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



that is always true (since it must be ξ>1). We then have:

μ 2y2 ,,
- ∖∂Td∂n J >


2π   ∂2π

H2 > 0 ⇒ —- ∙ -----2

∂n2 ∂ (Td)2

that implies:

α (α - 1) A (1 - ρ)1-α (hL)1(Td)1 α nα-2 - ξ(ξ1)(1—ρ^pnξ-2

(1 - α) A (1 - ρ)1-α (hL)1-α (Tdyα-1 nα] +

- α (1 - α) A (1 - ρ)1-α (hL)1-α (Td) nα-1i 2 > 0

that leads to:

α (1 - α) ξ (ξ - 1) A (1 - ρ)1-α+θ ρη (hL)1-α (Td¢ -α-1 nα+ξ-2 > 0

that is always true (since ξ>1). We finally have:

H3 < 0 det H<0

that can be checked during the simulations (because it is not possible to obtain an
analytic solution for this inequality). In this case the second-order conditions of the
problem of the firm are satisfied and the value found is effectively a maximum.

7.2 Steady-state in the decentralized economy

The steady-state of the decentralized economy is obtained considering all the quan-
tities constant in the first-order conditions of the problem of the firm and of the
household and in the market equilibrium conditions, that is:

αA (hTdL} 1 α (1 - ρ)1-α nα = ∣nξ (1 - ρ)θ ρη               (23)

(1 -α)A hTdL (1 - ρ)1-α nα =w


(1 - α) A (hTdL¢1 α (1 - ρ)1-α nα


= ndξ (1 - ρ)θ ρη P -


η (1 - ρ)
ρ


1β

- = -(1 + r)

cc


h          _ βδ (1 - Ts)

(1 - δ) Ehδ (1 - Ts)-δ =    1 - δ


c = whTs + ra


h= Ehδ(1-Ts)1-δ


(24)

(25)

(26)

(27)

(28)

(29)


29




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