Chapter 11, Problem 3NP

a.

To determine

To describe: The equation of IS curve, as per Keynesian closed economy theory.

Answer to Problem 3NP

The equation for IS curve will be $\text{Y=1500-1666}\text{.67r}$ .

Explanation of Solution

Given data:

Consumption	$\text{C=388+0}\text{.4}\left(\text{Y-T}\right)\text{-600r}$
Investment	$\text{I=352-400r}$
Government purchases	$\text{G=280}$
Taxes	$\text{T=300}$
Full employment output
Money supply	$\text{M=12,600}$
Real money demand	$\text{L=1,750+0}{\text{.75Y-8,750(r+π}}^{\text{e}}\text{)}$
Expected inflation	${\text{π}}^{\text{e}}\text{=0}\text{.02}$

The IS curve equation in the following manner:

  ${\text{Y=C}}^{\text{d}}{\text{+I}}^{\text{d}}\text{+G}$

Substitute values from above,

  $\begin{array}{l}\text{C=388+0}\text{.4(Y-T)-600r}\\ \text{I=352-400r}\\ \text{G=280}\\ \text{T=300}\end{array}$

Then,

  $\begin{array}{l}\text{Y=388+0}\text{.4(Y-300)-600r+352-400r+280}\\ \text{Y=388+0}\text{.4Y-120-600r+352-400r+280}\\ \text{Y-0}\text{.4Y=388-120+352-1000r+280}\\ \text{0}\text{.6Y=900-1000r}\end{array}$

Or, $\text{Y=1500-1666}\text{.67r}$

Equivalently, $\text{r=0}\text{.9-0}\text{.0006Y}$

b.

To determine

To describe: The equation of LM curve in the short run, while the price level remains fixed at ${\text{P}}_{\text{sr}}\text{=7}$ .

Answer to Problem 3NP

The equation for LM curve will be $\text{Y=300-11,666}\text{.67r}$ .

Explanation of Solution

  $\begin{array}{l}\frac{\text{M}}{\text{P}}\text{=L}\\ \frac{\text{12600}}{\text{7}}\text{=1750+0}\text{.75Y-8750(r+0}\text{.02)}\\ \text{1800=1750+0}\text{.75Y-8750r-175}\\ \text{225=0}\text{.75Y-8750r}\\ \text{0}\text{.75Y=225+8750r}\end{array}$

Or, $\text{Y=300+11666}\text{.67r}$

Equivalently, $\text{r=-0}\text{.0257143+0}\text{.0000857143Y}$

Or, $\text{r= }\frac{\text{-9}}{\text{350}}\text{+}\frac{\text{3}}{\text{35000}}\text{Y}$

c.

To determine

To describe: The new output levels, real interest rate, consumption and investment.

Answer to Problem 3NP

The new output level is $1,350$ , real interest rate is $9\%$ , consumption is $754$ and investment is $316$ .

Explanation of Solution

The equilibrium of short run is achieved at a point where the curves IS and LM intersect each other.

Now, we shall equate both the equations,

  $\begin{array}{l}\text{Y=1500-1666}\text{.67r}\\ \text{Y=300+11666}\text{.67r}\end{array}$

On solving these two equations, we get,

  $\text{r=0}\text{.09}$ and placing value of r in equation $\text{I=352-400r}$

We get,

  $\text{I=316}$

Then, we get

  $\begin{array}{l}\text{Y=1350}\\ \text{C=754}\end{array}$

d.

To determine

To describe: The new output levels, real interest rate, consumption, investment and price level for long run.

Answer to Problem 3NP

The new output level is $1400$ , real interest rate is $6\%$ , consumption is $792$ and investment is $328$ and price level for long run is $6$ .

Explanation of Solution

The real interest rate can be calculated as follows:

  $\begin{array}{l}\text{Y=1500-1666}\text{.67r}\\ \text{1400=1500-1666}\text{.67r}\end{array}$

We get,

  $\text{r=0}\text{.06}$

As the price is variable in the long run, the new LM curve can be derived as follows:

  $\begin{array}{l}\frac{\text{M}}{\text{P}}\text{=L}\\ \frac{\text{12600}}{\text{P}}\text{=1750+0}{\text{.75Y-8750(r+π}}^{\text{c}}\text{)}\\ \frac{\text{12600}}{\text{P}}\text{=1750+0}\text{.75Y-8750(r+0}\text{.02)}\\ \frac{\text{12600}}{\text{P}}\text{=1750+0}\text{.75Y-8750r-175}\\ \text{0}\text{.75Y=}\frac{\text{12600}}{\text{P}}\text{-1575+8750r}\end{array}$

The results will be as follows:

Substitute value of $\text{r=0}\text{.06}$ , in equation $\text{I=352-400r}$

We get,

  $\text{I=328}$

Substitute, given values: $\overline{\text{Y}}\text{=1400}$ and $\text{T=300}$ in equation $\text{388+0}\text{.4(Y-T)-600r}$

We get, $\text{C=792}$ and then $\text{P=6}$

e.

To determine

To describe: The velocity value in the equilibrium of long run.

Answer to Problem 3NP

The velocity value in the equilibrium of long run is $0.66$ .

Explanation of Solution

According to the quantity theory of money;

  $\text{M×V=P×Q}$

Now, substitute the value of $\text{M=12,600}$ and $\text{P=6}$ in the above equation.

We get,

  $\begin{array}{l}\text{12,600×V=6×1,400}\\ \text{V=0}\text{.66}\end{array}$

f.

To determine

To describe:

If $\text{G=350}$ and investment $\left(\text{I}\right)\text{=320}$ , price level $\left(\text{P}\right)\text{ = 6}$ and inflation rate $\text{(π)=0}\text{.02}$ , the level of taxes (T) and money supply (M), to achieve this long run equilibrium.

Answer to Problem 3NP

The level of taxes (T) is $425$ and money supply (M) is $11,550$ , will achieve this long run equilibrium

Explanation of Solution

When $\text{I = 320}$ , the real interest rate, r will be:

  $\begin{array}{l}320=352-400r\\ 400r=32\\ r=0.08\end{array}$

With the proposed conditions, the long run IS curve equation will turn out as follows:

  $\begin{array}{l}{\text{Y=C}}^{\text{d}}{\text{+I}}^{\text{d}}\text{+G}\\ \text{1400=388+0}\text{.4(1400-T)-600r+320+350}\\ \text{1400=388+560-}\text{.04T-600X0}\text{.08+320+350}\\ \text{0}\text{.4T=388+560-48+320+350-1400}\\ \text{0}\text{.4T=170}\\ \text{T=425}\end{array}$

Now,

  $\text{0}\text{.75Y=}\frac{\text{M}}{\text{6}}\text{-1575+8750(0}\text{.08)}$

Substitute $\text{Y=1400}$ we get,

  $\begin{array}{l}\text{1925=}\frac{\text{M}}{\text{6}}\\ \text{M=11,550}\end{array}$