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Explain how the money multiplier works in theory
The money multiplier measures the maximum amount of commercial bank money that can be created by a given unit of central bank money. That is, in a fractional-reserve banking system, the total amount of loans that commercial banks are allowed to extend (the commercial bank money that they can legally create) is a multiple of reserves; this multiple is the reciprocal of the reserve ratio. We can derive the money multiplier mathematically, writing M for commercial bank money (loans), R for reserves (central bank money), and RR for the reserve ratio. We start with the reserve ratio requirement that the the fraction of deposits that a bank keeps as reserves is at least the reserve ratio:
R/M=RRR/M=RR
Taking the reciprocal:
M/R=1/RRM/R=1/RR
Therefore:
M=R×(1/RR)M=R×(1/RR)
The above equation states that the total supply of commercial bank money is, at most, the amount of reserves times the reciprocal of the reserve ratio (the money multiplier).
If banks lend out close to the maximum allowed by their reserves, then the inequality becomes an approximate equality, and commercial bank money is central bank money times the multiplier. If banks instead lend less than the maximum, accumulating excess reserves, then commercial bank money will be less than central bank money times the theoretical multiplier. In theory banks should always lend out the maximum allowed by their reserves, since they can receive a higher interest rate on loans than they can on money held in reserves.
Theoretically, then, a central bank can change the money supply in an economy by changing the reserve requirements. A 10% reserve requirement creates a total money supply equal to 10 times the amount of reserves in the economy; a 20% reserve requirement creates a total money supply equal to five times the amount of reserves in the economy.
steve williams answered the question on January 23, 2018 at 10:47
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