the optimal price is a constant markup (ε/ (ε - 1)) over a weighted average of nominal
marginal cost over the two periods, where the weight on the future is
θt,t+1 =
βλt+1ct+1Ptε+-11
βPtε+-11
ε-1 ε-1 ε-1 ε-1 .
λtctPt + βλt+1ct+1Pt+1 Pt + βPt+1
(12)
The weights on current and future nominal marginal cost represent the shares of marginal
revenue associated with the current and future periods.
2.3 Defining Complementarity in Price Setting
The standard definition of complementarity — contained, for example, in Cooper and
John [1988]— is that the optimal action of one decision-maker is increasing in the actions
of other similar decision-makers. In our context, we are interested in complementarity in
price-setting in equation (11). The left-hand side of this expression is the action of the
particular decision-maker under study: the optimal price of an individual monopolistically
competitive firm that is currently making a price adjustment. Other monopolistically
competitive firms are also simultaneously adjusting prices: these firms take an action P0,t
that influences the right-hand of (11). The price chosen by the representative adjusting
firm influences the price level directly because Pt = [2Pj-ε + 2P1-ε]1-ε and may also
affect current nominal marginal cost. Given that prices are sticky, there can be real
effects of variations in the price level, so that these could influence nominal marginal cost.
Finally, the weights on the present and the future in (11) also depend on the price level.
To determine whether there is complementarity, we must work through these mechanisms
and determine the sign of the relevant partial derivative. The extent of complementarity
will depend on the behavior of the monetary authority.
2.4 Timing
The sequence of actions within a period is as follows. In the first stage, the monetary
authority chooses the money stock, Mt, taking as given P1,t , the price set by firms in the
previous period. In the second stage, adjusting firms set prices (P0,t). Simultaneously,
wages are determined and exchange occurs in labor and goods markets.
There are two important consequences of these timing assumptions. First, since price-
setters move after the monetary authority, they cannot be surprised by the monetary
authority during the initial period that their price is in effect. Accordingly, the monetary
authority faces an economy in which it can surprise some agents (those with pre-set prices)