Bank reserves are maintained to ensure that all the cheques written every day clear when presented. If a bank doesn't have enough reserves then cheques drawn against it will bounce.
Answer: False
The answer is False.
Banks can always get reserves from the central bank. So if they have extended loans to credit-worthy customers these loans are made independent of their reserve positions. Depending on the way the central bank accounts for commercial bank reserves, the latter will then seek funds to ensure they have the required reserves in the relevant accounting period.
They can borrow from each other in the interbank market but if the system overall is short of reserves these "horizontal" transactions will not add the required reserves. In these cases, the bank will sell bonds back to the central bank or borrow outright through the device called the "discount window". There is typically a penalty for using this source of funds.
At the individual bank level, certainly the "price of reserves" will play some role in the credit department's decision to loan funds. But the reserve position per se will not matter. So as long as the margin between the return on the loan and the rate they would have to borrow from the central bank through the discount window is sufficient, the bank will lend.
So the idea that reserve balances are required initially to "finance" bank balance sheet expansion via rising excess reserves is inapplicable. A bank's ability to expand its balance sheet is not constrained by the quantity of reserves it holds or any fractional reserve requirements.
The bank expands its balance sheet by lending. Loans create deposits which are then backed by reserves after the fact. The process of extending loans (credit) which creates new bank liabilities is unrelated to the reserve position of the bank.
The major insight is that any balance sheet expansion which leaves a bank short of the required reserves may affect the return it can expect on the loan as a consequence of the "penalty" rate the central bank might exact through the discount window. But it will never impede the bank's capacity to effect the loan in the first place.
So a cheque will only bounce if the account that the cheque is drawn on has insufficient funds and there is no overdraft arrangement in place. That process has nothing to do with banks running out of reserves.
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