МОДЕЛЬ УСТОЙЧИВОГО ЭКОНОМИЧЕСКОГО РОСТА

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  • -

    14 CONTROL SC I ENCES 3 2007

    338(075.8)

    . .

    -

    XX . . - - . - , , . , , - . - - . - , , [1]. 1987 . , . , - , - [1]. , , ( -). (, ), . .

    , , - , - , - .

    1.

    [2, 3] - : . - , - . - -. . , - ( , ), - - . . - , . .; , -, , - .

    , - , , - .

    , - . - - (- ). , , , , , - . , - -

    , - : , . - - .

  • -

    15 3 2007

    . - - . - , . 1.

    Y , I -

    . , - Y + I.

    , , , . Y = Y(t), K = K(t) . .

    . (I ).

    Y = C + I + P, (1)

    C (, ), I , - - I2 I1, . .

    I = I1 + I2; , I = (s1 + s2)Y, I1 = s1Y1, I2 = s2Y2,

    Y2 Y1

    , , s = s1 + s

    2 -

    ; P -, P = s3Y, s3

    , s = s1 + s2 + s3 -

    C = (1 s)Y.

    t -

    L(t) = L0egt, (2)

    L0 t0, g

    , g m 0. K

    = I mK, K(0) = K0, m = const, (3)

    m , K0

    .

    - - K

    2

    K1, . . K = K1 + K2.

    :

    = I1 m1K1, K1(0) = K10, m1 = const,

    = I2 m2K2, K2(0) = K20, m2 = const,

    m1 m2 .

    - ( ). , - -. u , -.

    = Y2 uY + eP, K(0) = K0, (4)

    e ,0 m e m 1, e = 1.

    Y Y = f(K, L, Pr), K, L Pr, Pr , .

    , P = 0 (1)(4) - . , - , Y

    Y = AK L, - , t - [3]. -, - [2]., - - .

    2.

    , - , P > 0 , , . [3],

    Y Y = Y0(K/K0)(L/L0)

    1 , , -

    . 1. , :

    Y ; I ; K

    2 K

    1 -

    ;I1, I

    2, C P

    dKdt-------

    dK1

    dt----------

    dK2

    dt----------

    dK

    dt-----------

  • -

    16 CONTROL SC I ENCES 3 2007

    [3],

    C/L = (1 s)Y/L = E(1 s)s/(1 ),

    E = (Y0/L

    0)(Y

    0/((m + g)K

    0))/(1 ) = const.

    z(s) = (1 s)s /(1 ) = (1 s

    )(s

    s

    3)/(1 ),

    , - so = + s3(1 ).

    so< + s

    3(1 ), dz(s

    )/ds

    > 0, z(s

    )

    , so > + s3(1 ) . -

    , - -. s

    3 = 0,

    so = s, s =

    . s = s s3,

    ,

    s = (1 s3), s3 = (1 s/). (5)

    , P > 0 , . - .

    , (4) , -

    -

    - -, K

    eP l Y2 + uY. (6)

    d , u , . (7) es3Y l dY + uY, s3 l (d + u)/e.

    , , . -, , - , - - . , , - - 0,29 ( 20022005 .), e = 1, .

    , , , , - , . (5) (6) .

    3.

    , , : - , - , - .

    - , - .

    - (4) ( -), -. , - , , .

    , - . u K

    0, (4), .

    - ( , ), , - . , , (4) - . , - .

    , . , 1992 . ( ..) 71 200,8, 13 0,00256512 [4]. 2005 ., - (2), 68865,64883, 0,3 %, , -: ( 19901998 -, 1999 . ). , g , .

    - [5], , 1998 2003 . , [5] . [5] .

    - -, -, [4], ,

    dK

    dt----------- 0=

  • -

    17 3 2007

    , , [5], :

    Y = 1,09(K/L)0,47(Z/L)64,62L, (7)

    Y = 59,74(K/L)0,53(Z/L)1,1(X/L)0,068L, (8)

    Z , X ( , - ).

    , , , - . [4] (7) (8) 4 2 % . , , - , K

    t = K

    t 1 + 0,67Y

    t 1 0,038K

    t 1 579,27

    . - 1997 2003 . - 5 % (. ).

    - 9 %. 56 % 45 , . -, - , , . , -

    , 0,04, 15 - , - (. 2). , 0,5 %, - , - 40 2003 .

    - , , - . - , , , , - 0,3 % 4 % .

    - .

    . - - . , .

    1. : . .: , 1989.

    2. . . . .: , 2000. 861 .

    3. . . - . .: , 1997. 224 .

    4. 2004. . . /. ., 2004.

    5. . . - 19922003 . .

    e-mail: lax@tomsk.su

    . . .

    . 2. 4 %

    Y - (

    ) K

    L

    X

    - , . .

    Y, (8)

    1997 2343,0 13286,0 61,0 51,0 62879 2339,88 2470,3141998 2630,0 14126,0 64,6 175,0 61412 2604,09 2543,5471999 4823,0 14246,0 106,4 823,0 63964 5092,47 4928,3752000 7306,0 16605,0 147,3 1463,0 64327 7025,57 7014,4222001 8944,0 20241,0 199,2 1134,0 65124 8734,18 8672,6152002 10675,0 24431,0 259,6 1144,0 66266 10683,65 9995,5362003 12829,0 30556,0 339,0 1515,0 67152 13074,22 11101,02

    . Y, K, L X . ., 1998 . . . .