During the Great Depression years from 1930 to 1933, both the currency ratio c and the excess reserves ratio e rose dramatically. What effect did these factors have on the money multiplier?

The Impact of the Rise of Currency Ratio on the Money Supply:

Banking crises continued to occur from 1931 to 1933: Money stock fell rapidly in 1931 and 1932 and continued through April 1933. Similarly, the money stock composition changed. In March 1931, the currency ratio was 18.5%; two years later it was 40.7 %.

Why did the money supply decrease due to a rise in the currency ratio?

The decline in money supply was partly due to bank failures because banks did not have the reserves to cover customer withdrawals. In failing, banks destroyed deposits, thus reducing the money supply.

These failures further reduced the money supply in that they caused depositors to lose confidence, resulting in an even higher currency ratio.

The rise in the currency ratio (and also the excess reserves ratio) reduced the money multiplier and hence sharply contracted the money supply.

The relation between money supply (M), the money multiplier and the monetary base (MB) is given by:
$M=m\times MB\to \left(1\right)$

Where,

$m:$money multiplier$=\frac{(1+c)}{(r+e+c)}$localid="1647898106521" $=\frac{(1+\mathrm{c})}{(\mathrm{r}+\mathrm{e}+\mathrm{c})}\dots \dots .\left(2\right)$

$c:$Currency ratiolocalid="1647896388083" $=\frac{\left[C\right]}{\left[D\right]}$

$r:$Reserve ratio$=\frac{\left[R\right]}{\left[D\right]}$localid="1647898112758" $=\frac{\left[R\right]}{\left[D\right]}$

$e:$excess reserves ratio$=\frac{\left[ER\right]}{\left[D\right]}$

$M,$Money Supply $[C+D]$

$MB,$Monetary Base $=[C+R]$

$ER:$Excess reserves held by the banks.

$D:$Total checkable deposits

$C:$Currency in circulation

Keeping everything else constant, money supply, $M$, is negatively related to currency holdings and hence the currency reserve ratio. Once checkable deposits convert into currency holdings, a component of the money supply that expands multiple times no longer exists. Thus, the overall level of multiple expansion declines and the money supply falls.

Thus, as the currency ratio rose during the years of the Great Depression people switched over from deposits to currency and the money supply declined.