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90 wfien ] is lower), and when labor supply is more responsive to the real wage (that is, when is lower). The fact that equilibrivmi output is inefficiently low imder imperfect competition has important implications for fluctuations. To begin with, it implies that recessions and booms have asymmetric effects on welfare (Mankiw, 1985). In practice, periods when output is imusually high are \lewed as good times, and periods when output is unusually low are viewed as bad times. Now consider a model where fluctuations arise from incomplete nominal adjustment in the face of monetary shocks. If the equilibrivmi in the absence of shocks is optimal, both times of high output and times of low output are departures from the optimvun, and thus both are imdesirable. But if equilibrivun output is less than optimal, a boom brings output closer to the social optimvun, whereas a recession pushes it farther away. In addition, the gap between equilibrium and optimal output implies that pricing decisions have externalities. Suppose that the economy is initially in equilibrium, and consider the effects of a marginal reduction in all prices. M IP rises, and so aggregate output rises. This affects the representative individual through two channels. First, the prevailing real wage rises (see [6.43]). But since initially the individual is neither a net purchaser nor a net supplier of labor, at the margin the increase does not affect his or her welfare. Second, because aggregate output increases, the demand curve for the individuals good, Y(Pi IP)", shifts out. Since the individual is selling at a price that exceeds marginal cost, this change raises his or her welfare. Thus under imperfect competition, pricing decisions have externalities, and those externalities operate through the overall demand for goods. This externality is often referred to as an aggregate demand externality (Blanchard and Kiyotaki, 1987). The final implication of this analysis is that imperfect competition alone does not imply monetary nonneutrality. A change in the money stock in the model leads to proportional changes in the nominal wage and all nominal prices; output and the real wage are unchanged (see [6.46] and [6.47]). Finally, since a pricing equation of the form (6.45) is important in later sections, it is worth noting that the basic idea captured by the equation is much more general than the specific model of pricesetters desired prices we are considering here. Equation (6.45) states that p*  p takes the form i6y; that is, it states that a pricesetters optimal relative pnce is increasing m aggregate output. In the particular model we are considering, this arises from increases in the prevailing real wage when output rises. But in a more general setting, it can also arise from increases in the costs of other inputs, from diminishing returns, or from costs of adjusting output. The fact that pricesetters desired real prices are increasing in aggregate output is necessary for the flexibleprice equilibrium to be stable. To see this, note that we can use the fact that = m  p to rewrite (6.45) as p* = + (1 ) + . (6.48)
The original versions of these models focused on staggered adjustment of wages: prices were in principle flexible but were determined as markups over wages. For simplicity, we assume Instead that staggered adjustment applies directly to prices. Staggered wage adjustment has essentially the same implications. If is negative, an increase in tfie price level raises each pricesetters desired price more than oneforone. This means that if p is above the level that causes individuals to charge a relative price of 1, each individual wants to charge more than the prevailing price level; and if p is below its equilibrium value, each individual wants to charge less than the prevailing price level. Thus must be positive for the flexibleprice equilibrium to be stable. 6.7 Predetermined Prices Framework and Assumptions We now turn to the Fischer model of staggered price adjustment. In particular, we consider a variant on the model of the previous section where pricesetters cannot set their prices freely each period. Instead, each pricesetter sets prices every other period for the next two periods. As emphasized in Section 6.5, the pricesetter can set different prices for the two periods. In any given period, half of the individuals are setting their prices for the next two periods. Thus at any point, half of the prices in effect are those set the previous period and half are those set two periods ago.2 For simplicity, we normalize the constant in the equation for pricesetters desired prices, (6.45) (or [6.48]), to zero; thus the desired price of individual i in period f is p,* = +(1  ) 1. Otherwise the model is the same as that of the previous section. The behavior of m is treated as exogenous; no specific assumptions are made about the process that it follows. Thus, for example, information about rut may be revealed gradually in the periods leading up to t; the expectation of m, as of period t  1, Etirut, may therefore differ from the expectation of rut the period before, £, 2"it Paralleling our assumption of certainty equivalence in the Lucas model, we assume that an individual choosing his or her prices in period t for the next two periods sets the log prices equal to the expectations, given the information available through t, of the profitmaximizing log prices in the two periods. As in the Lucas model, pricesetters form their expectations rationally. Solving the Model In any period, half of prices are ones set in the previous period, and half are ones set two periods ago. Thus the average price is
Pt = (Pr + Ph (6.49) where denotes the price set for f by individuals who set their prices in f  1, and pf the price set for t by individuals setting prices in f  2. Since we have assumed certaintyequivalence pricing behavior (and since all pricesetters in a given period face the same problem), p} equals the expectation as of period f  1 of p,, and pf equals the expectation as of f  2 of p. Thus, p} = Etip* = {\[ 1 + ) ] (5 50) , imt + a  ){ 1 + pf), pfE,2P*t (6.51) = , + a )( 12 1 + pf), where £f denotes expectations conditional on information available through period t  . Equation (6.50) uses the fact that pf is already determined when Pf is set, and thus is not uncertain. Our goal is to find how the price level and output evolve over time given the behavior of m. To do this, we begin by solving (6.50) for p/; this yields We can now use the fact that expectations are rational to find the behavior of the individuals setting their prices in period t  2. Since the left and righthand sides of (6.52) are equal, and since expectations are rational, the expectation as of t  2 of these two expressions must be equal. Thus, Equation (6.53) uses the fact that £f2£fifnf is simply £f 2"if; otherwise pricesetters would be expecting to revise their estimate of either up or down, which would imply that their original estimate was not rational. The fact the current expectation of a future expectation of a variable equals the current expectation of the variable is known as the law of iterated projections.
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