Chapter 13, Problem 15E

To determine

(a)

To compute:

The maximum increase in the money supply, if the reserve requirement is $20$ percent.

Answer to Problem 15E

If the reserve requirement is $20$ percent, the maximum increase in money supply is $\$5,000$.

Explanation of Solution

Given information:

The banking system has vault cash of $\$1,000$, deposits at the Fed are of $\$2,000$ and demand deposits are of $\$10,000$.

As in the balance sheet, the total assets are equal to total liabilities. Therefore, the amount to be taken is $\$7,000$.

$\begin{array}{c}\text{Total}\text{assets}=\text{Vault}\text{cash}+\text{Deposits}\text{in}\text{Fed}+\text{Loans}\\ =\$1,000+\$2,000+\$7,000\\ =\$10,000\end{array}$

Total liabilities are of $10,000.

Calculation for increase in money supply:

$\begin{array}{c}\text{Increase}\text{in}\text{money}\text{supply}=\text{Deposit}\text{Expansion}\text{Multiplier}\times \text{Excess}\text{Reserve}\\ =\text{5}\times \$1,000\\ =\$5,000\end{array}$

Working Note:

Calculation for the required reserve:

$\begin{array}{c}RR=r\times D\\ =\frac{1}{20}\times 10,000\\ =\$2,000\end{array}$

Calculation for the excess reserve by calculating total legal reserve:

  $\begin{array}{c}\text{Legal}\text{Reserve}=\text{Vault}+\text{Deposit}\\ =\$1,000+\$2,000\\ =\$3,000\end{array}$

Now, calculation of excess reserve:

$\begin{array}{c}\text{Excess}\text{Reserve}=\text{Legal}\text{Reserve}-\text{Required}\text{Reserve}\\ =\text{\$3,000}-\$2,000\\ =\$1,000\end{array}$

Calculation for the deposit expansion multiplier:

  $\begin{array}{c}\text{Deposit}\text{Expansion}\text{Multiplier}=\frac{\text{1}}{\text{Reserve}\text{Requirement}}\\ =\frac{1}{20}\times 100\\ =5\end{array}$

Economics Concept Introduction

Required reserve:

It refers to a certain amount of cash from the deposit that a bank needs to keep according to the guidelines of the central bank.

Required reserve is calculated by,

$RR=r\times D$

Here, RR is reserve, r is percentage of required reserve and D is the total amount in deposits.

Excess reserve:

It refers to the amount left after separating the required reserve ratio of the financial institution.

$\text{ER}=\text{Cash}\text{Reserve}-\text{Required}\text{Reserve}$

To determine

(b)

To compute:

The excess reserves of the banking system.The amount by which the money supply is increased, if the money purchased by Fed is $\$100$ worth of the government bonds from private bond dealers.

Answer to Problem 15E

The excess reserve of the banking system after Fed buys $100 bonds $900.

The maximum increase in money supply after the Fed buys $100 bonds is $4,500.

Explanation of Solution

Given information:

The banking system has vault cash of $\$1,000$, deposits at the Fed of $\$2,000$ and demand deposits of $\$10,000$.

According to the given information, the change in balance sheet after the Fed buys the $\$100$ worth bonds are as follows:

Particulars	Amount ($)	Particulars	Amount ($)
Vault Cash	$\$900$	Demand deposits	$\$10,000$
Deposit in Fed	$2,000
Bonds	$100
Loan	$\$7,000$
Total	$\$10,000$		$\$10,000$

Table (1)

Calculation for excess reserve:

$\begin{array}{c}\text{Excess}\text{Reserve}=\text{Legal}\text{Reserve}-\text{Required}\text{Reserve}\\ =\$2,900-\$2,000\\ =\$900\end{array}$

Therefore, the excess reserve would be $900.

Calculation for increase in money supply:

$\begin{array}{c}\text{Increase}\text{in}\text{money}\text{supply}=\text{Deposit}\text{Expansion}\text{Multiplier}\times \text{Excess}\text{Reserve}\\ =\text{5}\times \$900\\ =\$4,500\end{array}$

The maximum increase in money supply after the Fed buys $\$100$ bonds is $\$4,500.$

Working Note:

Calculation for the required reserve.

$\begin{array}{c}RR=r\times D\\ =\frac{1}{20}\times 10,000\\ =\$2,000\end{array}$

Calculation of the excess reserve by determining total legal reserve.

  $\begin{array}{c}\text{Legal}\text{Reserve}=\text{Vault}+\text{Deposit}\\ =\$900+\$2,000\\ =\$2,900\end{array}$

To calculate maximum increase in the money supply, calculate the deposit expansion multiplier.

  $\begin{array}{c}\text{Deposit}\text{Expansion}\text{Multiplier}=\frac{\text{1}}{\text{Reserve}\text{Requirement}}\\ =\frac{1}{20}\times 100\\ =5\end{array}$

Economics Concept Introduction

Required reserve:

It refers to the certain amount of cash from the deposit that a bank needs to keep according to the guidelines of the central bank.

Required reserve is calculated by,

$RR=r\times D$

Here, RR is reserve, r is percentage of required reserve and D is the total amount in deposits.

Excess reserve:

It refers to the amount left after separating the required reserve ratio of the financial institution.

$\text{ER}=\text{Cash}\text{Reserve}-\text{Required}\text{Reserve}$