Question

Consider an economy described by the following:

C = \(4 trillion

I = \)1.5 trillion

Short answer

Aggregate output with $\pi =2$is $\$86.25$trillion and $\pi =4$is $\$115$trillion.

Step-by-step solution

:Concept Preface 

Introduction Monetary course is applied by the halfway bank to check the liquidity of moneybags from scrimping to bring the frugality to sound shape. This is served through the care of the claim rate and the moneybags stock.

Calculation

Given,

$\overline{C}=\$4$trillion

$\overline{I}=\$1.5$trillion

$\overline{G}=\$3$trillion

$\overline{T}=\$3$trillion

$\overline{NX}=\$1.0$trillion

$$\begin{gathered} \overline{f}=0 \\ mpc=0.8 \\ d=0.35 \\ x=0.15 \\ \lambda =0.5 \\ \overline{r}=2 \end{gathered}$$

Equation of MP curve can be written as follows:

$r=\overline{r}+\lambda \pi$

Here,

$\overline{r}$is the autonomous real interest rate.

$\lambda$is the responsiveness of real interest rate to the inflation rate.

According to the given case, the equation of the MP curve is:

$r=2+0.5\pi$

Equation of AD curve can be written as follows:

$Y=|\overline{C}+\overline{I}-d\overline{f}+\overline{G}+\overline{NX}-mpc\times \overline{T}|\times \frac{1}{1-mpc}-\frac{d+x}{1-mpc}\times (\overline{r}+\lambda \pi )$

According to the given case, the equation of AD curve is:

$Y=\left(\begin{array}{l}\mid \$4\text{trillion}+\$1.5\text{trillion}-0+\$3.0\text{trillion}+\$1\text{trillion}\\ -0.8\times \$3\text{trillion}\mid \times \frac{1}{1-0.8}-\frac{0.35+0.15}{1-0.8}\times (2+0.5\pi )\end{array}\right)$

Calculation 

Explanation of Solution

Given,

$$\begin{gathered} \overline{C}=\$4trillion \\ \overline{I}=\$1.5trillion \\ G=\$3trillion \\ T=\$3trillion \\ \overline{NX}=\$1.0trillion \\ f=0 \\ mpc=0.8 \\ d=0.35 \\ x=0.15 \\ \lambda =0.5 \\ \overline{r}=2 \end{gathered}$$

According to the given case, the equation of MP curve is:

$r=2+0.5\pi \dots ..\left(\mathrm{I}\right)$

Real interest rate with $\pi =2$:

Substitute $\pi =2$in equation (I),

$$\begin{gathered} r=2+0.5\pi \\ =2+0.5\left(2\right) \\ r=3 \end{gathered}$$

Real interest rate with $\pi =4$:

Substitute$\pi =4$in equation (I),

$$\begin{gathered} r=2+0.5\pi \\ =2+0.5\left(4\right) \\ r=4 \end{gathered}$$

Calculation 

Thus, real interest rate with$\pi =2$is $3\%$and $\pi =4$is $4\%$.

According to the given case, the equation of AD curve is:

localid="1647546119339" $Y=\left(\begin{array}{l}\mid \$4\text{trillion}+\$1.5\text{trillion}-0+\$3.0\text{trillion}+\$1\text{trillion}\\ -0.8\times \$3\text{trillion}\mid \times \frac{1}{1-0.8}-\frac{0.35+0.15}{1-0.8}\times (2+0.5\pi )\end{array}\right)\dots .\left(\text{II}\right)$

Aggregate outputwith$\pi =2$:

Substitute $\pi =2$in equation (II),

localid="1647546628791" $Y=\left(\begin{array}{l}\mid \$4\text{trillion}+\$1.5\text{trillion}-0+\$3.0\text{trillion}+\$1\text{trillion}\\ -0.8\times \$3\text{trillion}\mid \times \frac{1}{1-0.8}-\frac{0.35+0.15}{1-0.8}\times (2+0.5\pi (2)\end{array}\right)\dots .\left(\text{II}\right)$

localid="1647546553745" $$\begin{gathered} =\left(|\$11.5trillion|\times \frac{1}{0.2}-\frac{0.5}{0.2}\times \left(3\right)\right) \\ =\left(\$11.5trillion\times \$7.5trillion\right) \\ =\$86.25trillion \end{gathered}$$

Aggregate output with$\pi =4$:

Substitute $\pi =4$in equation (II),

localid="1647546643930" $Y=\left(\begin{array}{l}\mid \$4\text{trillion}+\$1.5\text{trillion}-0+\$3.0\text{trillion}+\$1\text{trillion}\\ -0.8\times \$3\text{trillion}\mid \times \frac{1}{1-0.8}-\frac{0.35+0.15}{1-0.8}\times (2+0.5\pi (4)\end{array}\right)\dots .\left(\text{II}\right)$

$$\begin{gathered} =\left(|\$11.5trillion|\times \frac{1}{0.2}-\frac{0.5}{0.2}\times \left(4\right)\right) \\ =\left(\$11.5trillion\times \$10trillion\right) \\ =\$115trillion \end{gathered}$$

Thus, aggregate output with $\pi =2$is $\$86.25$trillion and $\pi =4$is $\$115$trillion.

MP curve andd AD curve