исследование динамики макроэкономического кругооборота

реклама
ɂɋɋɅȿȾɈȼȺɇɂȿ ȾɂɇȺɆɂɄɂ ɆȺɄɊɈɗɄɈɇɈɆɂɑȿɋɄɈȽɈ ɄɊɍȽɈɈȻɈɊɈɌȺ
ɎɂɇȺɇɋɈȼɕɏ ɉɈɌɈɄɈȼ ɋ ɍɑȿɌɈɆ ȼɁȺɂɆɈɋȼəɁȺɇɇɈȽɈ
ɎɍɇɄɐɂɈɇɂɊɈȼȺɇɂə ɊɕɇɄɈȼ ȻɅȺȽ, ɌɊɍȾȺ ɂ ȾȿɇȿȽ
Ȼ.Ƚ. ɂɥɶɹɫɨɜ, ɂ.ȼ. Ⱦɟɝɬɹɪɟɜɚ, ȿ.Ⱥ. Ɇɚɤɚɪɨɜɚ, Ⱥ.ɇ. ɉɚɜɥɨɜɚ, Ɍ.Ⱥ. Ʉɚɪɬɚɲɟɜɚ
6! 450000, 6!, . . 2, 12, %
[email protected], [email protected]
: +7 (347) 273-78-35, !: +7 (347) 273-78-35
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɦɚɤɪɨɷɤɨɧɨɦɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ, ɪɵɧɨɱɧɵɣ ɦɟɯɚɧɢɡɦ, ɤɪɭɝɨɨɛɨɪɨɬ ɮɢɧɚɧɫɨɜɵɯ ɩɨɬɨɤɨɜ, ɤɨɝɧɢɬɢɜɧɚɹ ɦɨɞɟɥɶ, ɞɢɧɚɦɢɱɟɫɤɚɹ ɦɨɞɟɥɶ
Abstract
The cognitive model of the macroeconomic system functioning regarding goods, labor and
money markets is presented. This article shows the characteristics of the dynamics of interaction
of macroeconomic goods, labor and money markets. The dynamic model of money market
functioning shows the dynamics of the interest rate formation. The results of experimental research of the controlled and uncontrolled scenarios considering behaviour of the macroeconomic
system are discussed.
ȼɜɟɞɟɧɢɟ
% ! - .
! [1-3]. 7 ! , . %#
! (2<() , ! !
" , . % !- ! 2<( .
1 Ʉɨɝɧɢɬɢɜɧɚɹ ɦɨɞɟɥɶ ɦɚɤɪɨɷɤɨɧɨɦɢɱɟɫɤɨɝɨ ɤɪɭɝɨɨɛɨɪɨɬɚ ɮɢɧɚɧɫɨɜɵɯ ɩɨɬɨɤɨɜ
Ɇɗɋ ɫ ɭɱɟɬɨɦ ɪɵɧɤɨɜ ɛɥɚɝ, ɬɪɭɞɚ ɢ ɞɟɧɟɝ
!
2<( : (2<&), : (!
), (), !
, , (. 1). ( !
(#
); !
(#
); (#
).
131
% - , -
, , " ! , " «»; -
, , " «»; -, , !
" «-» [4]. + !
, ! !, " . % , " , ! !
, " 2<( " .
% , " , ! ! " !, " .
Ib ,
I,
S ,
Ms ,
Yinc
Yinc ,
R e v
E x ,
Tp ,
A sun
1
Md ,
Tr
,
,
T
,
Nd
,
w,
Em
2
2
P
A s ,
,
e
Ad
Tr ,
Im,
R l ,
P g 12 ,
,
A d
( Yexp ,
Md ,
P g 11 ,
P,
Ns ,
0
W
,
U,
G ,
C ,
% 1 – !
2<( $ !
,
" 2<(, " .
-
, , . -
132
, . ( )
.
-
, " ,
" , . , "
!
.
-, " , . + «#» [5].
( , ; . A d A s , A d ɮɢɧɚɧɫɨɜɵɦ ɩɨɬɨɤɨɦ -
, " , A s ɦɚɬɟɪɢɚɥɶɧɵɦ ɩɨɬɨɤɨɦ, , ! # . %
Nd Ns , !
. 9 Md Ms " , Nd Ns !
, , # . , , «
» , ! ! " .
