — = L(r, Y)
Y = Y = F(K,
2.):
I).
,
,
.
(15.4)
,
. .
,
,
—
.
,
S(Y}
=
Y C G
=Y
f{ Y
T} G.
,
,
Y =Y
,
.
319
. 15.6
.
LM.
JS—LM
. 15.6.
LM
,
,
(15.4)
,
.
LM
.
.
/S
(RAD),
(RAS).
. 15.6
Y =Y —
—
AD—ASTSM,
,
, . .
.
,
, . .
(
. 15.7).
.
.
320
Y*
Y
RAD—RAS
. 15.7.
15.3.1.
(
)
, . .
(
. 15.8).
. 15.8.
RAD—RAS
321
(
).
IS—LM
.
,
IS—LM
,
.
(
),
,
,
,
.
15.3.2.
,
.
,
,
.
,
.
,
.
(
. 15.9)
,
(
. 15.10)
,
.
.
.
,
,
W
— = MPL).
(
,
,
,
,
.
322
,
. 15.9.
. 15.10.
RAD—RAS (
1)
RAD—RAS (
2)
,
,
.
,
.
323
,
(
,
).
15.4.
,
,
.
(
(
. 15.12)
( .
.
. 15.11)
.
. 15.11)
.
,
,
,
.
,
,
.
,
,
L]
L
. 15.12.
. 15.11.
(
(
)
324
)
,
,
.
.
,
,
,
(
,
,
. 15.13).
. 15.13.
,
,
,
.
,
,
.
,
,
(
. 15.14).
.
(
,
).
. 15.15
«
—
325
. 15.14.
»
. 15.15.
326
(w\
—
V
+1
\\w\
—
, \
\ " +\ J
.
(
,
,
L
,
,
)
W,
(
,
Wt+[
I— )
I
+1
,
),
,
.
. 15.10
,
(
,
—
).
,
,
.
—
v ^ +i
.
,
,
,
.
,
.
—
(
.
,
,
. 15.9).
15.5.
.
.
,
[16].
327
:
1.
RAS RAD,
2.
(
,
. .).
,
,
.
3.
,
.
4.
.
[16, 23]
,
,
,
,
.
,
.
,
,
,
,
—
.
,
,
.
15.6.
,
,
.
,
.
.
.
,
.
,
,
,
.
328
,
,
.
.
,
:
1.
,
,—
(
,
2.
3.
,
,
,
).
.
,
,
.
4.
—
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5.
,
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,
.
,
, . .
.
..
.
,
[16]
,
70%
,
.
,
.
,
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,
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,
.
,
,
,
.
329
,
.
:
,
,
.
.
,
,
.
.
,
.
.
,
,
,
.
,
.
,
.
,
,
,
,
.
,
.
,
,
.
,
,
330
.
,
.
,
.
,
.
.
.
,
.
—
,
.
,
,
,
.
,
,
.
—
.
,
,
,
.
.
,
.
,
—
.
,
,
.
,
.
,
,
331
,
,
.
—
,
,
.
,
.
,
,
,
.
.
,
,
,
—
.
1.
:
Ls= WOr,
Y= 3600(/ )""l/2,
)
)
=
—
lOKi/2L^2,
Y=
=81,
( %).
.
,
.
)
Y= 8100(r)"l//2.
,
.
2.
Y=5OOL]/2,
—
( %),
, G= 1000.
332
Ls=4\—
1
,
Y = 5000 + 2(7 — 500/ ,
—
)
,
,
.
)
1500.
,
,
.
'
,
?
)
[ = 0,2
,
= 1000.
?
)
,
.
3.
2
Y= 525Ll/1.
,
,
?
,
«»
4.
2?
2
/, =4,244832(—](l
+
~~ ] •
,
,
?
,
«»
2?
5.
,
,
.
IS L M
6.
.
«
—
»
7.
Y= 500Ll/2,
Ld = 62500(
2
)~ , {W —
.
:
U — 4(W/P){\ + )3,
).
333
.
8.
,
.
9.
?
.
10.
.
11.
.
,
12.
.
,
.
.
.
.
.
16
.
.
.
.
.
,
,
,
,
,
.
,
—
.
.
.
,
.
,
,
.
,
,
{political business cycle theory).
.
