Banks cover their funding needs through the interbank market that provides the overnight loans required to balance their books at the end of the day. Banks will raise deposit rates to attract deposits if they constantly find that they need to go to the interbank market to balance their books because it is cheaper.
The discount window is used when the bank is unable to access the interbank market which is usually an indicator the bank is expected to fail. The discount window provides liquidity for high quality assets at high costs (which is why it is called the discount window).
If the bank runs out of high quality assets and can’t raise capital it becomes insolvent (bankrupt) and the FDIC takes over the bank and winds it down.
> will raise deposit rates to attract deposits if they constantly find that they need to go to the interbank market to balance their books because it is cheaper
This is true for the largest banks. For many smaller banks, interbank lending is cheaper than deposits. Particularly if those deposits must come from new customers.
Your model is roughly correct over long, strategic time periods. But in tactical timeframes, deposits are assumed fixed or lightly. (In fact, the post-97 role of money centre banks has been to attract deposits to then lend to smaller banks.)
Yes, if a small bank is in an geographic area experiencing high loan demand the interbank market may be a cheaper source of funds. If the bank also has inefficient infrastructure to service retail customers they may find internal deposits more expensive then the interbank market.
Regulators however are less than thrilled if these imbalances persist long term because banks that rely heavily on hot funds tend to experience runs.
The discount window is used when the bank is unable to access the interbank market which is usually an indicator the bank is expected to fail. The discount window provides liquidity for high quality assets at high costs (which is why it is called the discount window).
If the bank runs out of high quality assets and can’t raise capital it becomes insolvent (bankrupt) and the FDIC takes over the bank and winds it down.