what is the relationship between cash-deposit ratio and money multiplier?
Dear Potharla,
It is not easy explain in a few words your question here because it is supposed from you to be familiar with the core monetary tools. What type of
the relationship is a relevant for you (empirical studies or general terms) ? In any way , let me introduce one book and one journal article relevant for your question....
BINDSEIL, U. (2004) Monetary policy implementation: Theory, past, present, Oxford University Press.
WOODFORD, M. (2007): How important is money in the conduct of monetary policy? , CEPR Discussion Paper Series, No. 6211.
Dear Srikanth
The cash-deposit ratio for a bank is equal to (total cash)/(total deposits). The bank must maintain liquidity to operate and will hold an amount of cash to service net withdrawals from customer activities such as drawing from their deposit (checking and savings) accounts.
The money multiplier is equal to 1/(reserves requirement) where the numerator amount of 1 is viewed as a deposit. The reserve requirements comes from the central bank (or federal government) that sets a percentage amount of deposits that need to be set aside or deposited with them as reserves. For example, if the reserve requirement is 5% then for every $100 of deposits $5 is put into reserves (held by the central bank/federal government). This leaves $95 that the bank can lend out in addition to the $100 and therefore has multiplied the money (more than one times). This multiplying effect continues as the new amount of $95 goes to another bank in the system and so on.
Comparing the two metrics you can see the relation between them as the deposits variable is common to both.
Prof. Raymond A K Cox thank you for your valuabel response.
I could not understant the sentence " This leaves $95 that the bank can lend out in addition to the $100 and therefore has multiplied the money (more than one times)".
can you please explain it in detail.
For example, with a 5% reserve the bank with the $100 deposit can lend $95 to a customer. That customer now has $95 cash that they can deposit (in the same bank or another bank). This new $95 deposit enables the bank to make a loan, less the 5%reserve requirement, of 95% (i.e. 100% - 5%) of $95 which is $90.25. Then this new customer will deposit $90,25 cash at the bank and the the bank can make another loan lending out 95% of the $90.25 and so on.
The currency to demand deposit ratio in monetary economics represents the total volume of currency in the hands of the public compared to the total volume of demand deposits. Generally, as the ratio rises, indicating the public's desire to hold more transactions money as cash, the multiplying effect on the money supply that Dr. Cox refers to above is diminished. Fewer dollars get to be multiplied (given a constant reserve requirement). The public's decision to transform deposits into currency drains some of the total volume of extant dollars away from the multiplier process.
An important factor in determining the ratio is the level of criminal behavior. Because cash is anonymous, it's used more for illegal activities.
I agree with previous answers by Dr. Cox and Dr. Bias. This money multiplication is possible since commercial bank applies fractional reserve banking system (FRBS). FRBS is believed to be one of the root causes of financial crisis by many economists.
Three things:
In the U.S. reserves are cash in the bank's vault and deposits with the Federal Reserve banks that are treated the same as cash in the vault. For most countries the arrangement is similar. Thus reserves are on the banks asset side of its balance sheet and deposits are liabilities.
Cash in the hands of the public are outside of the banking system per se. Changes in the ratio of cash in the hands of the public to bank deposits affect the money multiplier by increasing or decreasing bank reserves. Anna Schwartz and Milton Friedman analyzes this extensive among other ratios in their Monetary History of the United States.
If there is no central bank, the amount of reserves held will be a prudential decision by banks.
Dear Srikanth,
here is a slide from my lecture on the question you are interested in.
The relationship is, I believe, a standard relationship in monetary analysis. Let M = money supply, C = currency in circulation (that is, outside the banking system), D = deposits, B = monetary base, R = bank reserves (including cash held by banks). The money multiplier (m) is equal to M/B. By definition, B = C + R and M = C + D. Since m = M/B = (C + D)/(C + R) = [(C/D)+(D/D)]/[(C/D)+(R/D)], the relationship of m to (C/D) is straightforward. Let k = (C/D) and let r = R/D, then
m = (k +1)/(k + r).
The money supply in question would be M1, M2 etc., -- the deposit stock would be whatever deposit stock conforms with the aggregate.
I came across this and thought it may be helpful:
https://economictimes.indiatimes.com/definition/currency-deposit-ratio