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

Since we also have α < ξ (because the latter must be larger than 1 for the cost
function to be convex), this implies the following restrictions:

^ξ . . ʌ

ξ+θ <^α<^ξ

If η< 0, on the other hand, the restriction 0 < ρ< 1 requires:

ξ

^α (^{ξ +} П ^{+ θ}) ^{- ξ}< 0 ⇒ ^α<
ξ + η +θ

and also (since both the numerator and the denominator of the fraction that defines

ρ are negative numbers, so that the sign of the inequality must be reversed):

ξ

αη>α (ξ + η + θ) - ξ ⇒ α < —

so that we have the following restrictions:

. ^ξ . ʌ
θ <^ξ

that guarantee that in the steady-state the values of n, w, c, a are all positive. ■

The steady-state values obtained above can then be used for the comparative
statics analysis of the decentralized equilibrium. The results (see computations in
Appendix 7.3) can be summarized in the following Table (for the missing elements, it
is not possible to derive analytically the sign of the relationship between the variable
and the parameter that affects it, and it is necessary to resort to simulations to have
this indication):

Table 4: Comparative statics of the model

These results can be interpreted as follows (they are relative to the case η>0,
while in the case of η< 0 the only changes concern the elements of the column of
ρ, that change all their sign).

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