Модели производственно-технологического уровня

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  • . : f(x1,x2,,xn)=f(x1,x2,,xn) :F(K, L) =F(K,L): . (=1)

  • : K L:(11.1) (11.1) : = + L

  • : MYkK +MYLL = Y

    Y , , .

  • . 1 L =0.25 K=0.75. 200 . , 50. 10. .

    : . : Ak = Y/K = 200/50=4; AL = Y/L = 200/10 = 202. : MYK = KAK= 0.25*4 = 1; MYL= LAL=0.75*20 = 153. : MYKK = 1*50 = 50; MYLL = 15*10 = 150

  • .

    : .

    . : AY = Y(K, L )/Y = -1Y(K,L)

    . : MY = dY(K, L)/d = -1Y(K,L)

    . : = MY/AY =

    , : i =

  • >1 : .

  • (). , .

    K-L, .

    .

  • () : . : Du DL. Du , DL . . : K = q(L,Y) Y = Const .. Y = 10K0.25L0.75. .KL3 = (Y/10)4 K=(Y/10)4/L3 Y, K-L. .

  • (). Y = 10K0.25L0.75. .K = (Y/10)4L-3 Y, ., , . .KLY1Y2Y3

  • .. i- j- j- , i- . , , , , : dF/dxi*dxi + dF/dxj*dxj = 0 (11.1) i- j- :ij = -dxj/dxi =(dF/dxi) / dF/dxj) (11.2)

    . i- j- : ij =MYj/MYi = (i*xj)/(j*xi) (11.3)

  • K L (11.1) : dF(K,L)/dK*dK + dF(K,L)/DL*dL = 0 (11.4) : LK = - (dF(K,L)/dK) / (dF(K,L)/dL) (11.5)

    k = K/L - . LK = LK/KL = (L/K)k

    F(K,L)=AKL .: LK = (/)*k .

  • . k LK 1 . LK = (dk/k)/(dLK/LK) = (dk/dLK)(LK/k)

    k 1 .

    . LK .

  • - 5. (CES).

    (CES) 1961 . K L (CS) : F(K,L) = (c1K- + c2L-)-/ (11.6) : 1 2 ; = (1- LK)/ LK (11.6) LK1 LK0.

  • - 5. (CES).

    (CES): , , .

    , .

    , .

  • - 5. (CES).

    CES.1. -. lim(F(K,L)) = cKL- = cKL1-

    2. lim(F(K,L)) = min(K/a, L/b)

    3. lim(F(K,L)) = c1K + c2L=>1=>0=>

  • - Y=F(K,L) =CKL(1-) : . 1928 .

    - .

    :- ;- ( );- ;- .

  • -6.1. :6.2. :

  • -6.3. : -

  • -6.4. 6.5. -

  • -6.6. :K=(Y/C)1/L1- . .

    :LK=LK/KL=(1-)/*k 1.

    - .

  • - 7. .

    . , . =1 : F(K,L) = min(K/a, L/b)

  • - 7. L*=K*a/bLYLAYLY L*=Ka/b L .AYL= MYL L Ka/b, AYL , MYL=0LKK=aL/b

  • - 8. . , . :F(0,L)F(K,0)0; d2F/dk2=d2F/dL2=0; .LK . LK=b/aK=Y/a-bL/a