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:

∂²π   ∂²π

H2 > 0 ⇒ —^-∙ ∙ -----2

∂n² ∂ (T^d)²

that implies:

α (α - 1) A (1 - ρ)¹-^α (hL)1^{-α (}T^d)^{1 α} n^α-2 - ^ξ(^ξ—¹)(1—^ρ^^pn^ξ-2

-α (1 - α) A (1 - ρ)¹-^α (hL)¹-^α (T^dy^α-1 n^α] +

- α (1 - α) A (1 - ρ)¹-^α (hL)¹-^α (T^d) ^-α n^α-¹i 2 > 0

that leads to:

^α (1 - α) ξ (ξ - 1) A (1 - ρ)¹-^α+θ ρ^η (hL)¹-^α (T^{d¢ -α-}1 n^α+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 ⁽hT^dL} 1 ^α (1 - ρ)¹-^α n^α = ∣n^ξ (1 - ρ)^θ ρ^η               (23)

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