Strategic monetary policy in a monetary union with non-atomistic wage setters

through the CB reaction function (equation (28)). The higher is the degree of CBC, the
more severe are the employment consequences of wage aggressiveness²⁷. Drawing on Lippi
(2003) terminology we refer to it as adverse output effect.

On the other hand, since a conservative CB leads unions to perceive less the inflationary
impact of their wage, they also anticipate the real wage of other unions to decrease to a
lesser extent and, hence, the shift of labor demand towards cheaper labor types is smaller²⁸.
This adverse competition effect encourages wage aggressiveness (Lippi, 2003).

Now it may be interesting analyzing the two limit cases of a CB ultra-populist and
ultra-conservative. Letting the CBC go to zero, i.e. assuming that the CB does not care
about inflation but only about agents’ utility, we obtain the monopolistic competition level
of employment²⁹

" = £ (1 - ɪ) . (42)

When the CB is ultra-populist the strategic interaction channel between trade unions and
CB is halted³⁰. In such a case, the employment level is below the Pareto efficient one, ^,
and it depends on the degree of substitutability among labor types. As specified in section
5, an ultra-populist CB accommodates any domestic wage hike one-to-one which implies
that wage setters can not affect employment.

The other extreme case of a CB that cares only about inflation, i.e. an ultra-conservative
CB, yields the following equilibrium employment level under a NMP and a MU regime

respectively

a /

Iim I = — I 1 —

β→∞

⅛+βFθF

n_H k0_N +β_pΘ_f (1-o)

⁺ (¹^- nH) '

Iim I = ^α

β→∞

ɪɪ + (1 — ɪ U
пн 1-a у пн J

(43)

(44)

From the relation (42), (43) and (44), we can make the following remark.

²⁷Formally this can be seen by differentiating the first term of equation (41) with respect to CBC:

d ( SΘ_ndβ ∖ k

sn
1-«n

β^N ^sN

/ ^d3N ∖

β + ⅛)

where Θ_f = 1 — α(l — 7)

^k⁽¹^—oQ(ⁿH ^— 7⁾7 > Q

[ⁿH ⁽¹^—α^β2^β⁺^k(ⁿH ^—7⁾]²

____________________^k⁽ⁿH ^-¹X^k⁺^βF^kF ⁾²^N___________________

[^k⁽ⁿH ^—¹X^k⁺^βF ^kF ⁾⁺ⁿH ^ββF ®N ®F ⁽®F ^—¹⁾⁺ⁿH ^β^^+βF ®F X^β√]

and P_f is the degree of the Foreign CBC. In a MU, dβ ^βp^uΓ^ ₁-'_s,

²⁸Formally this can be seen by differentiating the second term of equation (41) with respect to CBC:

d I nH — 1 σ J
dβ ∖ nH 1 —Sn 7

dsN

nH — 1 σ__dβ

n H 1 s n 1 s n

Q and in a MU -⅛ ( ' ₁-2-ʌ) = —

^dβ ∖ ⁿH ¹^-^su J

=__kn²_H (k+βF Θ^F )²Θf [kθ h +βF ^dF (1 — a)]α________________

⁽ⁿH ^—¹⁾ [^k⁽ⁿH ^—¹X^k⁺^βF ®F ⁾⁺ⁿH^ββF ®N Θf ⁽9f ^—¹⁾⁺ⁿH ^β(^k⁺^βF ®F X^β√ P

_________^knH ⁽¹^—Q^β27g-_________ < Q

⁽ⁿH ^—¹⁾[ⁿH ⁽¹^—α^β2^β⁺^k(ⁿH ^— 7⁾]²

²⁹The values of η_r in the case of an ultra-populist and ultra-conservative CB are derived in the Appendix.

³⁰The CB has only one target (employment) and hence the trade-off between inflation and employment
in its optimal monetary policy is prevented. An increase in nominal wage will cause an equal increase in
money supply. This implies that labor unions can not affect their real wages.

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