1975 . [21].
335
,
.
:
.
—
[21, 26]
[9].
16.1.
.
,
,
,
(
,
[21]).
,
:
1.
,
,
?
2.
?
, . .
,
,
,
,
?
,
.
,
.
,
(
).
336
,
,
[14],
.
,
,
,
.
,
—
,
.
,
,
—
.
3.
?
?
,
,
,
.
4.
,
?
,
.
—
,
,
,
.
5.
—
?
,
,
.
,
.
,
,
,
.
,
—
.
. 16.1
,
,
.
.
337
16.1
, 1975 [21]
, 1977 |18]
,
1988 [24]
, 1977, 1987 [14]
,
, 1987 [9],
, 1988 [10]
16.2.
[21,26],
.
,
,
.
.
,
,
.
—
,
,
,
.
,
,
,
. .
.
.
(
),
.
,
,
,
338
,
,.
(16.1)
*—
,
".
,
, =0
,=
max , = .
( *, 0)
. 16.1
.
. 16.1.
—
,
,
—
.
,
:
* > > 2> >
,
4
.
,
,
,
«,,
,
, = *~
,+ ,
, (3>0.
(16.2)
339
nct = ,
,
, = " =—.
?= ,_,
(16 3)
SRPC ( ^= ),
.
(
. 16.2).
LRPC
'
. 16.2.
•
( ", 0),
,
,
(
. 16.3).
,
,
.
,
.
340
. 16.3.
,
,
:
= '=0,
>
{
< .
,
,
,
2
=
,
,
*=
,
2
".
(
2
< V*)
0
,
.
,
D,
.
,
,
.
.
:
bD bA.
,
.
,
,
341
:
)
,
—
.
,
,
,
,
,
.
.
,
,
,
;
)
.
.
,
,
,
.
,
,
.
,
,
,
,
.
,
,
,
.
.
,
.
.
1993—1996
342
.
[4]
,
,
:
•
;
•
.
«
»
—
,
,
.
16.3.
(partisan political business cycle theory),
,
,
.
[9,10].
,
,
,
.
.
.
16.3.1.
,
.
,
,
,
.
,
.
,
.
.
D
R
R
:
,
343
( = 0).
( = )
D
.
D
R
,
(
)
t
!!>
=l(l(nn, cf b'yt;
>=
(16.4)
z
z?, z? —
, —
D
,
,
R;
' > 0.
> 0,
,
,
ZD = iq'z!) =iq'\Un, c)2
' ,\,
(16.6)
4
1=0
q —
(16.7)
z
1=0
,
.
,
,
.
,
,
,
, = ( ,
,) + ,
>0.
(16.8)
(
,
D,
344
(16.8)
= 0),
(16.4)
zf =^(
b'y(n, n«) = i n ? b(n, < )
cf
, +i c 2 , (16.9)
b b'y> 0.
D
(16.9),
:
^
,
.
(16.10)
D
,
,
.
,
.
.
,
.
.
,
R.
(1 — ) —
,
,
.
,
.
.
,
—
(
).
.
16.3.2.
,
. .
,
,
.
,
.
345
:
,
.
\— .
,
, . .
? =mm\ n2t b[nt
'
n , b c
0.
\2
an.
, ].
(16.11)
(16.12)
,
D
—
/
(16.13)
R,
, . .
1
min zf = min — Ttf ;
(16.14)
,
^ = , =0.
,
t
*=0.
(16.15)
.
,
.
,
,
' =
,
346
,
,
+ ) + (1
) • 0=
+ ).
(16.16)
,={
(b + c,
D;
[ ,
R.
.
(16.8),
(16.17)
D
:
)>0.
( =0),
(16.18)
. .
.
R,
,
, = ( ,
P(b + )) = yP{b + ) < 0.
«) = (0
(16.19)
,
,
,
.
(16.18)
(16.19)
:
1.
.
,
(
0),
.
,
.
D,
2.
R.
,
.
,
3.
D
—
,
,
.
,
,
= 0.
347
£,D
,
£ tR •
(16.17)
,
D
+(1 />) 0 =
=
(
2
2
).
(16.20)
R
,
i ff
PP((bb + c ) )+ 2 ( (\ \P P) )0 0
,
2?
P(b + c ) 2 .
