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

from which:

At [(1 - Pt)    tL     nα = c, + n^{ξ (1} -^ρt)θ ^РП               (13)

and by the labour market equilibrium condition:

T^d = T^s = Tt
tt

(14)

We are now able to set the following definition of equilibrium for the economy
under investigation:

Definition Given the initial condition h₀ , an equilibrium is a path:

{rt, Tt, ht, ρ_t, nt, wt, ct, at}_t≥0

that satisfies the equations (4)-(6) and (9)-(13) derived above and the corresponding
standard transversality conditions.

4 Steady-state and comparative statics of the model

Given the decentralized economy considered in the previous Section, it is now possi-
ble to obtain the steady-state values of the different variables (for the computations
see Appendix 7.2), that are given by:

1 — β r =---- β	(15)
T =   1 — βδ 1 + β — 2βδ 1 β (1 — δ) h = E I-δ -—-------- 1 + β — 2βδ αη ρ a (ξ + n + θ) — ξ	(16) (17) (18)

α <αAd∖ ^ξ-^α , ,   1-α     1-α β β (1 — δ) (1 — βδ) ∖ ^ξ-α

n = I ------ I E(^1-δ)(^ξ-α) L^ξ-α I ---------------------•— I ∙

ξ ξ )                  ∖ (1 + β — 2βδ)2 J

• (a (ξ + θ) — ξ) —-^α (an)^α-ξ (a (ξ + n + θ) — ξ) ^α-ξ

w=

α                                                                          α(1 —ξ)

α     αdad-^{α ξ-α} ,        α(1^-ξ)    α(1-ξ) ββ (1 — δ) (1 — βδ}∖ ^ξ-α

(1 — a) I — I     A^ξ-α E^{(1— δ})(^ξ-α) L ^ξ-α I -------------------∙— I ∙ (20)

ξ ∖U                      ∖ (1 + β — 2βδ)2 J ^l ’

ξ-α(ξ+θ)         αη                                 α(ξ+η + θ) —ξ

• (α (ξ + θ) — ξ) ^ξ-α   (an)^α-ξ (α (ξ + η + θ) — ξ)   ^ξ-α

16