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The question is as follows: In a simple close economy, banks are required to maintain a liquidity ratio of 8%. An additional £15 billion of currency is deposited in the banking system. Calculate the bank multiplier and hence the increase in the total amount of deposits.

I am having trouble finding out how to calculate the bank multiplier. Please help.

Andrew Uzzell
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david
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  • Let $x$ be the ratio to be maintained. Then, $15(1-x)$ can be lent out. The recipients maintain deposits in the banking system, so you have $15(1-x)^2$ now to further lend, after keeping liquidity, and so on and so forth. So we have $15+15(1-x)+15(1-x)^2 +...$ in the system. Can you now make the GP to solve for the multiplier? – Macavity Apr 01 '13 at 17:07
  • Can you define liquidity ratio? – oks Apr 01 '13 at 17:19
  • @Macavity: you probably should put that in as an answer. – Ron Gordon Apr 01 '13 at 17:55
  • @RonGordon OK, I will if the OP responds on what he is unsure of... – Macavity Apr 01 '13 at 19:33
  • im still a bit unsure – david Apr 01 '13 at 20:24

1 Answers1

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If you define the liquidity ratio as the minimum fraction of customer deposits and notes that each commercial bank must hold as reserves then the liquidity ratio is $\frac{R}{D}$ where

$R$ is the "actual" currency reserves (notes and coins physically held by banks) and $D$ is the amount credited to customers in the form of deposits.

The bank multiplier is just $\frac{D}{R}$ i.e., n your case $\frac{1}{0.08}$ = 12.5.

So an extra £15 bn currency can multply into an extra $15 bn * 12.5 of deposits.

Put another way the liquidity ratio will continue to be $\frac{15 * 0.08}{15}$.

oks
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  • BTW if anyone cares about economics, the liquidity ratio probably won't remain constant in practice. Loans are made based on borrower creditworthiness and demand, not simply on reserve balance calculations. – dm63 Mar 10 '19 at 11:56