1. $\mbox{Money Multiplier (M)} = \displaystyle\frac{\mbox{Currency in cash with public + Deposits with banks (D)}}{\mbox{Currency in cash with public + Banks' total reserves with RBI = Reserves as part of CRR + Excess Reserves}}$
2. $\text{On dividing by Deposits with banks (D),}$
$\mbox{Money Multiplier (M)} = \displaystyle\frac{\left(\frac{\mbox{Currency in cash with public}}{\mbox{Deposits with banks}}\right) + 1}{\left(\frac{\mbox{Currency in cash with public}}{\mbox{Deposits with banks}}\right) + \left(\frac{\mbox{Reserves as part of CRR}}{\mbox{Deposits with banks}}\right)}$
> $\mbox{Money Multiplier (M)} = \displaystyle\frac{\mbox{c + 1}}{\mbox{c + r}} ; \mbox{where c = currency-deposit ratio, and r = reserves ratio}$
3. $\displaystyle{\textbf{Change in money supply} = \boldsymbol{M} \times \textbf{Change in monetary base}}$
4. If excess reserves are 0 and if the public has no cash, that is all the currency of the public is with banks as deposits ,
$\mbox{Money Multiplier (M)} = \displaystyle\frac{\mbox{Deposits with banks (D)}}{\mbox{Banks' Reserves as part of CRR with RBI (R)}}$
$\mbox{Money Multiplier (M)} = \displaystyle\frac{\mbox{1}}{\left(\frac{\mbox{Banks' Reserves as part of CRR with RBI (R)}}{\mbox{Deposits with banks (D)}}\right)}$
$\mbox{Money Multiplier (M)} = \displaystyle\frac{\mbox{1}}{r}$ ; where $\mbox{r}$ is the CRR ratio [^1]
[^1]: Note the actual CRR is Banks' Reserves with RBI/NDTL of a bank, which includes **liabilities towards the banking system net of assets with the banking system** as defined in Section 42 of the RBI Act, 1934 for scheduled banks, Small Finance Banks and Payments Banks or Section 18 of the Banking Regulation Act, 1949 for non-scheduled banks or Section 18 of the Banking Regulation Act, 1949 read with Section 56 thereof for nonscheduled co-operative banks and **liabilities towards others** in the form of demand and time deposits or borrowings or other miscellaneous items of liabilities.
$\displaystyle \text{Change in money supply} = m \times \text{Change in monetary base}\text{ becomes}$
$\text{Change in deposits} = \displaystyle\frac{1}{\text{r}} \times \text{Change in reserves}$
## References
1. https://2012books.lardbucket.org/books/finance-banking-and-money-v1.1/s18-the-money-supply-and-the-money.html
2. State University of New York at Albany, Department of Economics. (2013). Economics 350: Money and banking slides [Lecture notes on money multiplier]. [Link](https://www.albany.edu/~bd445/Economics_350_Money_and_Banking_Slides_Spring_2013/Money_Multiplier.pdf)
3.