Monetary Discretion, Pricing Complementarity and Dynamic Multiple Equilibria

2.7 Two distortions and monetary policy

The monetary authority in this model faces two distortions that are present in the private
economy and can be influenced by its actions. First, there is a markup distortion that
represents the wedge between price and marginal cost: it has consequences similar to
those of a tax on labor income. The markup is just the reciprocal of real marginal cost,
= 1 = 1 = ∂u(ct,lt)∕∂ct = ɪ
^μt ψt Wt    ∂u(ct,lt)∕∂lt    χct ■

From the derivations above, the markup depends on po,_t and m_t: μ_t = g(po,t)/(χmt) ■

Second, there is a relative price distortion that represents a wedge between inputs and
outputs:

nt/ct = ^δ(po,t) ≡ 2 ∙ [g (po,t)]^ε ∙ (p^-,t + 1) ■

The relative price distortion depends solely on po,_t. It takes on a value of unity at po,_t = 1
(this would be the case in a zero inflation steady state) and is higher for other values of po,_t.
The trade-off that the monetary authority typically faces between these two distortions is
that choosing a higher money supply decreases the markup (good) and raises the relative
price distortion (bad).

Just as we showed above that all real variables could be described in terms of po and
m, the distortions can be described similarly. The summary role of po and m, together
with the fact that at any point in time the monetary authority can choose m (i.e. choosing
m in the current period is no different than choosing M ) has a strong implication for the
analysis of discretionary monetary policy.³ It implies that the level of the predetermined
nominal price P1_,t does not restrict the outcomes a discretionary policymaker can achieve,
as long as the monetary authority in future periods behaves in the same manner.⁴

We now analyze outcomes under monetary discretion, proceeding in three steps (with
each a separate section of the paper). We begin by studying perfect foresight settings.
In section 3, we detail the nature of perfect foresight private sector equilibria under a
particular class of monetary policy rules. In section 4, we describe a full discretionary
equilibrium — with optimization by the monetary authority—in which policy is shown to
be in this class of rules. Finally, in section 5, we discuss stochastic discretionary equilibria.

³ It is important not to misinterpret the parenthetical statement: any choice of Mt can be replicated by
choosing mt = Mt/P1,t . However, a policy of keeping Mt constant is not the same as a policy of keeping
mt constant.

⁴ If the future monetary authority paid attention to nominal levels, it might be optimal for the current
monetary authority to do the same. We do not consider equilibria with this property.

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