(16.21)
,
D
.
D
,
,
,
.
D
.
16.3.3.
,
.
,
.
,
.
,
R
,
348
(0 < 6 ).
min Z, = min (zf + 0 , ),
0 < 0;
z*<|*.
(16.22)
minZ, = min P{ in?f
bin?
')
?
\+
(16.23)
(16.23)
R.
—
,
,
—
.
,
(16.22).
7ic
nf =
/
=
;
:=
=— .
1 +0
(16.24)
,
(16.24)
,
D,
,
R.
,
(. .
<7 > 1)
,
.
349
= P [I«) 2
CK? ] =
2 9)c 2
2(1 + 0) 2
(16.25)
ZD=zR cj2z1*.
(16.26)
N
. 16.4,
(
).
, . .
,
,
.
. 16.4.
9
.
,
9
R
350
.
,
0 —
,
.
D,
.
,
,
,
?
*,
0*.
,
,
,
,
:
) —<0;
)
*( |=1;
\2)
) Iim0*(/)) = O.
/>!
[9]
) lim 9* (/>) = <*>;
/> >0
1—
8*(/>) =
,
.
,
,
.
.
,
,
.
,
,
.
.
.
1.
,
?
.
2.
.
,
351
.
3.
,
?
.
4.
,
D
z
[>=L(n, cf by}.
.
5.
,
.
?
D
,
0,8.
6.
:
,
?
7.
?
?
V
.,
1.
2
.
2.
3.
4.
May
.
.:
.,
. 2
.
.,
, 1997.
.
, 1998.
.,
., 1997.
.
. .,
.
6.
352
.:
. .
.
.:
,
.
5.
.,
.
My
:
.,
.
,
.
.:
, 1996.
. .
, 2000.
.
.:
, 1994.
7.
.,
.
.
.
, 1996.
. .,
. .
2.
. .:
, 1998.
Alesina A. Credibility and Policy Convergence in a Two Party
System with Rational Voters//The American Economic Review.
1988, Sept. Vol. 78,
4.
Alesina A. Macroeconomics and Politics//NBER. Macroeconomics
Annual. Cambridge: MIT Press, 1988.
Blanchard O., Fisher S. Lectures on Macroeconomics. Cambridge:
MIT Press, 1989.
Chiang A. Fundamental Methods of Mathematical Economics.
Third Edition. McGraw Hill, 1984.
Hicks J. A Contribution to the Theory of the Trade. 3 nd ed. Oxford
University Press, 1956.
Hibbs D. Political Parties and Macroeconomic Policy//American
Political Science Review. LXXI (Dec. 1977).
King R., Rebelo S. Resuscitating Real Business Cycles. — Ch. 14
in Handbook of Macroeconomics/Ed, by M. Woodford and
J. Taylor. Vol. IB. Elsevier Science B.V., 1999.
Kydland F., Prescott E. Time to Build an Aggregate Fluctuations//
Econometrica. 1982.
50.
Leslie D. Advanced Macroeconomics: Beyond IS—LM. McGrow
Hill, 1991.
McRae D. A Political Model of the Business Cycle//Journal of
Political Economy. 1977. April.
Metzler L. The Nature and Stability of Inventory Cycles. Reading
in Business Cycle Theory, Richard D. Irvin, Inc., Homewood, 1944.
Nelson C.R., Plosser C.I. Trends and Random Walks in Macro
economic Time Series: Some Evidence and Implications//Journal
of Monetary Economics. 1982. Sept.
Nordhaus W. Alternative Approaches to the Political Business Cycle//
Brookings Papers on Economic Activity. 1989.
2.
Plosser Understanding Real Business Cycle//Journal of Econo
mic Perspectives. 1989.
3 (summer).
Prescott E., Kydland F. The computational Experiment: An Econo
metric Tool//Journal of Economic Perspectives. 1996. Winter.
.:
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
353
24. Rogoff K., Sibert A. Equilibrium Political Business Cycles//Review
of Economic Studies. 1988. Vol. 55 (Jan.).
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University Press. N.Y., 1997.
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Principle of Acceleration//Reading in Business Cycle Theory,
Richard D. Irvin, Inc., Homewood, 1944.
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economics: an introduction to competing schools of thought.
