Question

Consider an economy described by the following:

$$\begin{gathered} \overline{C}=\backslash (3.25trillion \\ \overline{I}=\backslash )1.3trillion \\ \overline{G}=\backslash (3.5trillion \\ \overline{T}=\backslash )3.0trillion \\ \overline{NX}=-\$1.0trillion \\ \overline{f}=1 \\ mpc=0.75 \\ d=0.3 \\ x=0.1 \\ l=1 \\ \overline{r}=1 \end{gathered}$$

a. Derive expressions for the MP curve and the AD curve.

b. Assume that $\pi =1$. Calculate the real interest rate, the equilibrium level of output, consumption, planned investment, and net exports.

c. Suppose the Fed increases r to r = 2. Calculate the real interest rate, the equilibrium level of output, consumption, planned investment, and net exports at this new level of r.

d. Considering that output, consumption, planned investment, and net exports all decreased in part (c), why might the Fed choose to increase r?

Short answer

(a) $Y=16.4-160\mathrm{\pi }$

(b) Real interest rate - 2%, Output level -14.8, Consumption - 12.1, Planned investment - 0.4, Net exports -0.2

(c) Y= 13.2, r= 3%,C =10.9, I=0.1,NX = -1.3

(d) To reduce inflation

Step-by-step solution

Step 1.Given Information

$$\begin{gathered} \overline{C}=\$3.25trillion \\ \overline{I}=\$1.3trillion \\ \overline{G}=\$3.5trillion \\ \overline{T}=\$3.0trillion \\ \overline{NX}=-\$1.0trillion \\ \overline{f}=1 \\ mpc=0.75 \\ d=0.3 \\ x=0.1 \\ \lambda =1 \\ \overline{r}=1 \end{gathered}$$

Step 2. Explanation Part (a)

(a) The MP curve shows the different points at which the money market is in equilbrium. The MP curve can be expressed as,

$$\begin{gathered} r+\pi =+\pi +\theta \times (\pi –\pi *) \\ r=\overline{r}+\theta \times (\pi –\pi *) \\ r=0.02+(\pi –0.01) \\ r=0.01+\pi \end{gathered}$$

The IS curve can be expressed as,

$$\begin{gathered} Y=C+I+\overline{G}+NX: \\ Y=1+0.75\times Y+1–30\times r+3.5–1–10\times r \\ 0.25\times Y=4.5–40\times r \\ Y=18–160\times r \end{gathered}$$

Combining the above two equations can give the expression for the aggregate demand curve,

$$\begin{gathered} Y=18–160\times (0.01+\pi ) \\ Y=18–1.6–160\times \pi \\ Y=16.4–160\times \pi \end{gathered}$$

Step 3. Explanation Part (b)

From the AD curve,

$$\begin{gathered} Y=16.4–160\times \pi \\ Y=16.4–160\times 0.01 \\ Y=16.4–1.6 \\ Y=14.8 \end{gathered}$$

From the MP curve

$$\begin{gathered} r=0.01+\pi \\ r=0.01+0.01 \\ r=0.02 \end{gathered}$$

The consumption level can be obtained as,

$$\begin{gathered} C=\overline{C}+mpc(3.25Y-T) \\ C=3.25+0.75(14.8-3) \\ C=12.1 \end{gathered}$$

The planned investment level can be obtained as,

$$\begin{gathered} I=\overline{I}-d(r+\overline{f}) \\ I=1.3-0.3(2+1) \\ I=0.4 \end{gathered}$$

The net exports can be obtained as,

$$\begin{gathered} NX=\overline{NX}-xr \\ NX=-1-0.2 \\ NX=-1.2 \end{gathered}$$

Step 4. Explanation Part (c)

From the MP curve,

$r=3\%$

From the IS curve,

$$\begin{gathered} Y=14.8-1.6\mathrm{\pi } \\ \mathrm{Y}=13.2 \end{gathered}$$

Consumption can be obtained as,

$$\begin{gathered} C=\overline{C}+mpc(3.25Y-T) \\ C=3.25+0.75(13.2-3) \\ C=10.9 \end{gathered}$$

The planned investment can be obtained as,

$$\begin{gathered} I=\overline{I}-d(r+\overline{f}) \\ I=1.3-0.3(3+1) \\ I=0.1 \end{gathered}$$

The net exports can be obtained as,

$$\begin{gathered} NX=\overline{NX}-xr \\ NX=-1-0.1\left(3\right) \\ NX=-1.3 \end{gathered}$$

Step 5. Explanation part (d)

The central bank might have increased the inflation rate to tackle the inflationary pressure. In case of inflation, contractionary monetary policy is adopted which aims to reduce the money supply in the economy. One of the ways to do so is by increasing the interest rate.