Monetary Discretion, Pricing Complementarity and Dynamic Multiple Equilibria

2 Model

The model economy that we study is a particular fully articulated “New Keynesian”
framework, featuring monopolistic competition and nominal prices which are fixed for
two periods. There is staggered pricing, with one-half of a continuum of firms adjusting
price in each period. Since all of the firms have the same technology and face the same
demand conditions, it is natural to think of all adjusting firms as choosing the same price.
We impose this symmetry condition in our analysis.

There are many different types of New Keynesian models, which differ in terms of
their implications for the extent of complementarity in price-setting. Our model assumes
that (i) there is a constant elasticity demand structure originating from a Dixit-Stiglitz
aggregator of differentiated products; (ii) there is a centralized labor market so that the
common marginal cost for all firms is powerfully affected by aggregate demand; and
(iii) preferences for goods and leisure display exactly offsetting income and substitution
effects of wage changes, as is common in the literature on real business cycles. Kimball
[1995] and Woodford [2002] have stressed that these assumptions make it difficult to
generate complementarity between price-setters when there is an exogenous money stock.
As we will, see our model has exactly zero complementarity in this situation. From
our perspective, this is a virtue because it highlights the importance of the policy-based
complementarity that arises from monetary policy under discretion.

2.1 Households

There is a representative household, which values consumption (c_t) and leisure (l_t) ac-
cording to a standard time separable expected utility objective,

∞

Et{^Xβ^ju(ct+j,lt+j)}                               (1)

j=0

with β being the discount factor. We assume that the momentary utility function takes
the form

u(ct, lt) = log(ct) + χlt                                     (2)

which implies that there are exactly off-setting income and substitution effects of wage
changes. It also has some other convenient implications that we describe later.

As is standard in the analyses of imperfect competition macro models that follow
Blanchard and Kiyotaki [1987] and Rotemberg [1987], we assume that consumption is an

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