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

The first constraint stems from the cost minimization problem of firms. The second one
is the result of the consumer problem derived previously. The usual profit maximization
condition that marginal revenue equals marginal cost may hence be written¹⁴:

⅛<z> f₁ _ H = 1 ⁱ¼_w⅛*

P ∖ λj a P ^{H ( 1}

In a symmetric equilibrium, where all firms have the same optimal price rule, the
price of a brand, P_c(z), coincides with the producer price index, P_c, and the output of a
representative firm Y_c(z) equals the output of the country Y_c for all z. Thus taking the
logarithms of condition (19) and using (13), the first order condition yields¹⁵

π∏ — π = a(ω — π) + (1 — a')(m∏ — π).                   (20)

This relation shows that, although prices are fully flexible, they do not completely
move when the money supply changes. As a matter of fact, it is not optimal for profit
maximizing firms to respond exactly in kind to the money supply as long as nominal
wages have not been changed. This implies that the monetary authority may affect real
variables, even when prices are fully flexible, for nominal wages are contractually fixed
(Cukierman, 2004).

Arranging equation (20), we obtain the following negative relation between real money
balances and wages:

тн — kh = — ι ^α _α (ω — z_π)                      (21)

From the definition of the CPI (2), the previous equations imply that the general price
level can be rewritten in terms of Home and Foreign wages and money supplies as follows:

π^u = (1 — a)mu + αωu

where ωu ≡ 7ω + (1 — 7)ω*.

An accommodating monetary policy operates in a country through the expansion of
the demand faced by each monopolistic firm boosting in this way the inflation rate. At this
stage Home and Foreign wages affect inflation in the country only through their impact
on input costs which in turn determine Home and Foreign good prices, respectively. In
the following sections we will see that the monetary policy is also influenced by Home and
Foreign wage settlements through strategic interactions.

¹⁴Coricelli et al. (2000) introduced for the first time the optimal price setting in the literature on nominal
wage bargaining systems.

¹⁵In deriving the following expression, we neglect the costant a log (_λ3₁)_q, .

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