Edit: I do understand this isn't how things work anymore, since we are in a "Ample-Reserves Framework" and the quantity of reserves no longer makes a difference that much and it is primarily IOR and ON RRP that has taken over as the Major Monetary Policy. But nonetheless, I was trying to understand through the point of view of pre 2008.
According to the Mishkin book “Excess reserves are insurance against deposit outflows, and the cost of holding these excess reserves is their OPPORTUNITY COST—the interest rate that could have been earned on lending these reserves out…then as the federal funds rate decreases, the opportunity cost of holding excess reserves falls... and the Quantity of Reserves Demanded rises”
I’m going to try and rephrase what he says in the way I understand it. Say I was a Bank, and I was ok with holding 100 million in excess reserves at a federal funds rate of 4%. That would mean I am ok with missing out on, assuming the Fed doesn’t pay interest on reserves, 100 * 0.04 = 4 million of interest payments (I know it’s not the correct number since loans are usually overnight and rates are annualized, but to keep it simple I went ahead with this.)
Now Imagine all of a sudden, the federal funds rate becomes 2.5%. That would mean me as a Bank would NOW be ok with holding $160 million because in the 2.5% scenario holding 160 mil in reserves costs me the same amount of Potential Money in Interest as 100 mil in the 4% scenario (100 * 0.04= X * 0.025, solve for X where X=160). The ADDED BENEFIT here is that I have even more buffering in terms of liquidity because I have an extra 60 million in reserves. But I’m not the only bank who thinks like this so every other bank would also prefer to hold more reserves for liquidity at a lower opportunity cost. On the other hand, the banks that are SHORT OF RESERVES would much prefer to borrow more money NOW because the COSTS are now much cheaper compared to the 4% scenario. Thus, keeping everything else the same, the overall “Quantity of Reserves Demanded” goes higher as Fed Fund rate drops both due to Banks wanting to hold on to Excess Reserves + Banks wanting to borrow cheaper reserves.
However, we also always hear that as Interest Rates drop banks are willing to give out more loans. But I’m having a hard time trying to reconcile this fact with that of as Fed Fund rate drops a bank wants to hold onto more reserves (hence, give out less loans). So how does it make sense that as Fed Funds rate decreases banks prefer more excess reserves(which technically means giving out less loans) and also are willing to give out more loans? It's contradictory