conservative, instead, the labor demand elasticities are49
1∙ _ ɪ__k + βF ^F__I A__ɪ ʌ
3→∞ "9n пн k() n + ^f$f(1 — a) ∖ nH / ’
Iim ηu = --1- +
β→∞ пн 1 — a
(1 - -l)
∖ nH√
σ.
(49)
These relations prove equation (42), (44) and (43). In general, the sign of dηββ- not only
depends on the adverse output and competition effect but also on the other CBC as follows:
dηN к(пн — 1)(k + βf^F)^n [k + βFkF — (k@N + βF^f(1 — α))σ]
(50)
dβ ~ [k(nn — 1)(k + β F θF )+ пн β(βF Θn Θf (1 — a) + kθN )]2
The sign of ddη-β- is
hence
k k + βFθF
s*9n Un + βFΘf(1
a—σ).
The sign of dβ^ is
instead always positive:
dηN
dβF
kβ(1 — Θf)Θf(1 — Θn)Θn [k(nH — 1)σ + пнβ^N]
[k(nH — 1)(k + βF&F ) + пн β(βF ^n @f (1 — a) + kθN )]
> 0.
(51)
In the case of a MU the sign of
dηu k(nн — 1)(1 — a) [1 — (1 — α)σ]
(52)
dβ [kfa — 1)+ пн (1 — α)2β]2
is given by
sign
(τ
σF
The first part of Proposition 5 is proved by taking the partial derivative of (38), (39) and
(40) with respect to CBC and using equation (50) and (52) as follows:
dl a 1 dηr
dβ k η2 dβ
dπ
dβ
|
a |
^1 + β dηr |
< 0 |
|
θr ηr β2 |
ηr dβ |
(53)
Notice that the term in brackets in equation (53) is always positive
since
β dηr
ηr dβ
adverse output effect under a NMP regime is an increasing function of βF anc
< 1. The
is always
smaller than the adverse output in a MU, ɪɪ^. Now what remains to assess is whether
the labor demand elasticity in MU and NMP intersect in the (β,ηr) plane. As a matter
49Note that
k+^F ®F1
(1-a)βp Θf +kθκ ^ 1-α ∙
32