Question

Consider the economy described in Applied Problem 23.

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

b. Assume that $\pi =2$. What are the real interest rate and the equilibrium level of output?

c. Suppose government spending increases to $4 trillion. What happens to equilibrium output?

d. If the Fed wants to keep output constant, then what monetary policy change should it make?

Short answer

Part (a) MP- $r=0.01+\mathrm{\pi }$; AD - $Y=16.4-160\mathrm{\pi }$

Part (b) r = 3%, Y= 13.2

Part (c) $Y=20-160r$

Part (d) Adpot a contractionary monetary policy

Step-by-step solution

Step 1.Given Information

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

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,

$$\begin{gathered} Y=16.4–160\times \pi \\ Y=16.4–160\times 0.02 \\ Y=16.4–3.2 \\ Y=13.2 \end{gathered}$$

From the MP curve

$$\begin{gathered} r=0.01+\pi \\ r=0.01+0.02 \\ r=0.03 \end{gathered}$$

Step 4. Explanation Part c.

Using the equation for IS curve,

$$\begin{gathered} Y=C+I+\overline{G}+NX: \\ Y=1+0.75Y+1–30r+4–1–10r \\ 0.25Y=5–40r \\ Y=20–160r \end{gathered}$$

Step 5. Explanation part d.

If the central bank wants to keep the output level constant, it should adopt a contractionary monetary policy. This would reduce money supply and this inflatioary pressure.