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

of the monetary policy under a NMP regime have a larger impact on CPI than the single
channel of the common CB in a MU.

5 Monetary policy

This section examines the optimization problem of the common CB under a MU regime
and how the CB responds to wage hikes. Monetary policy is decided in the second stage
of the game.

The CB chooses the union-wide money supply taking as given nominal wages in the
economy and internalizing the firms reaction function so as to maximize (16) under the
MU Phillips curve investigated in the previous section (25). In other words, the CB acts as
StackelbergTollower player vis-à-vis trade unions (Stackelberg leaders) and as Stackelberg-
leader vis-à-vis firms (Stackelberg followers).

The CB payoff (16) may be rewritten as

n= af' - ∣(l^u)² - ^βu (,^u)².

Thus the first order condition of the CB is given by¹⁷

dΩ
dmu
^α _- „ _- ^β_uπ^u(1 ^- a)
к             к

According to expression (28), as long as the employment level is below the competitive
one¹⁸, a/к (see equation (38)), it is optimal for the CB to fuel a positive inflation rate
through her monetary policy.

Moreover, relation (28) shows the role played by the Phillips curve in the CB balances
of unemployment and inflation. The weight attached to inflation depends on the degree of
conservatism and the slope of the Phillips curve. As a matter of fact, both CBC and the
slope of the Phillips curve have the same function: they determine the relative significance
attached to inflation by the CB. It is easy to see that, ceteris paribus, the effect of a
flatter Phillips curve is similar to the effect of smaller CBC. The CB will adopt a more
accommodating monetary policy either with a smaller degree of conservatism or a flatter
Phillips curve. In both cases the CB would realize a higher loss from reducing inflation
rather than unemployment¹⁹.

¹⁷Since the CB is a large agent, profits are not taken as given.

¹⁸i.e. the level of employment that maximizes the workers’ welfare equating the consumption∕leisure
marginal rate of substitution (⅛ log L) to the (efficient) technical rate of transformation (ɪ).

¹⁹We will see below that, since the CB’s reaction function is common knowledge for labor unions, workers
anticipate the incentive of the CB to inflate. In the "time-consistent" equilibrium the marginal benefit to
higher inflation exactly offsets the marginal cost. The monetary authority could inflate above and beyond

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