Bank Runs

macro

我的想法

Let the currency - deposit ratio be

And it is determined by the preferences of households about the form of money they wish to hold.

$$cu=\frac{Currency}{Deposits}$$

And the reserves-deposit ratio would be:

And it is determined by the business policies of banks and the laws regulating banks.

$$re=\frac{Reserves}{Deposits}$$

Then,

$$\begin{gathered} M=Cu+D \\ =D(\frac{Cu}{D}+1) \\ =D(cu+1) \end{gathered}$$

And,

$$H=Cu+Reserves=D(\frac{Cu}{D}+\frac{Re}{D})=D(cu+re)$$ $$mm=\frac{M}{H}=\frac{1+cu}{cu+re}>1$$

$mm$ is the Money Multiplier.

Ex. How money supply is created/affected by banks’ behavior? Suppose: $20,000isdividedbycash:$10,000 and deposits to banks in $10,000 (D)

Since $M=mm\ast H$ and $mm>1$

So, if $H\uparrow 1\%$ ,The $M\uparrow$ more than $1\%$

Remarks:

1. As $re\downarrow ,mm\uparrow$

2. As $cu\downarrow ,mm\uparrow$ (reason: $cu<1$)

---

Reference