Edward Elgar, Cambrige, Great Britain, 1999.
29. Turnovsky S. Methods of macroeconomic dynamics. The MIT
Press, 1995.
VI
,
.
.
,
.
,
.
,
,
.
,
—
,
.
.
17
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
,
,
,
,
.
—
.
—
.
357
,
.
,
,
.
,
.
.
,
.
,
,
,
,
.
,
[13].
,
.
ex post,
—
.
,
,
.
,
.
(
ex ante)
,
,
,
.
,
.
[12]
,
.
(time inconsistent),
358
,
,
,
,
.
ex ante
, . .
ex post.
(inflationary bias) —
,
.
[2,8]:
•
.
,
,
,
;
•
,
.
,
,
,
»,
«
,
.
,
[5—7, 14,15]
[12]
.
17.1.
,
,
,
.
/
= ( ,,
2
,
3
, ..., ,).
,
,
= ( {,
, xi, ..., ).
2
.
,
,
359
,
,
,
.
, . .
, = X{xv
2
,
3
, ..., x t _ v
,,
2
,
3
)
, ...,
(17.1)
V/, / (1, ).
(ex ante)
/,
(17.1)
U = U(xu x2, ..., ,_{,
,,
, ...,
7
).
(17.2)
(
ex post),
,,
{,
2,
, ..., ,_{,
3
(17.2).
,
:
max U = U(xv x2,
,,
2
)
(17.3)
2
x2=X2(xl,nl,n2).
,
2
,
^
{
,
(/
.
,
dU
dn2
360
=0.
(17.5)
dU =
dx, +
dx2
,
dx2+
dn,+
2
an2
ore,
=0.
(17.6)
,
, dxx = dnl = 0.
^
^
(17.5)
^
+
2
2
0
..
(17.7)
2
,
,
2
U(x{(nv
), X2(xv
,,
2
,
2
) , ,,
,
2
).
:
dU
,
dU
,
2
( ] 7 8 )
,
2
2
(17.8)
,
ex ante
ex post).
(
,
:
= + {
),
>0,
(17.9)
—
,
;
'
—
.
,
(14.1)
,
—
;
Y, Y —
(X > 0).
,
,
361
=)
+ ()
\
)
=1
+ b[()nP \nP_]) (\nPe P_l)]
=
= \nY+b(n ne),
/> = — >(), />_, —
.
.
(17.9).
17.2.
[12]
,
,
,
.
.
,
(17.9),
.
, . .:
\
a > 0,
(17.10)
.
,
*=0.
*=
,
> 1.
Z = {an2+\{y liyf.
(17.11)
,
.
,
.
,
.
362
= '.
(17.11)
(17.12)
(ex ante)
aZ\K,
(17.12)
(17.9)
(71)1
= Q
dn
. . .
.
..
'
( 1 7
1 3 )
\2
Z = 4<
*=
= 0.
(17.14)
' = 0,
,
— — °>
dz(n, n' = )
dn
+ ( + b(n
ky\b = 0.
)
ex post)
(
:
^
+
,
2
' + ^ £2
+
(17.15)
(17.15)
.
,
,
,
363
,
(17.16),
, . .
.
.
. 17.1
ex post)
(
.
,
,
ex post
.
..
. 17.1.
ex ante ( *)
( )
ex ante
,
(
)
.
—
.
,
,
.
17.3.
[15].
,
,
364
.
Z=\acn2+\{y ky)2,
>
> 0.
,
.
ex post
, . .
h = f(ne}
(17.15) (
. 17.2).
'•
=/{ )
. 17.2.
<
,
:
~] )
= 71 =
7
ni
'
(I /. 10 )
.
,
,
.
.
,
,
:
.
,
,
.
365
,
[10],
,
,
.
[10],
= / ,
(17.9)
,
.
< 1.
(17.9')
(17.11)
(17.9')
,
:
=
1
_
)
( 1 ? | 7 )
,
.
(17.17)
,
.
,
,
< 1.
£
— <—.
,
.
.
[15]
,
,
,
.
,
.
.
,
,
.
366
(
17.5).
17.4.
,
.
,
,
,
,
,
.
.
17.4.1.
,
[7,5],
.
,
Z=I8,z(1
0<5,<l,
(17.18)
/=i
8, —
,
.
