FED and Money Supply

Reserve ratio = $\frac{\text{reserves}}{\text{deposits}}$

fractional-reserve lending: reserve ratio < 1 (banks do some lending)

$M^s=$ currency + deposits $\Delta M^s$ = $\Delta$currency + $\Delta$deposits

Without currency money multiplier: $\frac{1}{R}$

$\Delta M^s$ = (Initial Injection)$(\frac{1}{R})$

if R $\downarrow ⟹M^s\uparrow$

Currency Deposit Ratio

$CU$: currency held by public

DEP: bank deposits

Currency-Deposit Ratio: $cu=\frac{CU}{DEP}$

Where

$cu$: desired currency-deposit ratio

$R$: bank reserve ratio

monetary base: total amount of money created by the central bank

MM > 1 if R < 1

if $cu\uparrow$ or R $\uparrow ⟹$ MM $\downarrow$