Chapter 14, Problem 3NP

a.

To determine

To describe:

The reserve deposit ratio, the money multiplier and the money supply, and the real output Y at which a real interest rate of $\text{0}\text{.10}$ clears the asset market.

Answer to Problem 3NP

The reserve deposit ratio is $20\%$ , the money multiplier is $2.33$ and the money supply is $140$ . Real output Y is $282$ .

Explanation of Solution

Given data,

$\text{res=0}\text{.4-2r}$

Currency deposit ratio is $0.4$

Price level fixed at $1.0$

Monetary base is $60$

Real quantity of money demanded is $\text{L}\left(\text{Y,i}\right)\text{=0}\text{.5Y-10i}$

If $\text{r = i = 0}\text{.10}$

Expected inflation is zero

Nominal interest rate and real interest rate is equal.

Substitute the values from given data in the formula, we get:

$\begin{array}{l}\text{res=0}\text{.4-2r}\\ \text{=0}\text{.4-2×0}\text{.10}\\ \text{=0}\text{.2}\end{array}$

And,

Formula used to calculate money multiplier is given below:

$\text{MoneyMultiplier=}\frac{\text{c+1}}{\text{c+res}}$

Substitute the value of c = 0.4 and res = 0.2, in the formula, we get:

MoneyMultiplier $=\frac{c+1}{c+res}$

$=\frac{0.4+1}{0.4+0.2}$

$=\frac{1.4}{0.6}$

$=2.33$

Now, the calculation of money supply is as follows:

Money Supply $=\left(\frac{c+1}{c+res}\right)\times$ Base

$=2.33\times 60$

$=140$

And, calculation of real output will be done as follows:

Here,

M^s = 140

$\text{L}\left(\text{Y,i}\right)\text{=0}\text{.5Y-10i}$

$\text{r = i = 0}\text{.10}$

Now, substitute the above value to the equation,

$\begin{array}{l}{\text{M}}^{\text{s}}\text{=L}\left(\text{Y,i}\right)\text{=0}\text{.5Y-10i}\\ \text{140=0}\text{.5Y-10×0}\text{.10}\\ \text{140=0}\text{.5Y-1}\\ \text{0}\text{.5Y=141}\\ \text{Y=282}\end{array}$

Thus, the money supplier will be $140$ , and the real output will be $282$ .

Economics Concept Introduction

Introduction: The IS-LM model is an extended Keynesian model, in this graphic representation of IS-LM curve that helps in maintaining balance in the economy by establishing equilibrium between money supply and interest rates. This model is very useful macroeconomic tool for analysis of the money market and analysis of the goods market, which together helps in determining the equilibrium levels of interest rates and output in the economy in a given prices. It presents the set of all possible combinations of the GDP and interest rates, where the money supply and demand matches. Where, IS stands for Investment Savings and LM stands for Liquidity Money.

b.

To determine

To describe:

When. $\text{r = i = 0}\text{.05}$ , find the reserve deposit ratio, the money multiplier and the money supply, at what real output Y, a real interest rate of $\text{0}\text{.10}$ clear the asset market.

Answer to Problem 3NP

The reserve deposit ratio is $30\%$ , the money multiplier is $2$ , the money supply is $120$ and Real output Y is $241$ .

Explanation of Solution

The formula to calculate reserve deposit ratio is as under:

$\text{res=0}\text{.4-2r}$

Given data,

$\text{r = i = 0}\text{.05}$

Substitute value r = 0.5, we get

$\begin{array}{l}\text{res=0}\text{.4-2r}\\ \text{=0}\text{.4-2×0}\text{.05}\\ \text{=0}\text{.4-0}\text{.10}\\ \text{=0}\text{.3}\end{array}$

And, Money multiplier is calculated using the following formula:

$\text{MoneyMultiplier=}\frac{\text{c+1}}{\text{c+res}}$

Substitute the value of c = 0.4 and res = 0.3, as calculated above.

