Money creation and fractional reserve

banking

November 12, 2014

Money supply,M = CU +DEP.

Monetary base,BASE = CU +RES.

Divide one equation by anotherM

BASE=CU +DEP

CU +RES=

CUDEP + 1CUDEP +

RESDEP

=cu+ 1

cu+ res

M = BASE cu+ 1cu+ res

> BASE

Example: cu = 0 CU = 0.

Central bank issues $1 currency.

People have $1 additional money. If cu = 0, they deposit the entireamount in banks.

1st round: Bankss deposit goes up by a $1.

Suppose res = 0.1. Banks then keep 0.1$1 = $0.1 as RES andloan out the rest ($0.9).

Somebody (household or firm) gets a loan of $0.9. Given cu = 0, thatperson deposits the entire amount in banks.

2nd round: Bankss deposit goes up by a $0.9.

Given res = 0.1. Banks then keep 0.1 $0.9 = $0.09 as RESand loan out the rest ($0.90.9 = $0.81).

Somebody (household or firm) gets a loan of $0.81. Given cu = 0,that person deposits the entire amount in banks.

3rd round: Bankss deposit goes up by $0.81.

Given res = 0.1. Banks then keep 0.1 $0.81 = $0.081 as RESand loan out the rest ($0.810.9 = $0.729).

The process continues...

Deposits increase by

1 + 0.9 + 0.92 + 0.93 + ... = 1 11 0.9

=1

0.1= 10

In general with cu = 0,

M = DEP = BASE 1res

= 10.

The amount of RES0.1 + 0.9 0.1 + 0.81 0.1 + ...

= 0.11 + 0.9 + 0.92 + 0.93 + ...

=

0.1

0.1= 1

In general, with CU = 0,BASE = CU +RES = RES = 1