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

From (21) we have:

∂c
∂E

^ξ⁽¹^-^a⁾

⁽¹^-^δ) (^ξ^-^α)

a ¢(1 — a)

∕dd∖ ~ _л ξ ¢(1-a) _1 ¢(1-") ∕β (1 — δ)(1 — βδ)∖ —

— A■ E (¹-^δ)(ξ-a) ¹L ^ξ ------—----'

U J к (1 + β — 2βδ)² J

• ⁽^a (^ξ⁺^θ) ^-^ξ)

g(ξ+ff)-ξ

αη

(αη)^a^- (α (ξ + η + θ) - ξ)

^α(^ξ+η+^θ)^-^ξ

ξ-a

" ^a "

(αd∖ ^ξ^-^a

ξ ^a⁽l ^-^ξ) ⁺^δ(^ξ^-^a⁾ ¢(1-")

A^ξ^-^a E (¹^-^δX^ξ^-^a) L ^ξ^-^a

¢(1 —a)

^μ β (1 — δ) (1 - βδ) λ ^ξ a

I (1 + β — 2βδ)² )

"(¢ + 0) —ξ aη

^α(^ξ⁺n ⁺ θ)^-^ξ

• (α (ξ + θ) — ξ) ^a^-^ξ (αη)^a^-^ξ (α (ξ + η + θ) — ξ)

ξ-a

and then:

∂c
∂L

^ξ⁽¹ — ^a)^ξ — ^α------------------------------------- . -----------------------

" ^a ɪ

(αd∖ ^ξ^-^a

. ξ ξ(¹-a) ¢(1-a) _1

A^ξ^-^a E⁽¹^—^δ)(^ξ^-^a⁾ L ^ξ^-^a

(β (1 — δ)(1
I (1 + β — 2βδ)

¢(1-a)
∖ ¢-a

a(C+£2-€ aη "(¢+^ + 0) -¢

• (α (ξ + θ) — ξ) "- (αη)"- (α (ξ + П + θ) — ξ) ^,e" =

. ¢ ¢(1-a) "(W)

A¢-" E ⁽¹^-⁵⁾^^-^a⁾ L ¢-"

( β (1 — δ)(1 — βδ) ∖ ⅛"²

I (1 + β — 2βδ)² )

"(¢+0) -¢ aη a(€+n + ^)-€

• (α (ξ + θ) — ξ) ^a^- (αη)"^- (α (ξ + η + θ) — ξ) ^^a

and also:

∂c
∂A

^a ,∖ ɪ
α αd∖ ^¢-ɑ

. ⅞ _1 ^1-a) ⅞(1-a)

A^t' ^a E(¹^-≡^-^a) L ^t' ^a

8β (1 — δ) (1 — βδ)
I (1 + β — 2βδ)²

¢(1-a)
- - a

a(C+£)-C aη "^+п + ^) -¢

• (α (ξ + θ) — ξ) "^- (αη) "^- (α (ξ + η + θ) — ξ) ^"

a ^¢⁽¹^-^a⁾ ¢(1-")

A¢-" E⁽¹^-^δ⁾⁽^¢^-^a⁾ L ¢-"

ββ (1 — δ) (1
к (1 + β — 2βδ)

ъ¹

¢(1-")
ʌ ¢-"

"(¢ + 0) -¢ aη "(¢+^ + 0) -¢

• (α (ξ + θ) — ξ) "^- (αη) "^- (α (ξ + П + θ) — ξ) ^"

and finally:

∂c
∂d

-1

α _i ɪ .. ¢(¹-") _τ

—A ¢-" E x-'XW^-") L
ξ

¢(1-")
¢-"

^μβ (1 — δ) (1 — βδ) ∖ ⅛""²1 (1+ β — 2βδ)2 )

"(¢ + 0) -¢ aη

• (α (ξ + θ) — ξ) "^- (αη) "^- (α (ξ + П + θ) — ξ)

^ɑ⁽^¢⁺η⁺^θ⁾^-^¢

¢-"

2a-¢
α² α adʌ ^"
ё Ш

; ξ(¹-a) ξ(¹^-^a⁾

A¢-^a E (¹^-^δ)K-" L ¢-^a

∕β (1 — δ) (1 — βδ) ∖ ';^-"
к (1+ β — 2βδ)² )

"(¢ + 0) -¢ aη

• (α (ξ + θ) — ξ) "^- (αη) "^- (α (ξ + П + θ) — ξ)

^a⁽^¢⁺η⁺^θ⁾^-^¢

¢-"

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