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

Using (22) and (24), we explicitly solve (28) for the money supply

ɑ + [k — ɑ(l — θ-)βu] ωu
к + β _u (1 — α)²

Drawing on Proposition 1 and equation (28), it is apparent that the marginal cost
faced by the CB is lower in the MU than under a floating exchange rate regime. It follows
that, ceteris paribus, the CB is encouraged to inject more money in the monetary system
so as to equate the marginal benefit and marginal cost. However, the common CB cares
about MU employment that is not necessarily equal to the Home country level.

Now from equation (29) we can investigate how the CB reacts to change in Home
and Foreign wages. The following proposition underlines the importance of the degree of
conservatism in determining the tightening or the accommodation in the monetary policy
to a wage increase.

Proposition 2 For values of CBC below (above) β_u = _a(!_—a) the CB accommodates
(contracts) the money supply response to Home and Foreign wage increases.

Proof. At a symmetric equilibrium, from equation (29) we obtain ^)^
whose sign depends clearly on the CBC. ■

A rise in wages increases both inflation and employment. A conservative CB, i.e.
when βu > ɑ(ʌɑɔ, responds to any wage hike by tightening her money supply since she
attaches more weight to inflation than unemployment. Conversely, a populist CB, i.e.
when βu < _a(i—_a), cares more about unemployment than inflation and so her response to
wage is accommodating.

6 Wage setting

In this section we evaluate how wage setting is affected by the a shift from a NMP regime
to a MU.

In the first stage of the game unions act as Stackelberg leaders vis-à-vis the monetary
authority and firms, i.e. the labor unions anticipate the reaction functions of the CB and
firms. Home union i chooses the rate of growth of the nominal wage, ω⅛, so as to maximize
(15) subject to (4) and (29). In doing that the union takes profits, Di, and the nominal
wages set by the other unions at Home and abroad as given. The typical union i first
order condition is hence²⁰

α(---y—— — s_r — ε_r) + ε_rkli = 0, r ∈ [A^, U]                 (30)

dωi

the worker (rational) expectations, but it is not in her interest to do so.

²⁰See the Appendix for details.

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