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Definitions of Money
There are different definitions of money. The two most widely used measures of money in the U.S. are:
The M1 Money Supply: cash, checking accounts and traveler's checks. This is the narrowest definition of the money supply. This definition focuses on money's function as a medium of exchange.
The M2 Money Supply: M1 + savings + small time deposits + retail money funds. This definition focuses on money's function as a medium of exchange and store of value.
Credit cards are not purchasing power, but instead are a convenient means of arranging a loan. Credit is a liability acquired when one borrows funds, while money is a financial asset that provides the holder with future purchasing power. However, the widespread use of credit cards will tend to reduce the average quantity of money people hold.
Deposits are money, but checks are not - a check is an instruction to a bank to transfer money.