422 | P A R T I V Business Cycle Theory: The Economy in the Short Run

The Short-Run Equilibrium

The economy’s short-run equilibrium is determined by the intersection of the dynamic aggregate demand curve and the dynamic aggregate supply curve. The economy can be represented algebraically using the two equations we have just derived:

Yt =

pt =

−	+ avY)](pt − p*t ) + [1/(1	+ avY)]et.
Yt – [avp /(1			(DAD)
	−
pt −1 + f(Yt − Yt) + ut.			(DAS)

In any period t, these equations together determine two endogenous variables:

inflation pt and output Yt. The solution depends on five other variables that are
exogenous (or at least determined prior to period t). These exogenous (and pre-
		−
determined) variables are the natural level of output Yt, the central bank’s target
inflation rate	p t	et	ut	, and the previ-
	*, the shock to demand	, the shock to supply

ous period’s rate of inflation pt −1.

Taking these exogenous variables as given, we can illustrate the economy’s short-run equilibrium as the intersection of the dynamic aggregate demand

curve and the dynamic aggregate supply curve, as in Figure 14-4. The short-run

−

equilibrium level of output Yt can be less than its natural level Yt, as it is in this

figure, greater than its natural level, or equal to it. As we have seen, when the

economy is in long-run equilibrium, output is at its natural level (Yt = −t

Y

.

)

The short-run equilibrium determines not only the level of output Yt but also the inflation rate pt. In the subsequent period (t + 1), this inflation rate will become the lagged inflation rate that influences the position of the dynamic aggregate supply curve. This connection between periods generates the dynamic patterns that we will examine below. That is, one period of time is linked to the next through expectations about inflation. A shock in period t affects inflation in period t, which in turn affects the inflation that people expect for period t + 1. Expected inflation in period t + 1 in turn affects the position of the dynamic

FIGURE 14-4
Inflation, p	Yt		The Short-Run Equilibrium The
		Natural level	short-run equilibrium is determined
		of output	by the intersection of the dynamic
Short-run			aggregate demand curve and the
			dynamic aggregate supply curve. This
equilibrium		DASt	equilibrium determines the inflation
			rate and level of output that prevail in
			period t. In the equilibrium shown in
			this figure, the short-run equilibrium
			level of output Yt falls short of the −
			economy’s natural level of output Yt.
		DADt
	Yt	Income, output, Y