let r= .05 be the reserve rate. which of the following is the money multiplier?

Question

anonymous · Answer

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

anonymous · Answer

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 · Answer

https://gyazo.com/6feefbd797e1eccfa97348edbe643ebf

anonymous · Answer

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 · Answer

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