Chapter 13, Problem 1TY

To determine

To Describe: The quantum of money supply for the reserve ratio.

Answer to Problem 1TY

The size of money supply for reserve ratio of $10\text{ percent}$ , $12\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\text{ percent}$ and $16\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\text{ percent}$ are $\$600,000,000,000$ , $\$480,000,000,000$ and $\$359,928,014,397$ respectively.

Explanation of Solution

The bank has $\$120\text{ billion}$ in cash, of which half is being held back as required reserves, which means that the required reserves is $\frac{\$120\text{ billion}}{2}=\$60\text{ billion}\text{.}$

By using the following formula, the size of money can be calculated:

$Money\mathrm{supply}=\frac{1}{m}\times RR$............. (eq: 1)

Where RR is the required reserves held by bank.

For $10\text{ percent}$ required reserve ratio, the size of money supply can be calculated by substituting values in equation (1):

$\begin{array}{l}Money\mathrm{supply}=\frac{1}{0.10}\times 60,000,000,000\\ \text{ = }600,000,000,000\end{array}$

Therefore, the size of money supply for reserve ratio of $10\text{ percent}$ is $\$600,000,000,000$ .

Similarly, for $12\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\text{ percent}$ required reserve ratio, the size of money supply can be calculated by substituting values in equation (1):

$\begin{array}{l}Money\mathrm{supply}=\frac{1}{0.125}\times 60,000,000,000\\ \text{ = 480},000,000,000\end{array}$

Therefore, the size of money supply for reserve ratio of $12\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\text{ percent}$ is $\$480,000,000,000$ .

Similarly, for $16\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\text{ percent}$ required reserve ratio, the size of money supply can be calculated by substituting values in equation (1):

$\begin{array}{l}Money\mathrm{supply}=\frac{1}{0.1667}\times 60,000,000,000\\ \text{ = 359,928,014,397}\end{array}$

Therefore, the size of money supply for reserve ratio of $16\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\text{ percent}$ is $\$359,928,014,397$ .

Economics Concept Introduction

Introduction: Reserves are assets held with bank in order to cater the requirements of transactions done daily, which includes fund withdrawals, fund transfers between banks, to clear collection checks etc.