Technological progress, organizational change and the size of the Human Resources Department



From (17) we get:


∂h

∂E = 1


E τ⅛
δ


1 β (1 - δ) = E ⅛β

1 + β - 2βδ       1 + β -

and also:


∂h
∂β


„1 (1 - δ) (1 + β - 2βδ) - β (1 - δ) (1 - 2δ)
E
1—0

(1 + β - 2βδ)2


■ 1 + β 2βδ δ βδ + 2βδ7 β + 2βδ + βδ 2βδ7
Ej 1 δ --------------------------------------------------------------------------------------------

(1 + β 2 ••■■■ 2

ι 1 δ

E I—0 -----------------

(1+ β 2βδ)2

and then:

∂h
∂δ


1 β (1 + β 2βδ) + 2β2 (1 — δ)
Ej 1—0 -------------------------------------------------------

(1 + β 2βδ)2


β(1 δ)     1     1

1 + β 2βδE—S (1 δ)2


log E =


E  β β2 + 2β2δ + 2β2 2δ + Eʌ        β        l σ E

(1 + β 2βδ)2       +     (1 δ)(1 + β 2βδ)lθg

1

E1-0


β2 β
(1+ β
2βδ)2


1


β

(1 δ)(1 + β 2βδ)


log E =


E 1⅛     ∣^ β (β 1)   , β

1 + β 2βδ [1 + β 2βδ + 1 δ

From (18) we have:

∂ρ = (α (ξ + η + θ) ξ) η αη (ξ + η + θ) =

^          (α (ξ + η + θ) ξ)2         ^

αξη + αη2 + αθη ξη αξη αη2 αθη           ξη

(a (ξ + η + θ) ξ)2                  (a (ξ + η + θ) ξ)2

and then:

∂ρ        -№пα                 α2η

  (α (ξ + η + θ) ξ)2     (α (ξ + η + θ) ξ)2

and also:

∂ρ oq1)           αη (1 α)

dξ   (a (ξ + η + θ) ξ)2   (a (ξ + η + θ) ξ)2

and finally:

∂ρ      (α (ξ + η + θ) ξ) ααη α

dη ~       (α (ξ + η + θ) ξ)2      "^

α2ξ + α2η + α2θ αξα2η     α [α (ξ + θ) ξ]

(a (ξ + η + θ) ξ)2        (a (ξ + η + θ) ξ)2

33



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