(17.10, 17.11)
, . .
:
=la^ (y, y).
(17.19)
Zl
,
,
*,=1< ?
,
(17.9).
/
( ,
?).
(17.20)
.
]
,
.
,
,
(17.18).
367
.
{\
. — b = 0,
, = —.
,
. = , =—.
,
,
,
2
.
z, = — •
1
,
.
,
1
; = ,.
,
zt = ^
^.
, z] =0.
* = ^' = 0,
,
.
,
.
,
^'=0
,
.
z, =\cm]
(17.20)
bit,.
2
,= ;
,
*,= —.
2
:
368
,
. 17.1,
,
.
,
.
17.1
—
, '
,z
'=
71* = 0
* =0
.
2
.
b
=—
b
=—
b2
.
'=
Z=
~Ya
,
.
[7]
,
.
,
,
.
[5,7]
,
:
1)
2)
,
;
{trigger strategy)
,
.
[7]
* = <—
:
1
,
7 =71,
(17.21)
= —,
:
369
=
/
t+ 1
'+] = — .
b2
• 71
/+ 2
t+ 1
= ,
.
,
,
S(n).
( )
,
,
,
(z* z,)<
2\
(17.22)
•7
0 <8 < 1—
,
.
1
1+8
^ 7
'"»2) 7
(17.23)
,
,
.
370
(17.24)
=—,
,
.
,
,
,
.
. 17.3
(
),
.
,
.
S(K)
1+8
{ )
. 17.3.
=
,
,
1 5
_
1 + S'e
,
,
.
,
.
,
.
=
— \=S — =0.
\)
\)
,
,
,
.
371
17.4.2.
[4,7].
,
,
.
,
,
,
.
—
—
,
—
—
.
:
,
,
*.
,
.
,
.
.
t
S{t) = \z*, z,)= — ,
4
'
la
( / + /), / = 1, 2, 3, ...
1 5 ' | = !—-£-.
,=i
,
2
2
1 5
5>
.
.
372
,
(17.25)
,
'
.
(5< ),
.
17.4.3.
[5, 16,],
,
.
—
—
[1IJ,
[5, 8, 16].
.
,
,
W,= \cm]+b{nt
<);
(17.26)
,
,
:
1—
,
0
,
2 —
,
,
;
,
,
:
b = 0.
* = 0, . .
,
,
(
(1 — ) —
,
.
,
,
.
1),
,
,
373
.
,
.
:
,
q
(1 — q) —
= —.
.
,
.
,
%'=—
,
(17.26),
b
= —.
,
.
,
,
'2
,
—.
= ^ (1 5)
2
(17 27)
.
.
,
,
( ),
374
2 ( ).
,
.
:
( / = 0) =
( = 0/ )
( )
.,_...
( = / ) • Prob{C) + Prob(n = / ) • Prob(H)'
( ),
.
—
,
,
—
.
,
,
,
(17.29)
1+]
—
.
,
(17.29)
,
:
l)<o.
)
,
.
(17 30)
:
'2=
nl<b .
"
pq + {\ p) a
a
,
,
:
,
,
.
(17.31)
q:
«
»
(
(17.31))
.
q= ,
,
,
q = 1.
—
, . .
,
,
.
.
1.
q
:
WINF>
).
(17.32)
,
1
,
, . .
.
q=0
,
(17.32)
5< , . .
.
,
.
2.
,
. .
q=\.
,
:
WlNF<
,
W{\).
(17.33)
8> —
.
2(1 — /')
,
,
,
1
.
,
.
376
3.
W{\) < W,NF< W(Q),
,
—
.
<8<
!
.
2
2(1 / 1)
(17.34)
,
,
, . .
,
.
1—
= ——(25 — 1)
(17.34).
,
.
,
,
.
,
.
,
.
.
,
16.
,
,
.
,
,
(
).
,
.
5.
377
17.5.
17.2,
,
,
,
.
[10]
,
,
—
.
,
,
,
,
,
.
.
,
.
,
S.
,
R,
S
.
,
SH
,
.
(
R
S:
)
,
.
,
(R, S)
.
,
.
. 17.4
,
,
.
.
378
,
;
,
.
. 17.4.
. 17.4.
,
( /).
,
,
F:
,
,
,
,
.