2 Ɏɭɧɤɰɢɨɧɚɥɶɧɵɟ ɫɯɟɦɵ ɞɢɧɚɦɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ ɦɚɤɪɨɷɤɨɧɨɦɢɱɟɫɤɨɝɨ ɤɪɭɝɨɨɛɨɪɨɬɚ ɮɢɧɚɧɫɨɜɵɯ ɩɨɬɨɤɨɜ Ɇɗɋ ɫ ɭɱɟɬɨɦ ɪɵɧɤɨɜ ɛɥɚɝ, ɬɪɭɞɚ ɢ ɞɟɧɟɝ
' ! 2<( (. 2). ' : Ⱥ1-Ⱥ4 ! Ⱥ5-Ⱥ7 ! , . ( !
,
!
.
2 Ⱥ1 ! , " !
: + Y Y 0 ; + (+
Yinc ) ! R l !
Tp ! P g , 12
! ; ! A s ,28 Y 0 inv ; ! " Ib 0
I11
I ; 133
R e v -
A sun . * " Ⱥ1
! , . , " Pdyn dW . +, " !! krlc.
A s
Ib
C
X
n
P0
G
Y 0
Ib10
Yinv0
R e v
A sun
Pdyn
kad
Nd
dW
R e v
A sun
Pdyn
kad
A d
P
A d e
k rlc
I
Tr1
A s
Ib
St1
R l
P g12
Y
Y
k rlc
Un
W0
Un0
NΣ
R l
P g12
St2
Tr2
T2
S
Pdyn
Tp
Tp
Nd
dW
C
Sa
inc
T2
P
A d e
C a
G 0
k ad
Tr1
Tr2
St4
G
S
k ad
Y
inc
Yinc
Md
P
MS 0
r0
St3
I
r r
% 2 – 9 ! 2<(
, 2 Ⱥ2 ! , R l P g12 ! ɋ , S T . +
!2
:
ɋ a , S a . * Ⱥ2 : -
, ! ɋ a0 ! " Pdyn; -
, ! "
!! kad, !.
2 Ⱥ3 ! !
, S ! I 0 ! I , a
134
. * Ⱥ3 " Yinc " r ! I .
2 Ⱥ4 ! , ! Tp T2 G ! Tr Tr .
1
2
2 Ⱥ5 ! , -
, ! " P P0 " Pdyn; , -
, " !! kad, ! kas, . * Ⱥ5 !! A d e 2<( , Nd.
2 Ⱥ6 ! " N, Un, " !! krlc dW. ! : Ns, " ; " P, " " Nd; !!
A d e , " ! . ' 2<( ! W0 Un0. * " ( ) .
2 Ⱥ7 ! ! " Ms, " P " Yinc , " Md. 9 " r
! r0(t) " rdyn. ( r ! . + ! .
3 Ɉɫɨɛɟɧɧɨɫɬɢ ɩɨɫɬɪɨɟɧɢɹ ɞɢɧɚɦɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɞɟɧɟɝ
2 ! [6]. ! "" ! 2<( [7].
+ , r, , () ". ( " !, " # . " rdyn "
() r 0 # , . %"
2<&, !" , , . + 135
! , " , " rdyn .
(!
" ! , 2<(.
-
, " !, 2<( " . * ! 7 # - .
-
, ! ! r Md MS .
-, " !, 2<( ! .
% ! ! Md , 1
, !, # .
, ! Md: , [8].
( 1 # .
< , Yinc ( +). +1 , " .
, 1
, " Yinc . + (
Yinc ), 1 − .
(
# 1 ! ! !
. 3 ,
, , - !
, " . + r . 5 # r,
# , , # Md.
( " , , r.
' # ,
! !:
(1) Md = k ⋅ Y − k ∗ r ,
my
inc
md
kmy kmd – !!
, " Md . + (1) 136
", !
2<&.
% ! ! !! , " Md, Ms r.
' " , !, 7
. ( ! .
( , . ( , ! ! , , , !. ( , "
7 !, , #
. & , !, – . $ , " r0 # . " rdyn .
+ 2<( ( &) r0 Ms0, :
Md=Ms=Ms0 (. 3).
k md
% 3 – 8 Md(r) Ms(r)
% ( B), r ′ ΔMd ! ΔMd r , ! ΔMd nr (" Md Md ′ )
' ( [5] # !! , "
( Ⱥ′ ):
(2)
(3)
d ( r 0 + rdyn )
= k r [ Md ( rdyn , t ) − Ms(t )] .
dt
," ! " :
Md (t ) = Md 0 − k md ⋅ rdyn (t ) + ΔMd nr (t ) .
