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

a ξ(1 —a)

_c = ^ξ-α (ad∖^a _a ξ-a E ^—^ L a⅛-a (/( (1 - ¹ - βS) ∖ ∙

ξ ∖ + J к (1+ β - 2βδ)² J

a(ξ+θ) — ξ aη a(ξ+η + θ) — ξ

• (α (ξ + θ) - )) ^a-ξ (dη)^a-ξ (α (ξ + η + θ) - )) ^ξ-a

Finally from (28) we obtain:

ɪ (c - whT)
r

^{a a} ɪ
d αd∖ ^ξ-a ₁ ξ

∖~ξ ) ^a^ξ^-^α

ξ(1 —a)

ξ(¹^-a) ξ(1-a) {β (1 - δ) (1 - βδ)∖ ^ξ-^a

E (1—δ)(ξ-a) L ■ ■ _2------LS----__

к (1 + β - 2βδ)² J

a(ξ + θ) — ξ aη a(ξ+η + θ) — ξ

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

. . fdd∖ — „ î a(1—ξ) a(1—ξ) ∕β (1 - δ) (1 - βδ) ∖ ~

- (1 - d) — A■a E (1—*)«—a) L ξ a ^------LS---J

к ) J к (1+ β - 2 2 J

ξ — a(ξ + θ) aη a(ξ+η + θ) — ξ

• (d () + θ) - )) ^î^—^a (dη)^a^—^ξ (d () + η + θ) - )) ^{ξ a} •

_pμ_τ∙ β (1 - δ) 1 - βδ 1

• Ej 1 O •

1 + β - 2βδ 1 + в - 2вд_

a ξ(1

в )ζ - d_{τ 1} A fdd∖ ¢^^ ,, î(1— a) . a(1—¢) ββ (1 - δ)(1 - βδ)λ ~

a =1-e ∖iτ ^{- + d}JuJ ^{î—a (1}"^)(î~^a)^î—a к (1 + - - 2βδ)² J

ξ —a(ξ + θ) aη a(ξ+η + θ) —ξ

• (d () + θ) - )) ^î^—^a (dη)^a^—^ξ (d () + η + θ) - )) ^î^—^a

7.3 Comparative statics in the decentralized economy

The comparative statics of the model in the decentralized economy can be obtained
from equations (15)-(22). In particular, from (15) we have:

dr -β - 1 + β 1
dβ = β² = - β²

From (16) we then have:

∂T _ -δ (1 + β - 2βδ) - (1 - βδ)(1 - 2δ) _ -δ - βδ + 2βδ² - 1 + 2δ + βδ - 2βδ²∂β = (1 + β - 2βδ)² = (1 + β - 2βδ)²

_ δ - 1

= (1 + β - 2βδ)²

and also:

∂T _ -β (1 + β - 2βδ) + 2β (1 - βδ) _ -β - β² + 2β²δ + 2β - 2β²δ

∂δ = (1 + β - 2βδ)² = (1 + β - 2βδ)²

= β - β² = β (1 - β)

(1 + β - 2βδ)² (1 + β - 2βδ)²