When a central bank increases bank reserves by $1, the money supply rises by more than $1. The amount of extra money created when the central bank increases bank reserves by $1 is called the money multiplier.

a. The money multiplier is generally greater than 1 because:

i. in a fractional-reserve banking system, each dollar bill is spent more than once (velocity is larger than 1), thereby increasing the money supply by more than $1.

ii. in a fractional-reserve banking system, each dollar of reserves can support more than one dollar of deposits, thereby increasing the money supply by more than $1.

iii. in a 100 percent reserve banking system, each dollar of reserves supports exactly one hundred dollars of deposits, thereby increasing the money supply by $100.

iv. when a central bank increases bank reserves by $1, deposits are automatically increased by $1 as well, thereby increasing the money supply by $2.

ii) in a fractional-reserve banking system, each dollar of reserves can support more than one dollar of deposits, thereby increasing the money supply by more than $1.

Explanation:

In a  fractional-reserve banking system, banks only keep a fraction of total deposits on hand. They will usually only keep the amount required by the Fed, which is called the required reserve ratio. Banks will lend the rest of the money to customers, since they make money by borrowing from customers and lending it at higher rates.

E.g. you deposit $1,000 in the bank. The bank is required to keep 10% in reserves, but lends $900 to another client. That client will spend the money and purchase something. The seller of that good or service then deposits the money into his/her bank. That second bank will then separate $90 as reserves and lend $81 to a different client which will again purchase something, and the cycle goes on...

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