Question

5. Consider the following modification of the DAS and DAD model in class. a) Suppose the monetary-policy rule has the wrong natural rate of interest. That is, the central bank follows this rule: where ρ, does not equal p, the natural rate of interest in the equation for goods demand. The rest of the dynamic AD-AS model is the same as in the textbook. Solve for the long-run equilibrium under this policy rule. (5pts) Suppose that the shock et were to increase permanently to a positive constant E. The rest of the dynamic AD-AS model is the same as in the textbook. Solve b) te rc e panie inflation rate return to its target in the long run? (5pts)

Answer 1

Answer-Aggregate Demand Models.
Model 1: Traditional AS-AD Model
In order to develop an interactive AS-AD model we start with the following linear model:
Aggregate Supply (AS): Yt = Yn + c(Pt – Pt e), c>0 (1)
Aggregate Demand (AD): Yt = a-bPt, a, b >0 (2)
Adaptive Expectations: Pt e = Pt-1 (3)
where Yn denotes the natural rate of output and Pte the price level expected to prevail in period t.
For the purpose of our simulation we parameterize the above AS-AD model with the following baseline model:
AD: Yt = 550 – 50Pt (4)
AS: Yt = 400+ 50 (Pt –Pte) (5)
and, Yn = 400 (6)
The purpose of this simulation is to demonstrate how the economy adjusts following a demand shock. We begin by drawing the graphs of the above aggregate demand and aggregate supply curves using Excel’s chart drawing tool. As shown in figure 1, initially the economy is at long run full employment equilibrium with real GDP at the natural rate of output of 400 and P = Pe=3.
As the first step of our simulation we need to demonstrate how a demand shock affects the AS-AD model. To accomplish this, we insert on our worksheet a ―spin button‖ from Excel’s toolbar (accessible from the Developer tab in 2007 excel or the View tab in 2003 excel). Using the linked cell property under the format control for the spin button we link cell I4 to the value of the spin button that controls the direction as well as the magnitude of the demand shock. By pressing the up or down arrow on the spin button, students can choose the demand shock. Figure 1 shows the impact of a positive demand shock of 100. When students generate a positive demand shock of 100, the AD curve shifts to the right and as shown on the worksheet and the accompanying diagram real GDP increases to 450 and the price level rises to $4. But there is no immediate adjustment of expected price.