economies. We begin with a last period, in which firms are not forward-looking in their
price setting and deduce that there is a single equilibrium, including an optimal action for
the monetary authority mτ > m* and a unique equilibrium relative price po,τ. Then, we
step back one period, taking as given the future monetary action and the future relative
price. We find that there are two private sector equilibria. In fact, this is inevitable,
because the first step backwards creates a version of our point-in-time analysis above.
Consequently, this approach establishes that the phenomena are associated with forward-
looking pricing and homogenous monetary policy, rather than with an infinite horizon.
To construct stationary nonstochastic equilibria using this approach, we can iterate back-
wards from the last period, computing the optimal policy, {mT,mT-1 , } and stop the
process when |mt+1 - mt | is small, taking mt = m as an approximate fixed point.
In either computational approach, our work begins from the perspective that the rele-
vant dynamic equilibrium is one that is Markovian, in the sense of Krusell and Rios-Rull
[1999]. In general, this equilibrium concept restricts the actions of the policymaker to
depend on a set of fundamental state variables that have intrinsic relevance to the equilib-
rium. In our setting, there are no such state variables, so that search for a nonstochastic
Markov equilibrium corresponds to determining constant levels of public and private
actions. When we do so, we find that there is more than one nonstochastic Markov equi-
librium. We then consider a stochastic discretionary equilibrium in which each period’s
equilibrium outcome is determined by a sunspot that shifts private sector beliefs. When
we consider this extension, we continue to assume that the monetary authority makes its
actions a function of the state variables that are relevant to the private sector. We focus
on Markov equilibria because these impose the most structure on the problem (making
clear that our multiplicity arises from a single source) and provide the most tractable
solution. Furthermore, the Markov equilibria of the model have natural analogues in a
finite-horizon version of the model, making it clear that our results do not depend on
whether the model is literally an infinite horizon one or simply the convenient stationary
limit of a sequence of finite horizon models.
The numerical examples that we study next have the following common elements.
The demand elasticity (ε) is 10, implying a gross markup of 1.11 in a zero inflation
steady state. The preference parameter (χ) is 0.9, and for convenience we set the time
endowment to 5. Taken together with the markup, this implies that agents will work one
fifth of their time (n =1)in a zero inflation steady state. With zero inflation, c = n =1
since there are no relative price distortions, and thus m* = 1. Further, leisure (l) is then
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