The price system makes possible to communicate the combined knowledge from people each of whom possessed only a portion of it. Based on that divided knowledge people coordinate the utilization of resources, producing a solution. — F.A. Hayek.
The total amount of currency units is called Base Money.
A money substitute is a claim on a definite amount of money, redeemable on demand.
Money substitutes are generated through lending.
Lending is the giving of an asset in exchange for a voucher on the 'promise to pay it back', which is 'debt'.
The claim is settled when the borrower returns the asset.
Giving credit is lending with the connotation of trust in the borrower's ability to pay back.
The kind of money substitutes issued by a custodian are called money-certificates.
A custodian is the borrower that keeps all borrowings as reserve (reserve ratio = 1).
Reserve ratio = amount reserved / amount borrowed.
The kind of money substitutes issued by borrowers practicing fractional reserve (reserve ratio < 1) are called demand deposits or checking accounts. Those borrowers keep a fraction of the borrowings as a reserve to provide liquidity to the claims, and invest the rest.
Liquidity refers to how easily those assets can be converted into money.
Claims provide additional functionalities to money, so they proliferate when money lacks some of its properties. Thanks to them, the fiat system becomes somewhat functional despite having an inestable and fragile base.
In the fiat system, non-backed deposits encompass most of what is perceived as monetary value accesible on demand, so checking accounts become 'currency' then, often referred as 'bank money'.
Bank money implies the existence of various "liquid" claims per each fiat unit, so it is said that it “multiplies” the base money. Example:
Alice deposits 100$ at bank A.
Because bank A does not expect most of its depositors to require a withdrawal from their accounts at the same time, bank A holds 10% of the received deposits as a reserve, and it lends the rest.
So bank A keeps 10$ as a reserve and lends 90$ to Bob.
Alice's checking account shows she has 100$ available.
Bob uses the loan to buy a bike from Amy.
Amy deposits her 90$ in bank B.
Bank B keeps 9$ and lends 81$ to Henry.
Amy’s checking account shows she has 90$ available.
Henry uses the loan to buy a surfboard from Eva.
Eva deposits her 81$ in bank C.
Bank C keeps 8.1$ and lends 72.9$ to Pankun.
Eva’s checking account shows she has 81$ available.
from the initial 100$ from Alice, 271$ of bank money have been issued:
100$ in the Alice’s checking account in bank A
90$ in Amy’s checking account in bank B
81$ in Eva’s checking account in bank C
The initial 100$ now are distributed:
10$ in bank A
9$ in bank B
8.1$ in bank C
72.9$ on Pankun’s pocket.
Bank money: 100 + 90 + 81 = 271$
Money reserved in banks = 10 + 9 + 8.1 = 27.1$
Bank money + cash not reserved by commercial banks = 271$ + 72.9$ = 343.9$
If the 72.9$ would end up deposited in a commercial bank and the process would continue indefinitely with an constant reserve ratio of 10%:
Total amount of bank money = 100$ / 10% = 1000$
Base money and bank money do not maintain a constant relation.
If comercial banks' reserves are imagined as water contained inside a plastic bag, bank money would be the water that leaks through some holes of the bag.
If the amount of water inside the bag changes, the amount of water that leaks will not necessarily change in the short term; if the monetary base changes, the total bank money will not necessarily do at the same pace.
However, no water inside the bag implies no water will flow out. Base money is ultimately needed to settle payments that were made through claims.
The price of a "typical" basket of products and services of "consumers" is much more sensitive to changes in the total amount of 'currency' formed by bank money + cash, than to changes in the total amount of base money. That recognition led to the study of the money aggregates (M1, M2, M3), aka broad money, that are calculated aggregating different kind of money substitutes and other claims to cash.
Just before the global financial crisis of 2007-2010, the average M3 of the world's top 30 fiat currencies was 10 times greater than M0 (base money), i.e. there were 10 claims of 1$ per each $.
During the crisis the Central Banks' program called Quantitative Easing duplicated M0; nevertheless M3 even contracted in some countries due to a decreasing in private borrowing in such an uncertain economic time, which added to a higher preference for storing value using fiat, lead to a light deflation in "consumer prices".
Central Banks' main tool for influencing M3 in short-term, is the manipulation of the interest rates at which comercial banks lend reserves each other.
By lowering those interest rates, incentives for borrowing grow (new holes appear in the water bag), so bank money is created and M3 increases.
The opposite happens by increasing interest rates.