Question

Assume that the monetary policy curve is given by$r=1.5+0.75\mathrm{\pi }.$

a. Calculate the real interest rate when the inflation rate is$2\%,3\%,and4\%.$

b. Draw a graph of the MP curve, labeling the points from part (a).

c. Assume now that the monetary policy curve is given by $r=2.5+0.75\mathrm{\pi }.$Does the new monetary policy curve represent an autonomous tightening or loosening of monetary policy?

d. Calculate the real interest rate when the inflation rate is$2\%,3\%,and4\%,$ and draw the new MP curve, showing the shift from part (b).

Short answer

a. Calculate the real interest rate when the inflation rate is$2\%,3\%,4\%is3.0\%,3.75\%,4.5\%.$$\text{b.Derivation of MP curve with given inflation point is shown in the figure below:}$

c. The new monetary policy curve $r=1.5+0.75\mathrm{\pi }$shows an autonomous tight of the monetary policy to lower the rate of inflation.

d. The graph below shows the Derivation of MP curve with new given monetary policy curve. Where axis represents increasing real charge per unit and$y$ represents increasing rate. The upward slope of the MP curve shows the reaction of the financial organization to higher rate by increasing the important interest rates.

Step-by-step solution

Concept Introduction

Rate refers to the speed at which prices of the economy rises over time leading to a fall within the purchasing power. it's being calculated using the increase within the price of an outlined basket of product. The financial institution always attempts to confine inflation and maintain a strategic distance from deflation so as to stay the economy balanced. The real rate of interest is that the rate of interest an investor, saver or lender receives within the wake of taking under consideration inflation. It is depicted more formally by the Fisher equation, which expresses that the important rate of interest is roughly the nominal rate minus the rate.

Explanation of Solution (Part a)

Given monetary policy curve as $r=1.5+0.75\pi$

Where,

$-r$is the real interest rate

$-\mathrm{\pi }$is inflation rate.

When $\mathrm{\pi }is2$:

$r=1.5+0.75\left(2\right)$

$=1.5+1.5$

$=3.0\%$

$$\begin{gathered} When\mathrm{\pi }\mathrm{is}3: \\ \mathrm{r}=1.5+0.75\left(3\right) \\ =1.5+2.25 \\ =3.75\% \end{gathered}$$

$$\begin{gathered} When\mathrm{\pi }\mathrm{is}4: \\ \mathrm{r}=1.5+0.75\left(4\right) \\ =1.5+3.0 \\ =4.5\% \end{gathered}$$

Explanation of Solution (Part b)

In the above graph, $x$axis represents real interest rate and$y$ axis represents inflation rate. The upward slope of the MP curve shows the reaction of the central bank to higher inflation rate by increasing the real interest rates.

Explanation of Solution (Part c)

The new monetary policy curve $r=2.5+0.75\pi$shows an autonomous tight of the monetary policy to lower the rate of inflation.

As the increased rate of inflation also increased the important charge per unit causing the monetary policy curve move upward thereby helping the economy to contract and inflation to fall.

Explanation of Solution (Part d)

Given monetary policy curve as

Where,

$r$is the real interest rate

$\mathrm{\pi }$is inflation rate.

$When\mathrm{\pi }\mathrm{is}2:$

$$\begin{gathered} r=1.5+0.75\left(2\right) \\ =1.5+1.5 \\ =3.0\% \end{gathered}$$

$$\begin{gathered} When\mathrm{\pi }\mathrm{is}3: \\ \mathrm{r}=1.5+0.75\left(3\right) \\ =1.5+2.25 \\ =3.75\% \end{gathered}$$

$$\begin{gathered} When\mathrm{\pi }\mathrm{i}4: \\ \mathrm{r}=1.5+0.75\left(4\right) \\ =1.5+3.0 \\ =4.5\% \end{gathered}$$