Question

Suppose the monetary policy curve is given by $r=1.5+0.75\pi$, and the IS curve is given by $Y=13-r$.

a. Calculate an expression for the aggregate demand curve.

b. Calculate the real interest rate and aggregate output when the inflation rate is 2%, 3%, and 4%.

c. Draw graphs of the IS, MP, and AD curves, labeling the points from part (b) on the appropriate graphs.

Short answer

(a) The Aggregate Demand curve equation is $Y=11.5-0.75\pi$

(b) Output: 10, 9.25,8.5; Interest rate - 3%, 3.75%, 4.5%

(c)

Step-by-step solution

Concept Preface

Monetary course is applied by the central bank to check the liquidity of capitalist from frugality to convert the skimping to stablecondition.This is done through operation of interest rate and the plutocrat force.
Aggregate claim is the complete claim of commodities and graces in an frugality. Aggregate claim is the sum of consumption, blockade, administration charge and net exports.
affectedness is the overall increase in general price position of an frugality. affectedness causes increase in the price of goods and services which decreases exports and fall in aggregate demand.

Step 2. Explanation of  solution

Given,

Monetary policy curve is $r=1.5+0.75\pi$and IS Curve is $\mathrm{Y}=13-\mathrm{r}$.

A.

In equilibrium condition IS curve intersects the MP curve which implies IS is equal to MP.

Substitute the value of $r$in IS curve equation

$$\begin{gathered} Y=13-(1.5+0.75\pi ) \\ y=13-1.5-0.75\pi \\ Y=11.5-0.75\pi \end{gathered}$$

Hence, the Aggregate Demand curve equation is $\mathrm{Y}=11.5-0.75\pi$.

Step 3. Explanation of Solution

B.

Given,

Monetary policy curve$\mathrm{r}=1.5+0.75\pi$

Aggregate Demand Curve$\mathrm{Y}=11.5-0.75\pi$

Substitute value of inflation $2\%,3\%,and4\%$in monetary policy curve equation and aggregate demand curve equation.

:Explanation of Solution 

C.

Given:

In the MPwindillustration,
$X$axis represents affectation rate.$Y$axisrepresentsrealinterestrate.
MP wind shows the positive relationship between real interest rate and affectation rate. MP wind pitches overhead, with increase in affectation rate real interest rate also increase.

In the Aggregate demand illustration
$X$ axis represents the aggregate affair
$Y$axis represents the affectation rate.
Aggregatedemandwindshows therelationshipbetween aggregateaffairandaffectationrate. Thetotal
demand Wind shows the negative relationship which means with the rise in affectation aggregate affair cascade.

In the ISwindillustration
$X$ axis represents the aggregate affair
$Y$ axis represents the real interest rate
IS wind shows the relationship between the real interest rate and aggregate affair. There's negative relationship between real interest rate and aggregate affair which means that with rise in real interest rate aggregate affair cascade.