,
(N),
.
,
,
,
.
FN.
,
.
,
,
,
.
379
,
1990
.,
.
.
,
, . .
.
2,8%
,
.
,
.
1997 .,
,
,
,
.
.
,
,
.
,
.
—
—
.
.
,
,
,
,
,
.
,
,
.
,
,
,
—
.
,
1990
.
,
[9].
,
[18]
«
380
—
»
12
.
,
.
.
,
.
.
1.
—
,
*.
.
.
.
2.
—
.
.
.
3.
—
,
z, = \
2
+\(
)2.
4.
—
,
,
.
5.
,
.
6.
,
381
,
.
VI
.,
, 1997.
. .
1.
2.
3.
.:
.,
, 1996.
.
.
.
.
.:
.:
,
, 1994.
.
.
4.
Alesina A. Credibility and policy convergence in a two party system
with rational voters//The American Economic Review. 1988. Sept.
Vol. 78.
4.
5.
Backus D., DrifflllJ. Inflation and Reputation//American Economic
Review. 1985.
75. June.
Barro R. Reputation in a Model of Monetary Policy with Incomplete
Information//Journal of Monetary Economics. 1986.
17.
6.
7.
Barro R., Gordon D. Rules, Discretion and Reputation in a Model
of Monetary Policy//Journal of Monetary Economics. 1983.
12.
8.
Blanchard O., Fisher S. Lectures on Macroeconomics. Cambridge:
MIT Press, 1989.
9.
Fisher S. Central Bank Independence and the sacrifice ratio//Open
Economy Review. 1996. Vol. 7.
10. Hall S., Henry ., Nixon J. Central Bank Independence and
Co ordinating Monetary and Fiscal Policy//Economic Outlook.
1999. February.
11. Kreps D., Wilson R. Reputation and Imperfect Competition//
Journal of Economic Theory. 1982. Vol. 27.
12. Kydland F., Prescott E. Rules Rather than Discretion: The
Inconsistency of Optimal Plans//Journal of Political Economy.
1977. Vol. 87.
13. Lucas R. Econometric Policy Evaluation: A Critique//Studies in
Business Cycle Theory. Cambridge, Mass.: MIT Press, 1981.
14. Persson M., Persson ., Svensson L. Time Consistency and Monetary
Policy//Econometrica. 1988.
55.
382
15. Rogoff K. The Optimal Degree of Commitment to an Intermediate
Monetary Target//Quarterly Journal of Economics. 1985.
100
(November).
16. Romer D. Advanced Macroeconomics. McGrow Hill, 1996.
17. Turnovsky S. Methods of macroeconomic dynamics. The MIT
Press, 1995.
18. Walsh
Optimal Contracts for Central Bankers//American
Economic Review. 1995. Vol. 85.
1
1. )
,
,
.
)
,
.
)
,
,
.
2.
,
,
.
,
.
3. )
;
;
;
)
)
)
,
;
)
.
4. a) Y = 600,
= 400, / = 120, NFI = NX = 30, = 2, = 3,
£.,= 100, Sroc = 50, Smn = 150.
) = 600, = 435, / = 120, NFI = NX = 5 , = 2, , = 3,7,
S,,= 1 1 5 , ^ = 0, 5 = 115.
35,
• AT.
5. a) Y= 640, = 350, / = 120, NX = 30, = 3, = 6.
) = 640, = 350, / = 130, NX= 20, = 3, = 8.
) Y= 640,
= 350, / = 100, NX = 50, = 5, = 2.
)
384
=
640,
= 350, / =
120, NX=
30, =
3,
=
10.
7. )
,
.
,
,
,
,
.
)
;
,
.
,
,
,
.
10. )
,
,
.
)
,
.
2
1. ) = 1000,
= 700, S4 = 100, Sroc = 0, SHan = 100, / =
NFI = NX = 10, r= 2, er= 3;
) Y, C, S4 —
, AS
. = ASltlLll = 20, / =
ANFI = ANX = 8 , Ar = 0,4, Aer = 2,7;
) AT= 25, AC = 20, AS4 = 5, ASroc = 25;
r) Y = 1000,
= 700, S4 = 100, Sroc = 0, 5" = 100, / =
NFI = NX = 4, r = 2,3, £r = 5;
) Y = 1000,
= 700, 5 = 100, 5 r o c = 0, 5„ = 100, / =
NF/= NX= 16, /•= 2,2, e r = 1;
) Y = 1000,
= 700, S4 = 100, Sroc = 0, SHm = 100, / =
NFI= NX= 10, r= 2, er= 5.