137
" ( −k md ⋅ rdyn ) !
(1); " ( kmy ⋅ Y ) ! ΔMd nr (t ) .
! ! ".
+, ! 7
, MS. " P Ms !:
MS MS 0 ΔMS nr
=
+
= Ms 0 + ΔMsnr .
P
P
P
6 .
( (3) ! (2), :
Ms =
(4)
drdyn
dt
drdyn
dt
′ ) − Ms] ,
= k r [( Md 0 − k md ⋅ rdyn + k my ⋅ Yinc + ΔMd nr
= k r ⋅ ε r ( rdyn (t )) , kr - !!, " -
; ! Ms = Ms 0 + ΔMs nr . $
ΔMS # . , # .
Md # Ms (4) :
(5)
drdyn
1
1
⋅
+ rdyn =
⋅ ε nr ,
k r ⋅ k md
dt
k md
′ + k my Yinc − ΔMs nr − ε nr = ΔMd nr − ΔMs nr = ΔMd nr
, !. 6 (5) !!
k tr
1
! wmr =
, !! k tr k tr =
, τ mr s + 1
k md
τ mr τ mr =
1
.
k r ⋅ k md
!! ρ r , !! k tr , ρ r = kmd . < !! , # .
( A6 ! 4. ' , !" Md " . + MS , . $
138
! " Δr 0 , !, .
ΔMd r
ΔMd nr
Yinc
Md 0
Md
'
ΔMd nr
εr
MS 0 ∗
÷
P
Ms 0
ΔMsnr
rdyn
rdyn
r0
Δr
Ms
r
0
ΔMSnr ÷∗
% 4 – ( Ⱥ6 ! 4 ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɞɢɧɚɦɢɤɢ ɦɚɤɪɨɷɤɨɧɨɦɢɱɟɫɤɨɝɨ ɤɪɭɝɨɨɛɨɪɨɬɚ ɮɢɧɚɧɫɨɜɵɯ ɩɨɬɨɤɨɜ ɜ ɧɟɪɚɜɧɨɜɟɫɧɵɯ ɭɫɥɨɜɢɹɯ ɪɵɧɤɨɜ ɛɥɚɝ, ɬɪɭɞɚ ɢ ɞɟɧɟɝ
+
! 2<( . ' 5 .
1 () " , ! A s 0 (t ) = 10 ; ! C 0 (t ) = 2 ; S (t ) = 1,5 ; a
a
Ia0 (t ) = 0,5 ; ! G 0 (t ) = 3 . + + " !! !: k rl = 0,4 , k pg = 0,4 ; k t = 0,2 . 8 . + 90 .
2 () " ,
" . ( 2 " t=25 ! Ia0 (t ) . , # " !, . ( 1 , !! # 1 . . + P(t), # Tsum(t). St1, St2 St4. *, !
St3, , . + # # # - .
139
% 5 – .! ! , , !
, 3 () «#
» # " ΔMS (t )
( ) t=30. 7
; : , , . % !! . ' #, . , + .
140
6 " r(t), .. # , , . < I(t ) . % , C (t ) S (t ) # . 8 P(t), Tsum(t ) . St1, St2 St3. + , , # , A s(t ) , +
Y (t ) !.
Ɂɚɤɥɸɱɟɧɢɟ
% !
2<( , , " , " !
. %
, " , - , , ! .
+ ! ! 2<( , , " ! , . % ! " , .
%
, # - , , " +.
ɋɩɢɫɨɤ ɥɢɬɟɪɚɬɭɪɵ
[1] + &.&., + $... 2 %. // % . – 2009. – , 79, :6. – (. 492-506.
[2] 2 ./., ; &.%., (# (.(. + . — 2.: '
, 2007. – 304 .
[3] $ ., 6 2. %: // +
. – 2008. – : 3. – (. 12-25.
[4] $ ;..., $.., 2 -.&., . <.%. 2 !
!
// !
. – 2009. - :1 (61). - (. 28-38.
[5] , /.(., . +.$., / &.$. 2 : . 2.: # , 4-$, 2009. – 654 .
[6] 2 .-. . - 2.: ', 2008.– 221 .
[7] $ ;..., $.., 2 -.&., + &.'. 2 // +
: ,
XII 2 ! – (: (
%&', 2010. – (. 176-186.
[8] (" &.(. 2 – (+.: «$ «+», 2005. – 448.
141
Скачать