The Money multiplier

# The Money multiplier - inverse of reserves requirement so...

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The Money multiplier (MM) is referred to the multiple relationship between the money supply and monetary base . In order to prove the money multiplier formulae of multiple deposit creation, two assumptions are made. Firstly, no excess reserves held by banks Secondly, no currency held by depositors If any of the assumption here doesn’t hold, then the multiplier formula is not true. Let: R = total reserves RR = required reserves ER = excess reserves then: R = RR + ER Since no excess reserves held by banks, total reserves are just equal to required reserves (R = RR). Moreover, let: r = required reserves ratio D = deposits C = currency in circulation M = money supply = C + D MB = monetary base = R + C m = money multiplier (which can be demonstrated as the
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Unformatted text preview: inverse of reserves requirement so that m = 1/r) However, since we assume that no currency held by depositors, money supply is equal to deposits (M = D) and monetary base is equal to reserves (MB = R). And we can calculate required reserves as: RR = r * D Which is equivalent to: R = r * D or MB = r * D And then we have: D = (1/r) * MB or M = (1/r) * MB Since r &lt; 1 and 1/r &gt; 1, an increase in MB that flows into deposits gets multiplied. Therefore, m = 1/r Lets put this into an example, if required reserves ratio (r) is 10%, the money multiplier (m) can be calculated as: m = 1/0.1 = 10. Therefore if the monetary base is, for example\$100, then the deposits will be: \$100*10 = \$1000....
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## This note was uploaded on 09/19/2011 for the course FINS 3650 taught by Professor Arnold during the Three '11 term at University of New South Wales.

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