If the reserve requirement is 20% and a bank doesn't have excess reserves, why would a $100 deposit lead to a greater than $100 increase in the money supply.
answer posted above.
The reason a $100 deposit can lead to a greater than $100 increase in the money supply is due to the concept of fractional reserve banking. Fractional reserve banking allows banks to lend out a portion of the deposits they receive, while keeping a fraction in reserve to meet withdrawals.
In this case, the reserve requirement is set at 20%. This means that the bank is required to hold 20% of the deposited amount as reserves and can lend out the remaining 80%. So, if a $100 deposit is made, the bank is obligated to keep $20 (20%) as reserves and can loan out $80.
Now, the $80 loaned out is likely to be deposited in another bank, and the process repeats. The second bank is also required to keep 20% of the $80 deposit as reserves (which is $16) and can lend out the remaining $64. This cycle continues as the newly deposited funds are lent out and re-deposited, creating a multiplier effect.
Using the formula for the money multiplier, we can calculate the potential increase in the money supply. The money multiplier is the inverse of the reserve requirement ratio.
Money multiplier = 1 / Reserve requirement ratio
In this case, the reserve requirement is 20% (0.20). So the money multiplier would be:
Money multiplier = 1 / 0.20 = 5
By multiplying the initial deposit of $100 by the money multiplier, we can determine the potential increase in the money supply:
Potential increase in the money supply = Initial deposit * Money multiplier
= $100 * 5
= $500
Therefore, the $100 deposit can lead to a greater than $100 increase in the money supply, as illustrated by the fractional reserve banking system and the money multiplier effect.