In his Quantity Theory of Money article M. Friedman uses the following formula for the money multiplier: $$ M = H \times \frac{\frac{D}{R}(1 + \frac{D}{C})}{\frac{D}{R}+\frac{D}{C}} $$

where $M = $ money supply under fractional reserve, $H$ = high-powered money, $D$ = deposits, $R$ = bank reserves, $C$ = currency in the hands of the public.

Why did he write the formula in this unusual form? Are there any insights to be seen from it?

For me the usual form is the one given for example in Mankiw:

$$ M = H \times \frac{C+D}{C + R} = H \times \frac{\frac{C}{D} + 1}{\frac{C}{D} + \frac{R}{D}}$$


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