$\begin{array}{l}\text{=}\frac{\text{0}\text{.4+1}}{\text{0}\text{.4+0}\text{.3}}\\ \text{=}\frac{\text{1}\text{.4}}{\text{0}\text{.7}}\\ \text{=2}\end{array}$

Now, substitute the value of money multiplier i.e. 2, in the formula of money supply:

$\text{MoneySupply=}\left(\frac{\text{c+1}}{\text{c+res}}\right)\text{×Base}$

$\begin{array}{l}\text{=2×60}\\ \text{=120}\end{array}$

And,

The formula to Calculate the real output would be done as under:

${\text{M}}^{\text{s}}\text{=L}\left(\text{Y,i}\right)$

given,

M^s = 120

i = 0.05

$\begin{array}{l}\text{120=0}\text{.5Y-10×0}\text{.05}\\ \text{120=0}\text{.5Y-0}\text{.5}\\ \text{0}\text{.5Y=120}\text{.5}\\ \text{Y=241}\end{array}$

Thus, the money supplier will be $120$ , and the real output will be $241$ .

Economics Concept Introduction

Introduction: The IS-LM model is an extended Keynesian model, in this graphic representation of IS-LM curve that helps in maintaining balance in the economy by establishing equilibrium between money supply and interest rates. This model is very useful macroeconomic tool for analysis of the money market and analysis of the goods market, which together helps in determining the equilibrium levels of interest rates and output in the economy in a given prices. It presents the set of all possible combinations of the GDP and interest rates, where the money supply and demand matches. Where, IS stands for Investment Savings and LM stands for Liquidity Money.

c.

To determine

To describe:

If $\text{r = i = 0}\text{.054}$ , the output Y that clears the asset market clear in the case if the reserve deposit ratio is fixed at the value found in part (a) and is not affected by interest rates.

Answer to Problem 3NP

The asset market is clear in the case at output Y of $281$ .

Explanation of Solution

In this case, the multiplier is unchanged from part a, which is at $2.33$ , so the money supply is unchanged at $140$ .

Given data,

M=140

i = 0.05

Substitute the above values in the equation:

$\frac{\text{M}}{\text{P}}\text{=L }$ Gives,

$\begin{array}{l}\frac{\text{140}}{\text{1}}\text{=0}\text{.5Y-(10×0}\text{.05)}\\ \text{140+0}\text{.5=0}\text{.5Y}\\ \text{Y=281}\end{array}$

Economics Concept Introduction

Introduction: The IS-LM model is an extended Keynesian model, in this graphic representation of IS-LM curve that helps in maintaining balance in the economy by establishing equilibrium between money supply and interest rates. This model is very useful macroeconomic tool for analysis of the money market and analysis of the goods market, which together helps in determining the equilibrium levels of interest rates and output in the economy in a given prices. It presents the set of all possible combinations of the GDP and interest rates, where the money supply and demand matches. Where, IS stands for Investment Savings and LM stands for Liquidity Money.

d.

To determine

To examine:

Whether the impact on LM curve is flatter or steeper when the reserve deposit ratio depends on the real interest rate than when it is fixed.

Answer to Problem 3NP

If the reserve deposit ratio is unaffected by the real interest rate, the LM curve is steeper than when it is affected by the real interest rate.

Explanation of Solution

Supposing there is a reduction in the interest rates, it will lead to lowering of the reserves for the banks. This means, a high reserve ratio will lead to lowering of money multiplier and thereby reducing the nominal money supply. Therefore, the LM curve will be steeper when it is unaffected by the real interest rate more than that of when affected by the real interest rate.

Economics Concept Introduction

Introduction: The IS-LM model is an extended Keynesian model, in this graphic representation of IS-LM curve that helps in maintaining balance in the economy by establishing equilibrium between money supply and interest rates. This model is very useful macroeconomic tool for analysis of the money market and analysis of the goods market, which together helps in determining the equilibrium levels of interest rates and output in the economy in a given prices. It presents the set of all possible combinations of the GDP and interest rates, where the money supply and demand matches. Where, IS stands for Investment Savings and LM stands for Liquidity Money.