but not others (those adjusting prices) within a period. This gives rise to a relative price
distortion across firms in the discretionary equilibrium that we construct, which in turn
means that there is an interior solution for the monetary authority’s choice problem. If we
reversed the timing order so that the monetary authority moved last, we conjecture that
there would not be a discretionary equilibrium unless some other aspect of the economy
were modified, such as allowing firms to reset their prices after paying an adjustment
cost.2 Second, the fact that the price-setters move after the monetary authority means
that there is the potential for more than one equilibrium price to correspond to a given
monetary policy action.
2.5 Complementarity with an exogenous money stock
We now consider a situation in which Mt = Mt+1 = M . Under the assumptions of our
model, it turns out to be easy to investigate the influence of other adjusting firm’s actions,
i.e., to compute the effect of P0,t on the right-hand side of (11). The constant velocity
assumption (Ptct = Mt) and the particular utility function together imply Ψt = Ptwt =
Pt(χct). Hence, equilibrium nominal marginal cost is exactly proportional to the money
stock, Ψt = χMt . Since the nominal money stock is assumed constant over time, nominal
marginal cost is also constant over time and (11) becomes
Po,t = -ε7χM.
ε-1
This equilibrium relationship means that there is an exactly zero effect of P0,t on the
right-hand side: there is no complementarity in price-setting in this model when the
nominal money supply is constant.
2.6 Summarizing the economy by p0 and m
Under discretionary policy, the monetary authority will not choose to keep the nominal
money supply constant. Therefore, the optimal pricing condition (11) will not simplify to
a static equation. In general, however, equilibrium will be a function of just two variables:
a measure of the price set by adjusting firms and a measure of monetary policy. We
construct these variables by normalizing nominal prices and money by the single nominal
2The nonexistence of a discretionary equilibrium is a feature of Ireland’s [1997] analysis of a model
in which all prices are set simultaneously, before the monetary authority determines the current money
supply.
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