Chapter 5, Problem 3PA

 (a)

To determine

The velocity of money.

Explanation of Solution

An expression for the velocity of money can be derived using the quantity equation.

$\text{M}\times \text{V}=\text{P}\times \text{Y}$

The quantity equation can be re-written as follows:

$\frac{\text{M}}{\text{P}}=\frac{\text{Y}}{\text{V}}$ (1)

Here, M is the quantity of money and P is the price of one unit of output. Therefore, $\frac{\text{M}}{\text{P}}$ indicates the real money supply, which is equal to the money demand. Therefore, an expression for velocity of money can be derived as follows:

$\begin{array}{c}\frac{\text{Y}}{\text{V}}=\frac{.2\text{Y}}{i^{1/2}}\\ .2\text{V}=i^{1/2}\\ \text{V}=2i^{1/2}\\ =5i^{1/2}\end{array}$

Therefore, the velocity of money is $\text{V}=5i^{1/2}$.

This velocity of money has positive relation with nominal interest rate because when nominal interest rate is high then, people will hold less money. As a result, the money that people hold are used more often and velocity increases.

Economics Concept Introduction

Velocity of money: Income velocity of money describes about the number of times a dollar bill enters someone's income in a given period of time.

 (b)

To determine

The velocity of money.

Explanation of Solution

The value of velocity of money can be calculated using the expression of velocity, which is found in part (a).

$\text{V}=5i^{1/2}$.

Here, ‘i’ is the nominal rate, if it is 4 percent, then the value of velocity of money can be calculated as follows:

$\begin{array}{c}\text{V}=5i^{1/2}\\ =5\times 4^{1/2}\\ =10\end{array}$

Therefore, if the nominal rate is 4 percent then, the velocity of money is 10 percent.

Economics Concept Introduction

Velocity of money: Income velocity of money describes about the number of times a dollar bill enters someone's income in a given period of time.

 (c)

To determine

The price level (P).

Explanation of Solution

The value of price level can be calculated using Equation (1).

Re-write the equation as follows:

$\frac{\text{M}}{\text{P}}=\frac{.2\text{Y}}{i^{.1/2}}$ (2)

Now, substitute the respective vales into Equation (2).

$\begin{array}{c}\frac{1,200}{\text{P}}=\frac{\left(.2\times 1,000\right)}{4^{.1/2}}\\ \text{P}=\frac{1,200}{0.2\times 1,000}\times 4^{0.5}\\ \text{P}=\frac{12}{2}\times 2\\ =12\end{array}$

Therefore, the price level is $12.

 (d)

To determine

The fisher effect on the nominal interest rate.

Explanation of Solution

The fisher effect describes that 1 percent increase in the rate of inflation turn causes a 1 percent increase in the nominal interest rate. This one-to-one relationship is called the Fisher effect. Therefore, an increase of expected inflation rate by 5% also causes a 5% increase in the nominal interest rate where the initial nominal interest rate is 4 percent, therefore, according to Fisher effect, the new nominal interest rate is 9% $\left(5\%+4\%\right)$.

Economics Concept Introduction

Nominal interest rate: Nominal interest rate is the interest rate that the bank pays.

 (e)

To determine

The new velocity of money.

Explanation of Solution

The velocity of money can be calculated using the expression of velocity which is found in part (a).

$\text{V}=5i^{1/2}$.

Here, ‘i’ is the nominal rate and the new value of nominal interest rate is 9 percent. Therefore, the value of velocity of money can be calculated as follows:

$\begin{array}{c}\text{V}=5i^{1/2}\\ =5\times 9^{1/2}\\ =15\end{array}$

Therefore, if the nominal rate is 9 percent then, the velocity of money is 15 percent.

Economics Concept Introduction

Nominal interest rate: Nominal interest rate is the interest rate that the bank pays.

Velocity of money: Income velocity of money describes about the number of times a dollar bill enters someone's income in a given period of time.

 (f)

To determine

The new price level (P).

Explanation of Solution

The value of price level can be calculated using Equation (2) described in part (c).

Substitute the respective vales into Equation (2).

$\begin{array}{c}\frac{1,200}{\text{P}}=\frac{\left(.2\times 1,000\right)}{9^{.1/2}}\\ \text{P}=\frac{1,200}{0.2\times 1,000}\times 9^{0.5}\\ \text{P}=\frac{12}{2}\times 3\\ =18\end{array}$

Therefore, the new price level is $18. Here, when the nominal interest rate increases from 4 percent to 9 percent the price level also increases from $12 to $18 because the increase in nominal interest rate also increases the opportunity cost of money and thereby, reduces demand for real money balances.

 (g)

To determine

The supply of money.

Explanation of Solution

The value of price level (P) is keep as $12, the nominal interest rate (i) is $9, and the output (Y) is 1,000.

Now, the supply of money can be calculated using Equation (2) as described in part (c).

$\begin{array}{c}\frac{\text{M}}{\$12}=\frac{\left(.2\times 1,000\right)}{9^{.1/2}}\\ \text{M}=\frac{\left(.2\times 1,000\right)}{9^{.1/2}}\times \$12\\ =200\times \$4\\ =\$800\end{array}$

Therefore, the new money supply is $$800$.