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 ^β^z- evaluated at β = 0. The impact of CBC on money
supply elasticity in both regimes at β = 0 is

dηu        (1 — α)(1 — (1 — α)σ)

dβ J β=_o         k(n — 1)

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

^dβ _ β=o             k(n — 1)(k + βf@F)

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

which implies that there not exists a level of β = 0 where the labor demand elasticity
7∕_n and η_u 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 η_w and ηu intersect.
The second part of Proposition 5 is achieved by evaluating equation (50) at n_H = 1 and
∏H → ∞. ■

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

dη_w          [(k^N + βF^F(1 — α))σ — (k + βf^dF)] Z2

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

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

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

^dηu = ^{( —1 +} Mu⁾ [^{1 — (1 — o}P^σ]

^{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

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