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.

because of the money multiplier.

A $100 deposit (e.g., into a checking account) gives the bank both a $100 liability and a $100 extra total reserve, AND THEREFORE, an extra $80 excess reserve. What does the bank do with this excess? Lends it out. $80 of money supply just created. This $80 is put into that person's checking account or is immediately spent and goes to the merchant's checking account. Excess reserves at that bank rise by .2*80=$64 And the process repeats until there is no more excess reserves.

To understand how a $100 deposit can lead to a greater than $100 increase in the money supply, we need to take into account the concept of the money multiplier and the reserve requirement.

The reserve requirement is the percentage of deposits that banks are required to keep on reserve. In this case, the reserve requirement is 20%. This means that for every $100 deposit, the bank needs to keep $20 (20% of $100) as reserves and can lend out the remaining $80.

When a $100 deposit is made, it increases both the bank's liabilities (the $100 it owes to the depositor) and its total reserves (the $100 that was deposited). Since the bank already meets the reserve requirement, it has an additional $80 as excess reserves ($100 total reserves - $20 required reserves = $80 excess reserves).

With these excess reserves, the bank can lend out money to other borrowers. Let's say the bank lends out the entire $80 to a borrower. This borrower now has $80 in their checking account. This $80 is considered a part of the money supply since it can be used for transactions and payments.

The borrower might choose to spend this money, for example, by purchasing goods from a merchant. The merchant then receives $80 in their own checking account. At this point, the bank's excess reserves increase by 20% of the $80 deposit, which is $16 (0.2 * $80 = $16).

The process can continue as the $16 in excess reserves can be lent out, which becomes part of the money supply, and so on. Each time the money is deposited and the bank's excess reserves increase, a fraction of that increase is lent out and becomes part of the money supply.

This multiplication process continues until there are no more excess reserves left in the banking system. Ultimately, the final increase in the money supply will be greater than the initial deposit because of the money multiplier effect. The money multiplier, in this case, is 1/0.2, which is equal to 5. That means that the initial $100 deposit can potentially lead to a $500 increase in the money supply ($100 deposit * money multiplier of 5 = $500 increase in the money supply).