Cash Withdrawals & changes in Money Supply?

Question

If a customer withdrew $2000 in cash from a bank & the reserve ration was 0.2, by how much could the supply of money eventually be reduced?

Answer 1

1/0.2=8

2'000*8= -16'000

Answer 2

The standard text book answer would be the change in money supply equals chnage in bank deposits of

-$2000/0.2= - $2000/ (1/5) = -$200*5= -$10,000 plus the change in currency with the public $2000 = $10,000-$2000= $8000.

Please note that  -$2000/0.2 is not equal to $8000 as shown elsewhere.

But most important is understand what happens:

A withdrawl of cash of $2000 means both the deposit liabilty and the Reserves go down by $2000 in the Banks Balance sheet. But of the lost reserves only $400 was supporting as the reserve requirement (0.2*$2000) for the lost deposit of $2000 through cash withdrwal, the remaining $1600 (=$2000- $400) was supporting as reserve requirement for another amount of deposits of $8000 (= $1600/0.2). Now the bank does not have reserves to support this $8000 of deposits. Therefore the bank has to withdraw loans and convert them into cash as reserveres or use the loans getting repaid for reserves. This means that the bank has to reduce the deposits it had created by giving loans to the extent of $8000 to satisfy the reserve requirement. Thus the bank deposits go down by $10,000 ($2000 initially withdrawn as cash and then  reduction in loan based deposits to the extent of $8000). This means that the bank deposit component of money supply decreased by $10,000. But the currency with the public component money supply increase as soon as the initial deposit withdrwal by cash took place. So the net effect is that money supply decreases by $8000.

You must be wondering what happened to the loss of deposits of the additional $8000 - they did not result in cash withdrwals? No, they did not because these deposits were loan based deposit account. The loans were withdrawn and hence the deposits got cancelled out. Looks funny. Not really, there is always fresh deposits in cash coming in or loans repaid to increase the reserves of the banks. What we are calculating is that the effect on ceteris paribus basis. Simple text book answer is if reserves go down by $X, deposits have to go down by $X divided by the reserve ratio specified by the central bank. If the bank was originally hoding more reserves than the legal requirement, it need not reduce its deposit liability by $X/ r, where r is the required reserve ratio.