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



of fact, the NMP and MU labor demand elasticity coincide when β = 0 and the latter is
larger than the former when
β → ∞. Thus it is sufficient to analyze if the slope of ⅛β1
evaluated at β = 0 is greater than ^βz- evaluated at β = 0. The impact of CBC on money
supply elasticity in both regimes at β = 0 is

u        (1 — α)(1 — (1 — α)σ)

dβ J β=o         k(n 1)

and


n        Θh [k + βp0“p (h + βp@f(1 α))σ]

_ β=o             k(n 1)(k + βf@F)

(54)


(55)


Note, first, that expression (55) is an increasing function of βF. When σ > ɪɪ the ratio

№] β=o.βr =o


Γ ⅛. 1

( dβ β=o


1 α7 (1 α7 )2σ
1
a — (1 α)2σ


(56)


which implies that there not exists a level of β = 0 where the labor demand elasticity
7∕n and ηu are equal. When σ < ɪɪ the expression (56) holds iff σ < 1-a^1-a^. ɪn such
a case there exists a level of β = 0 where the labor demand elasticity ηw and η
u intersect.
The second part of Proposition 5 is achieved by evaluating equation (50) at
nH = 1 and
H ∞. ■

Analysis of CSW and macroeconomic outcome. The marginal impact on labor
elasticity of a more decentralized wage setting is

w          [(k^N + βF^F(1 α))σ (k + βfdF)] Z2

dnH ^ [к(пн 1)(k + βFθF)+ пнβ(βFΘnΘf(1 a) + k¾)]2

where Z2 β^N [k2 + βfβ^N@F(1 a) + k(βfdF + β^N)] > 0 and the sign of ηN de-
pends on the

k        k+ βf^F    ʌ

"5n V N + βFΘf (1 a) )


By the same token, the derivative of the labor demand elasticity with respect to unions
numerosity is

u = ( 1 + Mu) [1 (1 oPσ]

dn    [n + a(1 + μu) Mu]2

and the sign is determined by the
which proves Proposition 7. bterestingly, both labor elasticity tends to σ in presence of
atomistic wage setting (i.e.
h → ∞). ɪn order to compare the effect of CWS in the two

sign


(σ


33



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