## anonymous one year ago let r= .05 be the reserve rate. which of the following is the money multiplier?

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1. anonymous

what is the actual question ? I a a little confused?

2. 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

3. IrishBoy123
4. 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 $$S/M=\frac1r$$

5. IrishBoy123

you couldn't make this up :p http://www.ronpaul.com/2009-11-14/end-the-fed-consider-outlawing-fractional-reserve-banking/