3. )
; )
; )
,
; )
2,
96,
84,
90,
.
.
«— »
4. )
90,
,
,
,
,
.
)
,
,
,
,
.
385
5. )
,
,
.
)
,
,
,
.
)
,
,
,
.
)
,
,
)
,
.
,
,
.
)
,
,
,
,
.
6. )
,
,
.
)
,
,
7.
)
.
;
,
,
,
.
.
)
;
,
,
,
.
.
8. )
,
,
,
,
.
)
,
,
;
.
9. a) IS: Y= 1800
120/ ; LM: Y= 1000 + 80 ;
)
= 1320; * = 4;
= 160; NFf = 20; $.* = 2,6; NX* = 20;
) Y* = 1480;
) Y* = 1440.
386
)
= 1400.
) KH* = 1600.
)
.
„ dY
I
3 ~ ^ = ;—7 >
dY
b
"7^ = ;—
„
/
.
4. a) IS: Y= 1800
200er;
LM: Y= 2(M/P) + 400.
) * = 1400, /* = 150, e* = 2,
* = 50, M* = 500.
) Y= 1700
+ AG
100 .
) Y* = 1800.
) YH* = 1400, M* = 500.
)
.
dY__
1_
dY
387
1,27*+ 1,6(7+ \,2 / .
6. a) Y = 720
) Y* = 1480.
) Y* = 1440.
)
,
,
.
,
,
.
4
1.
.
2.
.
3. )
,
7. ) 150, 90, 66;
)
)
)
.
=
2
=
.
1: 40, 50, 10.
.
2:
1: 40, 40, 0;
—
, 55,
2: —
, —44, —66.
.
)
88.
70,
2: 120,
1: 30, 50, 20;
—
388
55.
.
54,
66.
5
3. 182
.
4. )
0,6%;
)
1%.
5. 1,2%
6. ) 2%; )
7.
1%; ) 4%; ) 3%.
.
8.
=6,4%.
,
4,4%.
6
1. ) =232,2
2.
2 . .
3.
.
.; ) =177
.
=9,8%.
4.
.
5. =1,6%.
6.
.
.
7
4. =17%; 1/(6 ).
5. 50%.
6.
.
7.
.
8
1. )
,
2.
;
D
;
3%.
.
\na
389
9
1. ) g; 0; )
; )
.
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3. (1
4. 5,6%; 12,5
.
7.
1
10. 3,5%.
10
i
1. )
[
2. ) /4[
>
>
+(1 />) ]
l
;
)
\_
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+ (1 / ) ] >; )
l
«>; ) sAb* ( + 5).
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*.
5. 0,48.
9. 2,5%; 2,5%; 2,5%.
11
1.
.
2. 11%.
3.
;
) —=
)
.
4. )
7.
390
,
; )
,
,
.
; )
,
.
12
l
a)
^ = ( 9 ( i + .)(l + g ) ) 2 ;
|/3
(0,037) ;
)
)
°' 105 '
(0
'
5)1/3;
)
°'
1/3.
13
1.
.
2.
.
3.
.
4.
5.
)
.
) 1600; ) Y = 1600
,
; )
.
500(0,5)' + 200(0,25)';
2
= 1487,5;
14
1. a) * = 400; NX* = 50; $* = 1,5; = 1; * = 1,5;
) = 700 300
) Y, = ,_, + 3AG 300P,_xnt;
) , = 0,1; , = 520; 2 = 0,157; Y2 = 468.
2. a) Y* = 400; AW* = 133,3; * = 6,67;
y 2
+m
+2
•) = {f) '
)
* = 1,5;
i) '= ' " ( ") " "" ):
, = 0,1; , = 480;
2
=0,15;
2
= 439,3.
15
1. )
= 900 Vr;
2.
= 5181,82;
)
)
)
) 4; 400; 1800; ) 9; 900; 2700.
