anonymous
  • anonymous
let r= .05 be the reserve rate. which of the following is the money multiplier?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
what is the actual question ? I a a little confused?
anonymous
  • anonymous
which of the following is the money multiplier? A. 10* 0.05 B. 1/0.05^2 C. 0.05^2 D. 1/0.05
IrishBoy123
  • IrishBoy123
https://gyazo.com/6feefbd797e1eccfa97348edbe643ebf

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anonymous
  • anonymous
if the reserve rate is \(r=0.05\) then banks can lend out \(1-r=0.95\); suppose you give A to a bank that then lends out 95% of that M, and then 95% of that lent amount is even further lent out, etc. giving a total of \(S=M+0.95M+\dots+(0.95)^nM+\dots\): $$S=M(1+0.95+0.95^2+\dots)\\0.95S=M(0.95+0.95^2+\dots)\\S-0.95S=M(1)\\0.05S=M\\S=M/0.05=20M$$in other words, a reserve rate of \(r=0.05\) allows for an initial deposit of \(M\) to give rise to (strictly less than) *twenty* times that in terms of loans from the banking system. in particular, a reserve rate of \(r\) gives a geometric series \(S=M(1+(1-r)+(1-r)^2+\dots)=\frac{M}{1-(1-r)}=\frac{M}r\) so the money multiplier is the ratio of the total amount \(S\) of loan money made possible from an initial deposit \(M\), so \(S/M=\frac1r\)
IrishBoy123
  • IrishBoy123
you couldn't make this up :p http://www.ronpaul.com/2009-11-14/end-the-fed-consider-outlawing-fractional-reserve-banking/

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