✏️ Examples

✏️ Change in MS vs New MS

❔ Suppose in the republic of Cantabridgia the public holds $5M of cash and there are $10M of deposits. $\text{R}=0\%$ and $\text{E}=20\%$. The Cantabridgia central bank (their Fed) buys $1M of bonds. What is the change in the money supply? What is the new money supply?

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$Δ\text{Total Deposits} = \text{Initial Deposit} \times \frac{1}{\text{R}+\text{E}}$
$Δ\text{Total Deposits} = \$1\text{M} \times \frac{1}{0\%+20\%} = \$1\text{M} \times 5 = \$5\text{M}$
$Δ\text{MS} = Δ\text{Deposits} + Δ\text{Cash Held by Public}$
$Δ\text{MS} = \$5\text{M} + \$0 = \$5\text{M}$
$\text{Old MS} = \text{TotalDeposits} + \text{CashHeldByPublic} = \$10\text{M} + \$5\text{M}$
$\text{New MS} = \text{Old MS} + Δ\text{MS} = \$15\text{M} + \$5\text{M} = \$20\text{M}$

✏️ OMO Sale

Suppose instead that the Cantabridgia central bank sells $1.3M of bonds. What is the change in the money supply?

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$Δ\text{Total Deposits = \text{Initial Deposit}} \times \frac{1}{\text{R}+\text{E}}$
$Δ\text{MS} = Δ\text{Deposits} + Δ\text{Cash Held by Public}$
$Δ\text{Total Deposits} = -\$1.3\text{M} \times \frac{1}{0\%+20\%} = -1.3 \times 5 = -6.5\text{M}$
$Δ\text{MS} = -6.5\text{Ms} + 0 = -6.5\text{M}$
$\text{New MS} = \$15\text{M} -6.5\text{M} = \$8.5\text{M}$