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

where s_r is the impact effect (elasticity) of ω⅛ on inflation when the nominal wages of other
unions are taken as given in a monetary regime r ∈ [Æ, U]:

dπ^w    1

Sn ≡ —— = — [«7 + (1
dωi   n∏

dπ^u     7 _r,               ,                                 _z

^su ≡ ~₁   =    ^{[(1 —} a)μu ⁺ «^] ∈ (°^{7)                    (32)}

dωi   пн

with ∣ι∣∣∣∣ (^FH ) representing the reduced form elasticity of Home (Foreign) money supply
to Home aggregate wages under a NMP regime, while Mu is the elasticity of union-wide
money supply to union-wide wages under a MU regime²¹, ε_r is the elasticity of labor
demand to the nominal wage of union г in the monetary regime r:

dlN   A Mo s 1

^εN ≡ J = ^σ ( ¹      ) ^{+ (1 — MhH)}    )                 ⁽³³⁾

dω_i    П n_H J           пн

^εu ≡^— ~t^l = 7^σ f¹--^ ^{+ (1 —} Mu⁾ ɪ-                ⁽³⁴⁾

dω_i П n_H J          пн

Note that equation (33) and (34) are a weighted average of the elasticity of substitu-

tion among labor types and the elasticity of aggregate labor demand, Dividing (30) by
— s_r, we can express the first order condition in terms of the real wage elasticity
of labor demand, η_r, as follows²²

«(1 — η_r ) + kη_r Ii = 0.

Equation (35) shows that an increase in the union t’s wages has two opposing effects on
the utility of workers, On one hand it increases the real wage and reduces employment;
since the latter effect is larger, there is a reduction in consumption (the first term in
(35)), On the other hand, a wage rise increases utility through leisure (the second term in
(35)), Thus, each union sets a nominal wage growth according to her consumption∕leisure
preferences, k,

Under a NMP regime the elasticity of domestic labor demand (in absolute value) is
given by
where вн ≡ 1 — «7 and Θf ≡ 1 — (1 — 7)«,

Similarly we may derive the labor demand elasticity in the Home and Foreign country

²¹See Appendix for details,

²²Derivation in Appendix,

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