= 3,636; L = 107,4; W/P = 24,12;
= 5272,73; = 5,455; L = 111,21;
/3 = 23,71;
,
;
)
= 0,9649,
= 0,9483;
£—
/= 1017,54.
391
3. Y= 5416,29; r= 3,167; L = 106,44; W/P = 25,44;
,
L—
= 5275,86;
4.
= 3,448; L = 111,34;
,
.
.
/> = 23,69;
16
1.
3.
5.
.
.
,
,
= 0,8.
17
1.
,
,2
i
*
D
*
=
a>0;
/ *
_\
l
)
b I *
\
=71 + — V + V .
>
3.
:
4.
,
)
)
:
—;
(
= 0,5).
5
I.
1.
11
1.1.
12
13
15
1.1.1.
1.1.2.
1.1.3.
,
16
16
17
22
24
28
1.1.4.
1.2.
1.2.1.
1.2.2.
1
2.
32
2.1.
(
)
33
2.1.1.
34
2.2.
(
2.2.1.
2.2.2.
)
42
45
49
.
2
53
3.
3.1.
3.2.
58
59
60
3.3.
63
393
3.4.
71
3.4.1.
72
3.4.2.
74
3.4.3.
75
76
78
3
I
II.
4.
83
84
87
4.1.
4.2.
4.2.1.
4.2.2.
4.2.3.
87
88
92
95
4
5.
98
5.1.
98
5.1.1.
99
5.1.2.
(
)
99
5.1.3.
101
5.1.4.
102
5.1.5.
:
103
5.2.
106
5.2.1.
106
5.2.2.
,
110
5.2.3.
5
394
114
117
6.
119
121
6.1.
6.2.
,
124
6.2.1.
127
6.2.2.
129
6.2.3.
(
)
132
6.3.
133
134
6.4.
6
136
II
138
III.
7.
143
7.1.
143
7.2.
146
149
7.2.1.
7.3.
«
»
153
7
154
8.
8.1.
8.2.
.
8.3.
.
156
157
159
164
8.4.
8.5.
169
171
—
8
III
177
179
395
IV.
9.
9.1.
9.2.
9.3.
9.4.
185
187
190
191
.
.
195
9.5.
197
199
9.6.
9
203
10.
10.1.
10.2.
10.3.
206
/
208
213
,
216
217
221
223
225
10.3.1.
10.3.2.
10.3.3.
10
11.
11.1.
11.2.
11.3.
11.4.
11.5.
11.6.
11.7.
11.7.1.
228
228
233
234
235
237
239
241
.
11.8.
11.9.
11
12.
12.1.
12.2.
12.3.
396
—
242
—
245
247
.
250
252
253
254
257
12.4.
.
262
12.4.1.
12.4.2.
263
264
266
268
271
12.4.3.
12.5.
12
.
IV
272
V.
13.
:
279
13.1.
—
.... 280
13.2.
284
13
290
14.
292
14.1.
294
14.2.
296
14.2.1.
299
14.2.2.
300
14.3.
303
14.3.1.
304
14
15.
15.1.
15.2.
306
:
309
310
312
15.2.1.
313
397
15.2.2.
317
15.3.
«
—
»
15.3.1.
15.3.2.
319
321
322
15.4.
324
327
15.5.
15.6.
328
15
16.
16.1.
332
335
16.2.
16.3.
16.3.1.
16.3.2.
16.3.3.
16
V
336
338
343
343
345
348
351
352
VI.
17.
17.1.
17.2.
17.3.
17.4.
357
359
362
364
—
367
367
17.4.1.
17.4.2.
372
373
17.4.3.
17.5.
17
VI
398
378
381
382
384
1
384
2
385
3
387
4
388
5
389
6
389
7
389
8
389
9
390
10
390
11
390
12
391
13
391
391
15
391
16
392
17
392
. .
.
070824
. .
21.01.93.
15.12.2003.
25.05.2004.
60 90/|6.
.
Newton.
.
.
. . 25,0.
.
. . 22,2.
30 000
. (1 5000
.).
4404058.
«
»
127214,
,
, 107.
.: (095) 485 71 77.
: (095) 485 53 18.
E mail: books@infra m.ru
http://www.infra m.ru
«
603006,
».
,
ISBN 5 1
9 "7 8
.
001
, 32.
4
8641